ACKNO0WLEDGMENT S The author wishes to express his sincere appreciation and gratitude for the assistance of several people during the course of this work. I wish to thank Professor Joseph J. Martin, chairman of my thesis committee, for his continuous and enlightening encouragement and guidance. I would like to thank Professors Rane L. Curl, John E. Powers, Richard E. Sonntag and G. Brymer Williams for their constant help and advice. I especially would like to thank Messrs. Soharab Hossain and Bipin P. Vrra for their assistance in the laboratory work. Many thanks are due to members of the Department of Chemical Engineering and the Department of Materials and Metallurgical Engineering staff including C. Bolen, D. Connell, P. Severn, F. Drogosz and J. Wurster who assisted in equipment problems. I would also like to thank Mr. Lloyd Swan for his assistance in conputer programming. I wish to thank Messrs. Andre Furtado and Bruce F. Caswell for several useful discussions during the course of this research. I wish to thank Mr. J.C. Golba, Jr., and Miss Sue Bush for assistance in the preparation of this manuscript. Many thanks are due to Mrs. Alvalea May for her typing and compilation of this dissertation. In addition, I would also like to thank the following organizations for their equipment and financial support. ii

The E.I. du Pont de Nemours and Company generously supported the research project and supplied the substance under investigation, R-502. The Industry Program of the College of Engineering of The University of Michigan supported the printing costs of this dissertation. The Babcock and Wilcox Company and Mr. Rohinton K. Bhada allowed us to use their PVT equipment. The Thermasan Corporation financially assisted by paying tuition. Finally the author would like to thank his wife and family for their constant patience, encouragement and help. iii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES viii LIST OF FIGURES xiv NOMENCLATURE xvii ABSTRACT xxi I. INTRODUCTION 1 II. LITERATURE REVIEW 4 (A) Physical Properties of R-22, R-115 and R-502 4 1. Physical Properties of R-22 a) PVT Behavior 4 b) Vapor Pressure 11 c) Saturated Liquid Density 15 d) Critical Constants 18 2. Physical Properties of R-115 18 a) PVT Behavior 18 b) Vapor Pressure 26 c) Saturated Liquid Density 29 d) Critical Constants 32 3. Physical Properties of R-502 32 a) PVT Behavior 32 b) Vapor Pressure 32 c) Saturated Liquid Density 36 d) Critical Constants (B) Variable Volume Equipment for PVT Measurements 36 1. Constant Mass 39 a) Wet Method-Liquid Injected Piezometer 39 b) Dry Methods 44 i) Cylinder-Piston 44 ii) Bellows 46 2. Variable Mass 47 (C) Intermolecular Potential Functions 50 Intermolecular Forces 55 Electrostatic Contribution 56 Induction Contribution 57 Dispersion Contribution 59 Intermolecular Potential Functions 61 iv

TABLE OF CONTENTS (contd.) Page I) Angle-Independent Analytical Equa- 62 tions for Intermolecular Potential Energy 1) Hard Spheres Model 62 2) Point Centers of Repulsion 653 3) Sutherland Model 64 4) Lennard-Jones 12-6 Potential 65 5) Dymond, Rigby and Smith Potential 66 6) Guggenheim and McGlashan 67 7) Square Well Potential 68 8) The Buckingham-Corner Potential 69 9) Exp-6 Potential 71 10) Carra and Konowalow Potential 72 11) Modified Buckingham-Carra-Konowalow Potential 74 12) Morse Potential 75 13) Singer Potential 76 14) Boys and Shavitt Potential 76 II) Angle-Dependent Potentials 77 a) Angle-Dependency due to Shape of 77 the Molecules Kihara Potential 78 b) Angle-Dependency due to Polarity 81 of Molecules 1) Rigid Spheres with Imbedded 81 Point Dipoles 2) Stockmayer Potential 82 c) Angle-Dependency due to Shape and 83 Polarity Kihara Potential 83 III) Combination Rules for Intermolecular 85 Forces IV) Dipole Moments of R-22 and R-115 88 I. EXPERIMENTAL WORK 89 (A) PVT Behavior of R-502 89 a) Description of the Apparatus 89 b) Procedure of Operation 93 c) Experimental Precision 96 (B) Vapor Pressure of R-502 97 1. Low Vapor Pressure Measurements 97 a) Description of the Apparatus 97 b) Procedure of Operation 99 c) Experimental Precision 100 Vr

TABLE OF CONTENTS (contd.) Page 2. High Vapor Pressure Measurements 100 (C) Saturated Liquid Density of R-502 101 (D) Critical Temperature of R-502 103 IV. EXPERIMENTAL RESULTS 104 Vapor Pressure of R-502 104 Saturated Liquid Density of R-502 106 Critical Constants 109 Rectilinear Diameter 109 PVT Behavior of R-502 110 V. PREDICTION OF THE PROPERTIES OF R-502 131 PVT Behavior 131 Vapor Pressure 141 Saturated Liquid Density 150 Critical Constants 155 Intermolecular Potential Energy 159 VI. SUMMARY AND CONCLUSIONS 220 VII. RECOMMENDATIONS FOR FUTURE WORK 225 APPENDIX A - MEASUREMENTS FOR PVT BEHAVIOR 227 APPENDIX B - DETAILS OF VOLITME CALIBRATION 243 APPENDIX C - DETAILS OF VAPOR PRESSITPE MEASUREMENTS 247 APPENDIX n - DETAILS OF SATURATED TIOUIID DENSITY MEASUREMENTS 252 APPENDIX E - LABORATOPY DATA 257 APPENDIX F - THE EOUATION OF STATE 277 APPENDIX G - ALGEBRAIC CORRELATION OF VAPOR PRESSURE DATA 315 APPENDIX H - ALGEBRAIC CORRELATION OF SATURATED LIQUID DENSITY DATA 319 vi

TABLE OF CONTENTS (contd.) Page APPENDIX J - MIXING RULES FOR CRITICAL CONSTANTS 323 APPENDIX K - ANALYTICAL METHOD TO OBTAIN INTERMOLECULAR POTENTIAL ENERGY PARAMETERS 332 REFERENCES 341 vii

LIST OF TABLES Table Page II-1 Physical Properties of R-22 II-2 Ranges of PVT Measurements for R-22 6 II-3 Coefficients in the Equation of State 10 II-3 for R-22 11-4 Mean Deviations of Predicted Values by Eqn. 11 II-3 from Experimental Data II-5 Ranges of Vapor Pressure Measurements for R-22 12 II-6 Mean Deviations of Calculated Values by Eqn. 15 II-8 from Experimental Data II-7 Ranges of Saturated Liquid Density Measurements 16 for R-22 II-8 Critical Constants of R-22 19 II-9 Physical Properties of R-115 20 II-10 Ranges of PVT Measurements for R-115 21 II-11 Equation of State for R-115 24 II-12 Ranges of Vapor Pressure Measurements for R-115 27 II-13 Ranges of Saturated Liquid Density Measurements 30 for R-115 II-14 Critical Constants of R-115 II-15 Physical Properties of R-502 34 II-16 Critical Constants of R-502 37 11-17 Variable Volume Equipment for PVT Measurements 38 IV-1 Summary of Comparison of Eqn. IV-1 and Vapor 106 Pressure Data IV-2 Summary of Comparison of Eqn. IV-2 and 108 Saturated Liquid Density Values IV-3 Comparison of Eqn. IV-1 and Experimental Vapor 115 Pressure Data for R-502 obtained in this Work..1

LIST OF TABLES (contd.) Table IV-4 Comparison of Eqn. IV-1 and Vapor Pressure 117 Values for R-502 Reported by Badylkes (5,6,7) IV-5 Comparison of Eqn. IV-1 and Vapor Pressure 118 Values for R-502 Reported by Loffler (86) IV-6 Comparison of Eqn. IV-1 and Vapor Pressure 120 Values for R-502 Reported by Downing (42) IV-7 Comparison of Eqn. IV-1 and Vapor Pressure 121 Values for R-502 Reported by Du Pont (47) IV-8 Comparison of Eqn. IV-2 and Experimental 122 Saturated Liquid Density Data for R-502 Obtained in this Work IV-9 Comparison of Eqn. IV-2 and Saturated Liquid 123 Density Values for R-502 Reported by Badylkes (5,6,7) IV-10 Comparison of Eqn. IV-2 and Saturated Liquid 124 Density Values for R-502 Reported by Loffler (86) IV-11 Comparison of Eqn. IV-2 and Saturated Liquid 126 Density Values for R-502 Reported by Du Pont (47) IV-12 Comparison of Eqn. IV-3 and Rectilinear Diameter 127 Values for R-502 IV-13 Comparison of Eqn. IV-5 and PVT Data of R-502 128 V-1 Values of Constants in the Eqn. V-1 for R-22, 132 R-115 and R-502 V-2 Input Conditions to Solve Constants in the 134 Eqn. V-1 for R-22, R-115 and R-502 V-3 Summary of Comparison of Eqn. V-1 with the 136 Experimental PVT Data for R-115 V-4 Constants in the Vapor Pressure Eqn. V-8 and 145 Properties for R-22, R-115 and R-502 V-5 Summary of Comparisons of Eqn. V-8 with the 146 Vapor Pressure Values for R-22 V-6 Summary of Comparisons of Eqn. V-8 With the 148 Vapor Pressure Values for R-115 ix

LIST OF TABLES (contd.) Table Page V-7 Summary of Comparisons of Eqn. V-8 with the 149 Vapor Pressure Values for R-502 V-8 Constants in the Saturated Liquid Density 151 Eqn. V-19 for R-22, R-115 and R-502 V-9 Summary of Comparisons of Eqn. V-19 with the 152 Saturated Liquid-Density Values for R-22 V-10 Summary of Comparisons of Eqn. V-19 with the 153 Saturated Liquid Density Values for R-115 V-11 Summary of Comparisons of Eqn. V-19 with the 154 Saturated Liquid Density Values for R-502 V-12 Summary of Mixing Rules for Critical Constants 156 of R-502 V-13 Summary of Intermolecular Potential Energy 162 Parameters V-14 Comparison of Eqn. V-1 and PVT Data for R-22 164 Reported by Michels (99) V-15 Comparison of Eqn. V-1 and Isometric PVT Data 171 for R-22 Reported by Zander (140) V-16 Comparison of Eqn. V-1 and Isothermal PVT Data 177 for R-22 Reported by Zander (140) V-17 Comparison of Eqn. V-1 and PVT Data for R-115 181 Reported by the University of Michigan (136) V-18 Comparison of Eqn. V-1 and PVT Data for R-115 184 Reported by Mears et al. (98) V-19 Comparison of Eqn. V-1 and PVT Data of R-502 188 V-20 Comparison of Eqn. V-8 and Vapor Pressure 191 Values for R-22 Reported by Booth and Swinehart (17) V-21 Comparison of Eqn. V-8 and Vapor Pressure Values 192 for R-22 Reported by Benning and McHarness (12) V-22 Comparison of Eqn. V-8 and Vapor Pressure Values 193 for R-22 Reported by Du Pont (46)

LIST OF TABLES (contd.) Table V-23 Comparison of Eqn. V-8 and Vapor Pressure 194 Values for R-22 Reported by Downing (42) V-24 Comparison of Eqn. V-8 and Vapor Pressure 195 Values for R-22 Reported by Zander (140) V-25 Comparison of Eqn. V-8 and Vapor Pressure 196 Values for R-115 Reported by the University of Michigan (136) V-26 Comparison of Eqn. V-8 and Vapor Pressure 197 Values for R-115 Reported by Mears et al. (98) V-27 Comparison of Eqn. V-8 and Vapor Pressure 198 Values for R-115 Reported by Aston et al. (4) V-28 Comparison of Eqn. V-8 and Vapor Pressure 199 Values for R-115 Reported by Downing (42) V-29 Comparison of Eqn. V-8 and Vapor Pressure 200 Values for R-502 Obtained in This Work V-30 Comparison of Eqn. V-8 and Vapor Pressure 202 Values for R-502 Reported by Badylkes (5,6,7) V-31 Comparison of Eqn. V-8 and Vapor Pressure 203 Values for R-502 Reported by Loffler (86) V-32 Comparison of Eqn. V-8 and Vapor Pressure 205 Values for R-502 Reported by Downing (42) V-33 Comparison of Eqn. V-8 and Vapor Pressure 206 Values for R-502 Reported by Du Pont (47) V-34 Comparison of Eqn. V-19 and Saturated Liquid 207 Density Data for R-22 Reported by Benning and McHarness (12) V-35 Comparison of Eqn. V-19 and Saturated Liquid 208 Density Values for R-22 Reported by DuPont (46) V-36 Comparison of Eqn. V-19 and Saturated Liquid 209 Density Values for R-22 Reported by Zander (140) V-37 Comparison of Eqn. V-19 and Saturated Liquid 211 Density Values for R-115 Reported by the University of Michigan (136) xi

LIST OF TABLES (contd.) Table Page V-38 Comparison of Eqn. V-19 and Saturated Liquid 212 Density Values for R-502 Reported by Mears et al. (98) V-39 Comparison of Eqn. V-19 and Saturated Liquid 213 Density Values for R-502 Reported in This Work V-40 Comparison of Eqn. V-19 and Saturated Liquid 214 Density Values for R-502 Reported by Badylkes (5,6,7) V-41 Comparison of Eqn. V-19 and Saturated Liquid 215 Density Values for R-502 Reported by Loffler (86) V-42 Comparison of Eqn. V-19 and Saturated Liquid 217 Density Values for R-502 Reported by Du Pont (47) V-43 Comparison of Rectilinear Diameter Eqn. V-20 218 with Data for R-22 V-44 Comparison of Rectilinear Diameter Eqn. V-21 219 with Data for R-115 A-1 Characteristic Constants in Eqn. A-3 for 236 Platinum Resistance Thermometer B-1 Comparison of Eqn. B-3 with the Volumetric 245 Data of Carbon Dioxide B-2 Constants in the Eqn. B-2 and its Comparison 246 with the Experimental Data of Carbon Dioxide E-1 Laboratory Data for PVT Behavior of R-502 258 E-2 Laboratory Data for Volume Calibrations with 263 Carbon Dioxide E-3 Laboratory Data for Low Vapor Pressure Measure- 268 ments with R-502 E-4 Laboratory Data for High Vapor Pressure Measure- 270 ments with R-502 E-5 Laboratory Data for Saturated Liquid Density 274 Measurements with R-502 E-6 Laboratory Data for Critical Temperature Measure- 276 ments with R-502 xii

LIST OF TABLES (contd.) Table Page F-i Critical Isotherm of R-22 288 F-2 Values of AP and VR to evaluate cl and 285 ln f (Tc) R F-3 Isochore Slopes for R-22 293 G-1 Five Points on the Vapor Pressturo Plot for R-115 316 (Fig. V-4) Selected to Solve Unknowns in the Eqn. G-1 H-1 Four Points on the Saturated Liquid Density Plot 319 for R-115 (Fig. IV-2), Selected to Solve Unknowns in Eqn. H-1 J-1 Properties of Components and the Mixture R-502 323 K-1 Summary of Second Virial Coefficients of R-22, 340 R-115 and R-502 xiii

LIST OF FIGURES Figure II-1 Ranges of PVT Measurements for R-22 7 11-2 Ranges of PVT Measurements for R-115 22 II-3 Michels' Variable Volume PVT Apparatus 41 II-4 Keyes and Beattie Equipment 45 II-5 Bridgman Piston Cell 45 II-6 Bridgman Bellows Cell 49 II-7 Burnett Apparatus 49 II-8 General Representation of the Intermolecular 52 Potential Energy II-9 Interaction Between Spherically Symmetric 53 Molecules II-10 Interaction Between Molecules Having Two 53 Centers of Force II-11 Interaction Between Molecules Possessing 54 Dipole Moments II-12 Interaction Between Partially Penetrable 55 Molecules II-13 Electrostatic Interaction Between Two 56 Molecules II-14 Induction Interaction Between Two Molecules 58 II-15 Hard Sphere Interaction 62 II-16 Interaction for Point Centers of Repulsion 63 II-17 The Sutherland Model 64 11I-18 The Lennard-Jones 12-6 Potential 65 II-19 Dymond, Rigby and Smith Potential 66 II-20 Square Well Potential 68 xiv

LIST OF FIGURES (contd.) Figure P II-21 Buckingham Potential 69 II-22 Buckingham-Corner Potential 70 72 II-23 Exp-6 Potential II-24 Carra and Konowalow Potential 73 II-25 Modified Buckingham-Carra-Konowalow Potential 74 II-26 Morse Potential 74 II-27 Molecular Interaction for Corner Potential 80 III-1 Schematic for PVT Measurements Using Bellows Cell 90 III-2 Details of the Bellows PVT Cell 92 III-3 System for Low Vapor Pressure Measurements 98 III-4 System for Saturated Liquid Density Measurements 102 IV-1 Vapor Pressure of R-502 105 IV-2 Saturated Liquid and Vapor Density Plot for 107 R-22, R-115 and R-502 111 IV-3 PVT Behavior of R-502 112 IV-4 Compressibility Factor of R-502 V-1 PVT Behavior of Chlorodifluoromethane (R-22) 135 V-2 PVT Behavior of Chloropentafluoroethane (R-115) 137 V-3 Vapor Pressure of Chlorodifluoromethane (R-22) 144 V-4 Vapor Pressure of Chloropentafluoroethane (R-115) 147 A-1 Doty Magnet Adjustable Thermoregulator 229 A-2 Supersensitive Relay Installation 231 A-3 Schematic of Relay Circuit 232 A-4 Circuit Diagram for Temperature Measuring System 234 XV

LIST OF FIGURES (contd.) Page Figure Page 237 A-5 Temperature Fluctuations of the Bath A-6 Pace Diaphragm Pressure Transducer 237 A-7 Bridge Circuit to Convert Coil Inductance 241 Ratio into DC Output Voltage A-8 Bridge Output with and Without Filter 241 D-1 Saturated Liquid Density Bulb 252 F-l Plot of (PR-I) vs (PR-l) for R-22 at the 281 Critical Temperature F-2 Critical Isotherms of Chlorodifluoromethane 282 (R-22) and Carbon Dioxide F-3 Plot of APR (Eqn. F-12) vs. VR for Chlorodi- 284 fluoromethane (R-22) at the Critical Temperature. F-4 Plot of [(dP/dT) /(dP/dT) ] vs VR for 295 ChlorodifluoromeYhane (R-~) at the Critical Temperature K-1 General Representation of the Intermolecular 332 Potential Energy xvi

NOMENCLATURE ala2 9bl clc2 Constants used in the equation of state A1,B1,C1D1 Constants used in the saturated liquid density equation A,B,C,D,E Constants in vapor pressure equation A1,B,C,... B Constants in the equation of state Al,Bl,C1....B6 Constants in the equation of state b0 Volume factor in intermolecular potential energy B Second virial coefficient C Charge of a molecule C Third virial coefficient d Density and the distance parameter in the intermolecular potential energy function e Base of natural logarithm 2f 3' f 4f f5 Temperature functions in the equation of state F Symbol for functional relationship G Symbol for a property in general J Expression in mixing rule of Joffe k Boltzman constant k Exponential coefficient of temperature in the equation of state K Expression in mixing rule of Joffe M Vapor pressure parameter, Kihara potential parameter N Avagadro number P Pressure xv ii

NOMENCLATURE (contd.) q Quadrupole moment r Distance between molecules R Gas constant S Shape factor in Kihara potential t Temperature T Absolute temperature U Intermolecular potential energy U Minimum intermolecular potential energy V Kihara volume factor V Volume V Specific volume x Mass fraction y Mole fraction Z Compressibility factor a Constant in mixing rule of Leland-Muell ac,B3 Exponential coefficients in the intermo potential energy A Difference Azimuthal angle Dipole moment p Density Summation Polar angle W Accentric factor xviii

NOMENCLATURE (contd.) Subscripts a,b Substances a and b b To denote boiling point b To denote Boyle temperature c Critical point property h Height ij Components in a mixture m Minimum property mix Mixture property r Reduced property 0 Reference property 1 Components 1 11 Component 1 12 Interaction between component 1 and component 2 2 Component 2 22 Component 2 Superscripts c Charge ii Dipole moment Conversion Factors for Units Used in This Work atm 14.696006 psi bar 14.503830 psi cu in 16.38670 ml cu ft 28.317.017 ml dyne/cm2 1.4503830x105 psi g 980.44 cm/sec, for Ann Arbor xi x

NOMENCLATURE (contd.) g 2980.665 gm-cm/gmf-sec (universal) in 2.540051 cm lb 453.59243 g lb/cuft 0.016018369 g/cm3 psi 51.7147 mmHg R 10.73147 psi ft3/(R)(lb mole) R F+459.67 xx

AB STRACT PHYSICAL PROPERTIES AND INTERMOLECULAR POTENTIAL FUNCTIONS OF CHLORODIFLUOROMETHANE, CHLOROPENTAFLUOROETHANE AND THEIR MIXTURE OF COMPOSITION: CHLORODIFLUOROMETHANE, 48.8WT. % AND CHLOROPENTAFLUOROETHANE 51. 2WT. % by Vasant Lotu Bhirud Chairman: Joseph J. Martin Objectives of this research were: (1) to determine experimentally PVT behavior, vapor pressure and critical temperature of the azeotropic mixture (R-502) containing chlorodifluoromethane (R-22), 48.8Wt.% and chloropentafluoroethane (R-115), 51.2Wt.%, (2) to correlate the mixture experimental data algebraically, (3) to correlate literature values of properties of the components and formulate methods of prediction of properties of the mixture and (4) to analyze the second virial data for the components and the mixture to obtain characteristic intermolecular potential energy parameters by a new analytical method. PVT behavior of the mixture R-502 was determined over a temperature range of 100 to 250 F, pressure range of 80 to 2000 psia and densities up to two times the critical density. Experimental determinations were made using a bellows PVT cell capable of volume expansion of 14:1. Vapor pressure measurements covered a temperature range of 100F to the critical temperature. The PVT data of R-502 as well as its pure components R-22 and R-115 were fitted by an equation of the form, xxi

-kT -kT -kT RT +BT+C e A +B T+C e A4+B T+C4e RT 2 2 2 33 3 44 4 P V-b + 2 + 3 V-b (V-b) (V-b) (V-b) A5+B5T A6+B6T + + alv alv a2 e (le e (l+le ) e (C2e ) The vapor pressure data was correlated by the following equation: ZnP = A + - + C9nT + DT + FT n(F-T) T FT Saturated liquid densities obtained in earlier work were correlated by the following equation. 1/3 2/3 4/3 s = A + B(1-TR) + C(1-TR) + D(1-TR) + E(1-TR) In order to predict the properties of the azeotrope R-502 from the properties of its components, it was found necessary to predict the critical values of R-502 precisely. The critical volume and temperature were predicted by the following equations: V = x V +x V cm 1 cl 2 c2 T T TB2 Bm - B B2 T X1 T + X2 T cm cl c2 A new method was used to predict the critical pressure of the mixture and is given by the following equation: 1 X1 x2 P P P cm cl c2 A simplified method was used to determine two characteristic parameters of a modified Lennard-Jones intermolecular potential function from the second virial data. The second virial coefficient is given by the resulting equation, U U 31 2 m 16 m2 B(T) = 8N d3 1 +2 o 15 9 k- 315 kT The second virial coefficients for the mixture were predicted from the intermolecular potential energy parameters of the pure components. xxii

It is expected that other refrigerant mixtures could be treated by the methods developed here. xxiii

THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING PHYSICAL PROPERTIES AND INTERMOLECULAR POTENTIAL FUNCTIONS OF CHLORODIFLUOROMETHANE, CHLOROPENTAFLUOROETHANE AND THEIR MIXTURE OF COMPOSITION: CHLORODIFLUOROMETHANE, 48.8WT. % AND CHLOROPENTAFLUOROETHANE 51.2WT. % Vasant Lotu iBhirud A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Chemical Engineering 1973 April, 1973 IP-851

C'A` 1 I - %. X o i

CHAPTER I INTRODUCTION Midgley and Henne (102) first suggested that chlorofluoro derivatives of organic compounds could be used for refrigeration. Since then many compounds have been developed for commercial use. Azeotropic mixtures of refrigerants are unique in behavior in that their liquid and vapor phases have the same composition over a considerable range of temperatures and therefore practically no fractionation can occur in the refrigeration equipment in the event of a leak. One of such azeotropic mixtures is the mixture termed as R-502* which contains 48.8 wt% (63 mol %) chlorodifluoromethane (R-22*) and 51-2 wt % (37 mol %) chloropentafluoroethane (R-115*). Benning (11) patented this azeotrope in 1953 and it was introduced to the commercial market in 1962 by the Du Pont Company. This azeotrope has a normal boiling point of about -46 C. Refrigeration performance characteristics of R-502 have been published in the literature (33, 43, 45, 96, 111, 112, 130). Azeotrope R-502 has been found superior to an other popular refrigerant R-22 (43). In the design of refrigerating equipment, it is essential to know the physical and thermodynamic properties of refrigerant under consideration. Preliminary tables of thermodynamic properties of R-502 were published by Du Pont Company in 1963 (47) which were based on a few experimental determinations of vapor pressure and generalized correlations applicable to mixtures. Badylkes (5,6,7) developed similar tables * Name assigned by ASHRAE.

of thermodynamic properties in metric units for R-502 based on Du Pont's vapor pressure data and corresponding states theory. In 1967, Loffler (86) published results of experimental determinations of vapor pressure, saturated liquid density and critical temperature of R-502, but did not give any experimental data. Considering the limited amount of experimental data, this work was initiated in 1966. Objectives of this project are to detrmiane ap-riq - mentally following physical properties of R-502. 1. Pressure-volume-temperature (henceforth will be abbreviated to "PVT" behavior of the gas. 2. Vapor pressure of saturated liquid 3. Saturated liquid densities 4. Critical constants Further intent of the thesis was to use a variable volume technique to make PVT determinations. There are very few PVT cells with this capability and they are reviewed later. The PVT cell used in this study was first designed and used by Bhada (15). This cell consists of stainless steel bellows capable of giving a volume expansion of at least tenfold. During the experimentation the gas under study does not come into contact with any liquids and therefore the cell may be termed as a dry cell. The versatility of this PVT cell is enormous. In this investigation we improved the techniques of data measurements. First we used mercury as the hydraulic fluid which is used to compress the bellows. Levels of hydraulic fluid in a glass tube reservoir were measured by a cathetometer. Temperature control of the bath was improved by putting extra insulation and using carefully placed auxiliary knife heaters.

For the other properties, well known experimental equipment and apparatus described by Hou (62) are used. A further object of this thesis is to correlate these properties algebraically. To describe the vapor pressure of R-502, Martin, Kapoor and Shinn's equation (93) is used. Saturated liquid density data is correlated by the Martin-Hou equation (91). Algebraic correlations of PVT data using Martin's equation (89) were studied in detail and it is found necessary to modify the original techniques so as to be able to cover a wider range of experimental data. It was further the purpose of this work to formulate the methods of predicting algebraically the properties of R-502 from the properties of its components. The outcome of this study is the formulation of methods of predicting critical constants for azeotropes such as R-502. It was the object of this thesis to initiate intermolecular potential energy studies for chlorofluoro derivatives of organic compounds. An extensive literature study is presented on this subject. Several models are available for the potential energy of interaction between two molecules out of which the Lennard-Jones model (85) is selected. A new algebraic method of evaluating the parameters of Lennard-Jones' model is presented here. Thus the total work covers experimental measurements of physical properties of R-502 and their algebraic correlations, algebraic correlations of physical properties of the components R-22 and R-115, methods of predicting algebraically the mixture properties and finally the intermolecular potential energy studies of components as well as the mixture R-502,

II. LITERATURE REVIEW The literature survey is divided into three major sections as follows: A) Physical properties of R-22, R-115 and R-502 B) Variable volume equipment for PVT measurements C) Intermolecular potentials As noted in Chapter I, physical properties selected for this review are: 1) PVT behavior of gas 2) Vapor pressure of saturated liquid 3) Density of saturated liquid 4) Critical pressure, volume and temperature. For PVT measurements various equipment are used, section B deals with only variable volume equipment. In section C several analytical equations available to describe intermolecular potential energy are reviewed. A. PHYSICAL PROPERTIES OF R-22, R-115 AND R-502 A-i. Physical properties of R-22 Table II-1 lists works on the physical properties of R-22. Each work is discussed below. A-1. (a) PVT Behavior of R-22 Ranges of experimental determinations of PVT behavior of R-22 are given in Table II-2 and Figure II-1. Benning and McHarness (13) investigated PVT behavior of R-22. They used material obtained by multiple distillations of commercial grade R-22. Purity of the material was checked by determining freezing point and limiting vapor density measurements. Low pressure (0.3 to 2 atm.) vapor density measurements gave an apparent molecular weight of

TABLE II-i PHYSICAL PROPERTIES OF R-22 PVT Behavior Vapor Pressure Saturated Liquid Density Critical Constants 1) Benning and McHarness 1) Booth and Swinehart 1) Benning and McHarness (1940) 1) Booth and Swinehart (1940)...(13) (1935)...(17) a..(14) (1935)..(17) 2) Michels (1957)...(99) 2) Benning and McHarness 2) DuPont Bulletin T-22 2) Benning and Mclarness (1940)...(12) (1964).. (46)...(14 3) Du Pont Bulletin T-22 3) Klezkii (1964)...(80) 3) Zander (1968)...(140) 3) Du Pont Bulletin (1964)...(46) T-22 (1964)...(46) 4) Lagutina (1966)...(83) 4) Du Pont Bulletin T-22 4) Martin (1967)..(89) (1964)... (46) 5) Zander (1968)..(140) 5) Lagutina (1966)..(83) 5) Zander (1968)..(140) 6) Zander (1968)..(140)

TABLE II-2 RANGES OF PVT MEASUREMENTS FOR R-22 Maximum Minimum Maximum Minimum Critical Reduced Reduced Property Units Value Value Value Value Value Reference P psia 310 4 715.7 0.433 0.006 Benning and T R 743.67 536.67 664.47 1.12 0.808 McHarness ( p lbs/cu.ft. 4.961 0.057 34.46 0.144 0.0016 P psia 1880 93 721.9 2.61 0.1288 Michels (99) 0' T R 762 525 664.50 1.15 0.790 P lbs/cu.ft. 41.97 1.610 32.76 1.280 0.049 P psia 3030 225 723.74 4.19 0.313 Zander Isometric T R 745.2 516.6 664.79 1.12 0.777 Data (140) P lbs/cu.ft. 77.97 5.15 32.03 2.435 0.161 P psia 5080 145 723.74 7.02 0.20 Zander Isothermal T R 851.4 545.4 664.79 1.28 0.821 Data (140) p lbs/cu.ft. - - 32.03 - -

M M' N N' 2500 ABCDE Benning and McMarness (13) FGHIJK Michels (99) LMNO Zander Isochores (140) 2000 LMN'N' Zander Isotherms(140) HI <s 1500 looo~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'. G 500 K ~~B c __ _ _ _ __ _ _ _ __ _ _ _ 0~c __ __ __ 0' L 0~~~~~~~~~~~~~~~~~~~~~~ 50 E 100 150 200 250 D 300 350 400 Temperature (F) Fig. I 1. 1. Ranges of PVT Measurements for R-22

R-22 as 87.25 instead of the theoretical value of 86.46. This was attributed initially to impurity in R-22 and further purification by distillation at pressures of one and 0.2 atm. was carried out. Different fractions of the distillation had the same apparent molecular weight. Results of chemical analysis for chlorine and fluorine were inconclusive to solve this discrepancy. No other explanation was found for the anomalous molecular weight of R-22. In correlating PVT data, low pressure vapor density measurements were brought into agreement with the rest of the data by using a multiplier, k, to gas constant R in the Beattie-Bridgeman (9) equation of state. Mass recovery for PVT measurements was precise to 0.3% max. at lowest density and 0.06% max. at the highest density. Temperature of a bath surrounding the PVT cell was controlled to +0.1 C. Pressure was measured by Bourdon gauges. Constant volume cell was used for PVT measurements. Correlation of forty data points resulted in the following equation: P = 0.08132T D + (0.015044 T-12.69) D2 +(0.013796 T-3.794)D... (II-1) where P = pressure, atm. abs. T = temperature, K D = molar density, moles per liter R = 0.08206 (liter) (atm)/(g-mole)(K) Eqn. II-1 predicted experimental pressures with average deviation of 0.3%. Michels (99) used variable volume equipment to obtain isothermal PVT data. H{is 181 data points were correlated to Martin-Hou equation by Martin (89). The equation of state for R-22 is:

59 RT -kT A + B T + C ekT P RT + Ai + Bi + Ci e + 6 6 (v-b) i2 (v-b)i eav -kT A + B T + C e + A 7 7 T (II-2) 2av e where R = 0.124098 B5 = 5.355465 x 108 A =-4.353547 C =-1.845051 x 10-4 2 5 B 2.407252 x 10 A6 = 1.363387 x 108 C2 = -44.066868 B6 = -1.672612 x 10 A3 = -0.017464 C6 = A B7 = C7 =0 B3 = 7.62789 x 10 a = 548.2 C3 = 1.483763 b = 0.002 3J~~A4 = 2.310142 x 10 k = 4.2/Tc B4 = -3.605723 x 10-6 Tc = 664.50~R C4 = 0 Pc = 721.906 psia 4 A5 = -3.724044 x 10-5 Vc = 0.030525 ft3/lb OR = ~F + 459.69 Eqn. II-2 predicted experimental values of pressure with an average deviation of -0.01%, average absolute deviation of 0.07% and maximum deviation of 0.61%. An equation of state for R-22 was published by Du Pont Company (46). This equation was based on Michels (99) data and unpublished data at The University of Michigan. Eqn. II-2 supercedes the equation of state for R-22 given by the Du Pont Company (46). Lagutina (83) obtained 74 PVT data points which are not available. This data was compared by Zander (140) with his own data.

10 Zander (140) studied PVT behavior of R-22 taking 163 isometric and 107 isothermal data points. Purity of R-22 was 99.97%. His estimated precision of experimental measurements for isometric data points were: pressure: +0.01%, temperature: +0.01% and volume: +0.1%. Isothermal data points were obtained by using Burnett's apparatus (27). Maximum estimated error in the compressibility factors for isothermal data was 0.25%. All data was correlated by equation of state described by Stein (131) and is given as: 7 2 K(T, ) = Z ( C i ) (II-3) i=0 j=0 where 1 1 T V _ Tc P I =- = I CYPC- = a —Tc Vc, PcV c (11-4) 7- 1)~ = [Z(e- 1)-1] = K(e,0) Coefficients in the eqn. II-3 are given in Table II-3. TABLE II-3 COEFFICIENTS IN THE EQUATION II-3 FOR R-22(131) j = o j = 1 j= 2 CO, j -0.726090 1.597642 0.546733 C1, j 0.452179 -1.079114 2.293855 C2, j -0.178269 1.656474 -3.320042 C3, j 0.008353 0.617720 -1.094151 c j 0.184597 -1.005899 1.828942 C, j 0.034258 -0.170070 -0.369520 C6, j -0.043901 0.190471 0 c7, j -0.001196 0 0

11 Zander (140) used eqn. II-4 with values of coefficients given in Table II-3 to compare his and other available data (13, 83) and the results are summarized in terms of average percent deviation in Table 11-4. TABLE II-4 MEAN DEVIATIONS OF PREDICTED VALUES BY EQN. 11-3 FROM EXPERIMENTAL DATA (140) Average Percent Deviation Experimental Work in V in P 1. Zander's (140) isothermal data +0.18% +0.34% 2. Zander's (140) isometric data +0.69% +0.48% 3. Forty data points of Benning and McHarness (13) +1.07% +1.18% 4. Seventy-four data points of Lagutina (83) +0.50% +0.85% This completes the literature review of the PVT behavior of R-22. A.1 (b) Vapor Pressure of R-22 Ranges of experimental vapor pressure determinations for R-22 are given in Table II-5. Booth and Swinehart (17) measured vapor pressure of R-22 using a cailletet tube. Temperature control was of the order of +0.01 C. Pressure readings were accurate to within 0.1 atm. Nineteen data points are available which were not fitted to any analytical equation. Benning and McHarness (12) measured vapor pressure at six temperatures. They used same material as was used for PVT determinations (section II-A.l(a)). Temperature control was accurate to +0.01 C and

TABLE II-5 RANGES OF VAPOR PRESSURE MEASUREMENTS FOR R-22 Minimum Maximum Minimum Maximum Critical Reduced Reduced Property Units Value Value Value* Value Value Reference P psia 138 707.90 712.46 0.194 0.994 Booth and Swinehart (17) T R 532.35 665.01 664.48 0.80 1.00 P psia 5 674.84 715.7 0.007 0.943 Benning and McHarness (12) T R 381.40 658.35 664.47 0.547 0.989 P psia 0.08 692 721.9 0.0001 0.959 Du Pont Bulletin T R 304.67 664.48 664.48 0.459 1.00 T-22 (46) P psia 3 709.19 723.74 0.004 0.980 Zander (140) T R 365.98 622.85 664.79 0.55 0.995 *Critical constants of Du Pont Bulletin T-22 (46) are assumed when not available in the reference.

13 pressure measurements were precise to 0.3% or better. Vapor pressure data was fitted to the following equation. logl0P = A+ T + C log10 T + D T (11-5) where P = pressure in absolute atmospheres T = Degrees Kelvin = OC + 273.10 A = 25.1144 C = -8.1418 B = -1638.82 D = 0.0051838 Eqn. II-5 predicts their own data with an average absolute deviation of 0.4%. with maximum deviation of -0.6%. Data points of Booth and Swinehart (17) were predicted by Eqn. II-5 to average absolute deviation of 1.66% with maximum deviation of +3.58%. Klezkii (80) used static method for vapor pressure measurements, composition of R-22 used by him was 99.85 mole %, R-22, 0.1 mole %, R-12 and R-13, 0.05 mole %, CO2. Experimental equipment was checked for precision by measuring vapor pressure of water and carbon dioxide. He correlated his data by the following equation. 1404.99 -17 6 P = 13.51222 - 1404.99 -3.15464 log T + 3.4953 x 10 T (II-6) where P = pressure in 10-5 Newtons/m2 T = temperature in degrees Kelvin Eqn. II-6 predicts his data with a maximum deviation of 0.06% (80). Experimental vapor pressure data points of Klezkii (80) are not available.

14 Du Pont Company (46) published a vapor pressure equation of R-22 based on Michel's data (99) and unpublished data from The University of Michigan. The equation is: log P = A - C log10 T + D T + F(F-T) (II-7) where P = pressure in psia T = temperature in degrees Rankine = ~F + 459.69 A = 29.35754453 D = 0.002190939044 B = 3845.193152 E = 305.8268131 C = 7.86103122 F = 686.1 Eqn. II-7 predicted Michel's data (99) and unpublished data from The University of Michigan with an average deviation of 0.11% (46). Lagutina (83) took twenty vapor pressure data points for R-22 which are not available but were compared with his own data by Zander (140). Zander (140), using static method, obtained twenty three vapor pressure data points. Temperature measurements were accurate to +0.01 C and pressure values to +0.01%. He correlated his data using the following equation: 5 0 log Tr = Z Ai (1- 0)i (II-8) i=O where 0= T/Tc X = P/Pc A = 0 A = -4.325804 o 3 Al = -2.967411 A4 = 6.571489 A = 1.264675 A5 -5.903528

15 Predicted values by Eqn. II-8 were compared by Zander (140) with his and other's (12,80,83) data and results are summarized in Table II-6. TABLE II-6 MEAN DEVIATIONS OF CALCULATED VALUES BY EQN. II-8 FROM EXPERIMENTAL DATA (II-8) Reference No. of Data Average Percent Points Deviation 1. Booth and Swinehart (17) 18 + 1.95 2. Benning and McHarness (12) 7 + 0.35 3. Klezkii (80) 14 + 0.09 4. Lagutina (83) 20 + 0.54 5. Zander (140) 23 + 0.07 A.1 (c) Saturated Liquid Density of R-22 Ranges of experimental saturated liquid density measurements are given in Table II-7. Benning and McHarness (14), using sealed tube method and obtained nine saturated liquid density points for R-22. Material was same as used for PVT measurements (section II-A.l(a)). Temperature measurements were precise to 0.1 C. They correlated their experimental data by the following equations: For temperatures between -70 and 250C d = 1.2849 - 0.003450 t - 0.0000073 t (II-9)

TABLE II-7 RANGES OF SATURATED LIQUID DENSITY MEASUREMENTS FOR R-22 Minimum Maximum Minimum Maximum Critical Reduced Reduced Property Units Value Value Value* Value Value Reference ds lbs/cu.ft. 51.0 93.1 34.46 1.48 2.70 Benning and McHarness (14) T** R 658.83 367.47 664.47 0.99 0.553 ds lbs/cu.ft. 51.0 100.0 32.76 1.56 3.05 Du Pont Bulletin R 650.0 304.67 664.48 0.979 0.459 T-22 (46) ds lbs/cu.ft. 47.2 80.0 32.03 1.47 2.50 Zander (140) R 656.28 486.67 664.79 0.988 0.733 *Critical constants of Du Pont Bulletin T-22 (46) are assumed when not available in the reference. **Temperature values correspond to the density figures.

17 For temperatures between 25 and 650C d = 1.2652 - 0.002109 t - 0.000298 t (II-10) s where d = density in g/cc t = Temperature in degrees centigrade Eqns. II-9 and II-10 predict their data with a maximum deviation of 0.01%. Du Pont Company (46) published a saturated liquid density equation based on unpublished data of their own and from University of Michigan. The equation is: 1/3 T2/3 T T4/3 A+B (1 T )/3 T 2/) + D(1- 1-) + E(1- (II-11) d = A+B (i- (l- T)Tc T s Tc Tc where d = Saturated liquid density in lbs/cu.ft. T = temperature in degrees Rankine = OF + 459.69 T = 664.5 R C = 36.74892 A = 32.76 D = -22.2925657 B = 54.6344093 E = 20.47328862 Eqn. II-11 predicted experimental points with an average deviation of 0.08%. Zander (140), using calibrated glass pycnometer measured saturated liquid density of R-22 at thirty one temperatures. Estimated precision of density values was +.0.1% except near the critical point. He correlated his experimental data by the following equation:

18 4 dR =j= O D j 2 (1-0II-12) where dR = density of saturated liquid/critical density 0 = T/T C T = 664.79 R D2 = -9.687052 D = 1.0 D3 = 16.888054 D1 = 4.936493 D4 = -10.978106 Eqn. II-12 predicts data of Benning and McHarness (14) with deviations up to 2.8% and that of Zander (140) with average absolute deviation of 0.01% and maximum deviation of 0.011%. A.1 (d) Critical Constants of R-22 Table II-8 lists critical constants of R-22 as determined by different workers. A-2. Physical Properties of R-15 Table II-9 lists authors of papers dealing with physical properties of R-115 under each property. These works are discussed below. A.2(a) PVT Behavior of R-115 Ranges of experimental PVT measurements are given in Table II-10 and Fig. 11-2. Sixty one unpublished experimental PVT data points determined at The University of Michigan (136) were available. PVT data was taken using constant volume method. Sample of R-115 had an air composition of 0.0045% of the vapor. Mass recovery was within 0.28%, and usually less than 0.04% of mass charged. Experimental data was correlated by the following equation.

TABLE II-8 CRITICAL CONSTANTS OF R-22 Critical Critical Critical Critical Critical Pressure Volume DensiSy Compressibility Temp. R psia ft3/lb lb/ft Factor Reference 665.19 712.46 - - Booth & Swinehart (17) 664.47 715.7 0.029019 34.46 0.25182 Benning and McHarness (14) 664.48 721.906 0.030525 32.76 0.2673 Du Pont Bulletin T-22 (46) 664.48 721.906 0.030525 32.76 0.2673 Martin (89) 664.79 723.74 0.031221 32.03 0.27394 Zander (140)

TABLE II-9 PHYSICAL PROPERTIES OF R-115 Saturated Liquid PVT Behavior Vapor Pressure Density Critical Constants 1) University of Michigan 1) University of Michigan 1) Downing (1949)...(41) 1) University of Michigan (1951)... (136) (1951)... (136) (1951)... (136 2) Loeffler and Matthias 2) Aston, Wills, and 2) University of Michigan 2) Loeffler and Matthias (1966)...(87) Zolki (1955)...(4) (1951)...(136) (1966)..(87) 3) Mears et al. (1966) 3) Loeffler and Matthias 3) Loeffler and Matthias 3) Mears et al. (1966)...(98) (1966)...(87) (1966)...(87) 0..(98) 4) Mears et al. (1966) 4) Nears et al. (1966)...(98) *..(98)

TABLE II-10 RANGES OF PVT MEASUREMENTS FOR R-115 Maximum Minimum Maximum Minimum Critical Reduced Reduced Property Units Value Value Value Value Value Reference P psia 1015 175 457.93 2.22 0.385 T R 806.4 563.4 635.58 1.27 0.887 Mear et al. (98) p lbs/cu.ft. 55.23 6.18 38.27 1.443 0.162 H P psia 1300 34 453.0 2.84 0.0744 University of T R 887 470 635.56 1.395 0.737 Michi (136) p lbs/cu.ft. 42.01 1.1350 -37.2 1.101 0.0305

2009 ABC DE Mears et.aI. (98) FBGHI University of Michigan (136) G H B A ~ ~ ~ ~ IE~~~~ (4-4 0' 1 200 300 400 500 Temperature (F) Fig. 11. 2 Ranges of PVT Measurements for R-115

23 C P = A + B T - (II-13) where -3.1857748 0.028919059 17.4448 x 10-6 2 3 4 v V v 0.06941 0.00267975 1.18424 x 10-5 1.67627 x 10-7 v 2 3 4 v V v 8.343505 x 106 5984.903 C = 2 4 v v P = pressure in psia V = volume in ft3/lb T = temperature, ~R = ~F + 459.69 Eqn. II-13 predicted sixty-one experimental data points with an average deviation of 0.56% up to the critical density. Loffler and Matthias (87) obtained experimental PVT data for R-115 which is not available, but the correlating equation is: A. + B. T + C. exp (-k T/T ) p 1 C. (II-14) i=l (v - b)i where 2 P = pressure in kg/m2 T = 353.15 K ( K = C + 273.15) c v = volume in m3/kg A1 = C1 = B4 = C4 0 1 1 4 4 k = 5.475 b = 0.375621948 x 10 3 -3 B1 = 0.548844475 x 10 (gas constant) A2 = -0.630246499 x 10 3 B2 = 0.571969964 x 10

24 C2 = -0.105686282 x 10-1 A3 = 0.611915189 x 10-6 B3 -0.285392832 x 10 9 C = 0.159305901 x 10-4 A4 = -0.354925144 x 10 9 A -= 0.823490309 x 10 13 B = 0.568119622 x 1016 5 C5 = -0.351035219 x 10 Mears et al. (98), using a constant volume method obtained 90 experimental PVT data points. Samples of R-115 had a purity of better than 99.9 mole %. Estimated precision in pressure measurements was +0.02% or better, in temperature measurements +0.05% and in volume measurements, +0.1% or better. Mass recovery was within +0.03%. Experimental PVT data was correlated by BWR (10) and Martin-Hou (91) equations of state and the equations are given in Table II-11. TABLE II-11 EQUATIONS OF STATE FOR R-115 1) Benedict-Webb-Rubin Equation (10) p= __ B~ R T - A- C T 2 p RT +B R T - Ao 0- + b R T -a + a_ P V+ O 2 — + 3 +C( 1 + ) eY2 V2 (II-15) eT rV V where P = pressure in atmospheres V = volume in cc/g

25 T = temperature in degrees Kelvin R = 0.531179 (ml) (atm.)/(K)(g) A = 8.16931 x 101 0 B = 0.1124173 0 C = 4.062018 x 107 0 oc= 0.20052475 y = 1.22 a = 9.216943 x 102 b = 3.0806914 c = 7.675972 x 10 2) Martin-Hou Equation (91) -kT/T 5 A. + B. T + C. e c P + E I 1 1 (11-16) V-b i=2 (V-b)i where P = pressure in atmospheres V volume in cc/g T =temperature in degrees Kelvin R = 0.531179 (ml)(atm.)/(K)(g) TC = 353.1 K b = 0.3813516 K = 5.475 B3 = -0.5123829 C3 = 1.179472 x 104 A4 = -3.299045 x 10

26 A2 = -6.720228 x 10 B = 7.204497 x 101 C =-8.12817 x 103 A3 = 6.764326 x 102 B4 = C4 = 0 A = 1.379499 x 101 5 B5 = 0.2091698 C5 =-1.742745 x 103 Experimental PVT data for R-115 was predicted by BWR equation of state within an average deviation of 0.26% and maximum deviation of 1.1%. Respective figures for Martin-Hou equation were 0.34% and 1.2%. Values predicted by Eqn. II-13 on comparison with BWR equation of state showed average deviation of 1% except at high density isochor where deviation amounting to 15% was encountered. A.2(b) Vapor Pressure of R-115 Ranges of experimental vapor pressure measurement are given in Table II-12. Twelve vapor pressure data points for R-115 were obtained by static method at The University of Michigan (136). A sample of R-115 had an air composition of 0.0032% of vapor. Experimental data was correlated by the following equation: 66911.9 1879.080 log66911.9 1879 + 7.118882 - 0.00375058 T T2 T -6 2 + 2.58213 x 10 T (1I-17)

TABLE II-12 RANGES OF VAPOR PRESSURE MEASUREMENTS FOR R-115 Minimum Maximum Minimum Maximum Critical Reduced Reduced Property Units Value Value Value* Value Value Reference P psia 0.55 453 453.0 0.0012 1.00 Universi o Michigan (136) T R 324.13 635.56 635.56 0.51 1.00 P psia 0.45 14.7 453.0 0.0001 0.033 Aston et al. (4) T R 320.09 421.05 635.56 0.504 0.663 P psia 3.4 391.1 457.93 0.007 0.854 Mears et al. (98) T R 370.60 621.99 635.58 0.581 0.979 *Critical constants of University of Michigan (136) are assumed when not available in the reference.

28 where P = pressure in psia T = temperature in degrees Rankine Equation II-17 predicted experimental data within an average deviation of 0.19% and maximum deviation of 0.44%. Aston et al. (4), using 99.99% pure R-115 took eight vapor pressure data points which were correlated by the following equation 1823.225 log P = 1823225 11.51021 log T + 0.007503762 T + 36.185941 (II-18) where P = pressure in mm of mercury T = temperature in degrees Kelvin Loffler and Matthias (87) took vapor pressure data for R-115 which is not available but was correlated by the following equation within an average deviation of +0.02 atm. 1530.38 T log (P/P )+ 4.21313 - 4.58430 log -) + 0.120375 (T_) (II-19) where P = pressure in atmospheres T = temperature in degrees Kelvin ( C + 273.15) Tc = 353.15 K Pc = 31.874 Mears et al. (98) obtained thirty-six experimental vapor pressure data points of 99.9 mole % pure R-115. Pressure measurements were precise to +0.2% and temperature measurements to +0.05%. The following vapor pressure equation was obtained.

29 log P = A + T + CT + D log T (II-20) where P = pressure in atm. T = temperature, K A = 3.8949764 x 101 B = -1.9321347 x 103 C = 1.0064705 x 102 D = -1.3949179 x 101 Eqn. II-20 agrees with data of Mears et al. (98) and Aston et al. (4) within average deviation of 0.33% and maximum deviation of 1.34%. A-2(c) Saturated Liquid Density of R-115 Ranges of experimental saturated liquid density data are given in Table II-13. Downing (41) reported two saturated liquid density data points for R-115 which were used in the correlations at The University of Michigan (136). Using sealed tube method eight saturated liquid density measurements for R-115 were made at The University of Michigan (136). R-115 had an air composition of 0.0032% of vapor. Experimental data was correlated by the following equation. 1/2 d = 37.210 + 0.003648 (t -t) + 1.1893 (t -t) (II-21) s c c + 6.6857 (tc-t) + 2.8894 x 10 (tc-t) when d = density in lbs/cu.ft. t = temperature in F tc = 175.89 F

TABLE II-13 RANGES OF SATURATED LIQUID DENSITY MEASUREMENTS FOR R-115 Minimum Maximum Minimum Maximum Critical Reduced Reduced Property Units Value Value Value* Value Value Reference ds lbs/cu.ft. 75.63 90.46 37.20 2.033 2.432 Downing (41) T** R 561.64 470.38 635.56 0.883 0.74 ds lbs/cu.ft. 49.189 108.47 37.20 1.322 2.910 0 University of Michigan R 632.50 316.46 635.56 0.995 0.498 (136) ds lbs/cu.ft. 62.66 103.97 38.27 1.637 2.717 Nears et al. (98) R 613.38 355.34 635.58 0.964 0.558 *Critical constant of University of Michigan (136) are assumed when not available **Temperature values correspond to the density figures.

31 Equation II-21 represents the experimental liquid density values within an average deviation of 0.15%. Loffler and Matthias (87) took some experimental measurements of saturated liquid density of R-115 which are not available but were correlated by the following equation V = 1.691. /3 (11-22) 1+0.79(1-T + 1.9414 (1- T-) T Tc c where V = specific volume of saturated liquid, cm3/g T = temperature in K = C + 273.15 T = 353.15 K c Equation II-22 predicted their data within average deviation of +0.3%. Mears et al. (98) took 14 data points using 99.9% pure R-115. Volume measurements were precise to +0.1 or better, temperature measurements +0.05% or better and sample weight values +0.05% or better. Experimental data was correlated by Martin-Hou equation (92) which is: 1/3 2/3 4/3 d = dc + A(1-TR) + B(1-TR) + C(1-TR) + D(1-TR) (11-23) where d = saturated liquid density in g/cc TR = T/Tc Tc = 353.1 K d = 0.6131 g/cc c A = 1.5024 B = -2.0583 C = 4.0351 D = -2. 0214

32 Equation II-23 predicts their experimental values with average deviation of 0.08% and maximum deviation of 0.25%. A-2(d) Critical Constants of R-115 Table II-14 lists critical constants of R-115 as determined by different workers. A-3 Physical Properties of R-502 Table II-15 lists works dealing with experimental determination of physical properties of R-502. Each work is discussed below. A-3(a) PVT Behavior of R-502 No experimental data on PVT behavior of R-502 is available in the literature. A-3(b) Vapor Pressure of R-502 Nineteen data points covering temperature range of -30 to 150 F were available from Downing (42) which were correlated by Badylkes (5,6, 7) using the following equation T T log lP = A + B/(T/100) + C log10 ( ) - D (II-24) where P = vapor pressure in kg/cm2 abs T = temperature in K A = +7.246308 B = -13.738168 C = -3.3686219 D = -0.48709009 x 10

33 TABLE II-14 CRITICAL CONSTANTS OF R-115 Critical Critical Critical Critical Critical Pressure Volume Density CompressiTemp. R psia 3 3 bility ft /lb lb/ft Factodr Reference 635.56 453.0 0.02687 37.20 0.2757 U. of M. (136) Loffler and 635.67 468.42 0.02709 36.92 0.28736 Laffler and Matthias (87) 635.58 457.89 0.02613 38.25 0.2710 Mears et al. (98)

TABLE 11-15 PHYSICAL PROPERTIES OF R-502 PVT Behavior Vapor Pressure SaturatedLiqutd Density Critical Constants I) Downing (1964)....(42) 1) Badylkes (1964)....(5,6,7) 1) Downing (1964)...(42) None 2) Badylkes (1964)....(5,6,7) 2) Loffler (1967),...(86) 2) Badylkes (1964)..(5,6,7) 3) Loffler (1967)....(86) 3) Loffler (1967)...(86)

35 Equation II-21 predicted experimental data within a maximum deviation of 0.5%. Loffler (86) measured vapor pressure of R-502 from -40 to +40 C and correlated it by the following equation in ( ) _=_ 1449.7 + 3.9609 + 0.1132 (T —) c T -1.7742 In ({-) (II-25) C where P = pressure in atm. T = temperature in degrees Kelvin Tc = 355.85 K Pc = 42 atm. His experimental data which is not available, was predicted by Eqn. II-25 with average absolute deviation of 0.05 atm. and maximum deviation of 0.08 atm. This equation also predicts Badylke's (5,6,7) values with average absolute deviation of 0.015 atm. and maximum deviation of 0.05 atm. Compared with vapor pressure data from Du Pont Company (42) absolute average deviation of 0.038 atm. and maximum deviation of 0.16 atm. was found. A-3(c) Saturated Liquid Density of R-502 Loffler (86) took saturated liquid density data for R-502 which is not available but was correlated by the following equation. ~~V = I /1.787 s 1+0.85(1-TR) + 1.902(1-TR)1/3 (II-26) where V = specific volume of saturated liquid in cm /g TR = T/Tc Tc = 355.85 K

36 Equation II-26 predicted his data within a maximum deviation of 0.3% and average absolute deviation of 0.2%. Estimated precision of experimental determinations was 0.3%. Eqn. II-26 predicted values calculated from corresponding states theory by Badylkes (5,6,7) within average absolute deviation of 0.9% and maximum deviation of 1.8%. Also values obtained from generalized correlations by Du Pont Company (47) were predicted by Eqn. II-26 within average absolute deviation of 1.6% and maximum deviation of 4.2%. A-3(d) Critical Constants of R-502 Table II-16 lists critical constants of R-502 as reported by different investigators. B. VARIABLE VOLUME EQUIPMENT FOR PVT MEASUREMENTS History of PVT measurements goes back to about the 18th century. Ellington and Eakin (48) have published latest review of techniques of PVT measurements. High pressure techniques were reviewed by Bridgman (24). Ellington and Eakin (48) also reviewed constant volume method of PVT measurements. Variable volume equipment may be classified into two sections: 1) Constant mass methods: mass of the test sample remains constant for a series of experiments. 2) Variable mass method: mass of the test sample changes in a series of experiments. Constant mass methods are further divided into "wet" and "dry" methods depending on whether test sample comes in contact with a fluid during experimentation. Table II-17 lists works according to this classification.

37 TABLE II-16 CRITICAL CONSTANTS OF R-502 Critical Critical Critical Critical Critical Temp. R Pressure Volume Density Compressibility psia 3 lb/ft3 Factor References ft /lb 639.67 - 0.02875 34.80 Downing (42) 650.14 617.48 - - - Badylkes (5,6,7) 640.53 617.4 0.02865 34.93 0.28729 Loffler (86) 639.56 591.0 0.2857 35.00 0.27465 This Work

TABLE II-17 VARIABLE VOLUME EQUIPMENT FOR PVT MEASUREMENTS Constant Mass Variable Mass Wet Method Dry Method I) Liquid Injected Piezometer I) Cylinder-Piston 1) E.S. Burnett (1936) (27) 1) J. Canton (1762,1764) (30) 1) J. Perkins (1819,1820) (113) 2) G. Aime' (1843) (1) 2) C.A. Parsons and S.S. Cook (1911) (110) X 3) L. Cailletet (1880) (28) 3) P.W. Bridgman (1923) (22) 4) J.G. Tait (1881) (135) 5) E.H. Amagat (1893) (2) II) Bellows 6) Carnazzi (1903) (31) 1) P.W. Bridgman (1931) (23) 7) T.W. Richards (1903) (121) 2) R.K. Bhada (1968) (15) 8) P.W. Bridgman (1913) (21) 9) A. Michels and R.O. Gibson (1928) (100) 10) F.G. Keyes (1933) (73)

39 Burnett (27) first used variable mass and variable volume method for PVT measurements. Advantage of this method lies in non-requirement of mass balance which is sometimes a cause for major inaccuracies in PVT data. Since then many workers have used this method. B-l(a) Constant Mass - Wet Method History of PVT measurements goes back to the experiments of Canton (30). He proved water to be compressible by placing it in a large bulb connected to a capillary with a receiver of an air pump as a pressure generator. Changes in volume, however very small, were detected by observing meniscus of water in the capillary. For high pressure measurements mercury was used as a pressure transmitting fluid. Glass piezometers surrounded by hydraulic fluid, mercury in most cases, were used. In this set up mercury level in the piezometer could not be observed. To overcome this difficulty Cailletet (28) gilded interior of the capillary. From the extent to which gilding was dissolved, position of mercury and consequently volume of the piezometer was determined. This procedure resulted in giving one reading at a time. Tait (135) used a floating hair index on top of the hydraulic fluid. Inherent inefficiency in these one-reading methods was eliminated by Tait (135) using fused platinum contacts into the capillary. Volume of the piezometer corresponding to each platinum contact being well determined by a suitable calibration method, pressures for successive contacts of mercury with platinum wires were observed. This experimental set-up yielding multiple readings depending on the number

40 of fused platinum contacts, used by other investigators (2,55,100,125). Amagat (2) used a similar set up to study compressibility of gases as well as liquids. Michels and Gibson (100) used an inverted glass buret of bulbs (Fig. II-3). Pressure to these bulbs is transmitted through mercury by hydraulic oil. Complete piezometer assembly was immersed in a temperature controlled bath. Pressure of the oil corresponding to each contact of mercury with platinum wire was recorded. Precision of the experimental data of Michels and Gibson (100) is of the order of 1:10,000. This equipment has been used to pressures as high as 3000 atmospheres. Detailed description of this equipment and experimental procedure is given by Schamp (125). Hagenbach and Coming (55) used bulbs of sequenced size in their buret. This Tait's type experimental set up cannot be used above 200 C since above this temperature mercury dissolves the platinum contacts. On the other hand precision in volume is of high magnitude even at pressures as high as 3000 atmospheres, because compressibility of glass enters into calculations of piezometer volume well above this pressure. Carnazzi (31) designed slightly different equipment from that of Tait (135). He put a fine stretched wire along the bore of the capillary, whose electrical resistance can be measured. Electrical resistance of this wire varied according to the position of mercury in a capillary. However Carnazzi's method suffers from a drawback that capillary action is irregular thereby resulting into higher imprecision in volume than that obtained by the Tait method. While Tait and Carnazzi's methods are multiple reading methods, Richards (121) devised a single reading method based on the same idea

41 ~~t'`~r Y' \.... OilI'.L. ~Platinum Resistance Wire Fused Platinum Cont.cts.... -"-Sample Oil —,__->_~_.:,___ Mercury r -—' —=-': — —.::~;."' —: —_L-, ['vrv-... -.Thermost"t 71 / Fig. 13. Michel- - Volume PVT Apparatus. Fi g. tl. 3. MicIheis' Va ri;-~lot Volume PVT Ai.paratus

42 of contact of mercury with platinum. He joined a bulb to the capillary and fused a platinum contact at the junction. The bulb was set in an inverted position in a temperature controlled bath. A test fluid with a known amount of mercury would be filled in the bulb and pressure applied through hydraulic oil. Pressure of the hydraulic oil corresponding to the mercury contact with platinum would be noted. The same procedure can be carried out with different amounts of mercury in the bulb. While the principle of changing volume of test sample by mercury remained the same, this method of Richards was a stepwise procedure, involving one reading for one cycle of pressurization and depressurization of the cell. Methods of Tait, Carnazzi and Richards suffered from the disadvantage that due to dissolution of platinum wires in mercury, equipment could not be used above 200 C for PVT measurements. Bridgman (21) used indirect piston displacement which Aime (1) employed in crude fashion. Bridgman (21) changed volume of the piezometer by forcing piston driven hydraulic fluid through a valve at the bottom of the piezometer. Volume of the piezometer was directly related to displacement of the piston. Aime (1) used hydrostatic pressure of sea water to force mercury into the piezometer and by weighing the amount of mercury forced, volume of the piezometer was determined. Knowing the compressibility of the hydraulic fluid and displacement of the piston, volume of the test sample was calculated by Bridgman (21). He used a manganin pressure gauge placed in the cylindrical bomb for high pressure measurements up to 9000 kg/cm2. Similar equipment have been used by others (8,34,40,73). Complete

43 description of the advanced equipment and experimental procedure is given by Keyes (73) and Beattie (8). This equipment is presented schematically in Fig. II-4. Douslin (40) using similar equipment, claims a precision of 3:10,000 for temperature near ambient and 3:1,000 at 300 C and 400 atmospheres. There are other variations of the technique described above. Connoly and Kandalic (35) used a high strength glass capillary as a piezometer whose volume was calibrated. Pressure transmitting fluid was mercury and the volume of the capillary was determined by noting its unoccupied volume. This equipment was used to obtain low pressure PVT data on hydrocarbons to determine second virial coefficients. Precision of data was of the order of 3:10,000 around pressures of 10 atmospheres and 1:10,000 around pressures of 25 atmospheres. Doolittle et al. (39) used a stainless steel piezometer with mercury as the pressure transmitting fluid. An iron plug was placed on top of the mercury. Position of the column of mercury was determined by locating the iron plug using a differential transformer connected to a 1000 cycles/sec. bridge with a vacuum tube voltmeter as a null indicator. Volume measurements were claimed to be precise to 1:10,000 except around one atmosphere. Over all errors in density were estimated to be less than 4:10,000 up to pressures of 4000 kg/cm2. Using an iron plug to locate the position of the mercury column made possible PVT measurements above 200 C. The following classification may be made in summarizing these methods. 1. Platinum wire-mercury contact method 2. Indirect piston displacement method 3. Direct volume determination method.

44 B-l(b) Constant Mass - Dry Method In this type of equipment the test sample does not come in contact with a fluid. The simplest equipment is a cylinder piston assembly which has a history of about 150 years. Bellows type equipment required advanced technology which was available around 1920. Both these types are discussed below. I. Cylinder-Piston As early as 1819, Perkins (113) used this method to measure compressibility of water. He used a cannon equipped with a movable plunger. Tolerance between the cannon and the sliding plunger was so small that no soft packing was needed. Cannon containing water as the test fluid was plunged into the sea at various depths using hydrostatic pressure of seawater as a pressure generator. The plunger was equipped with a sliding ring which was left at extreme positions thereby enabling to determine volume of water inside the cannon at respective pressures. Compressibility results obtained by this method were four times too small. Limitation of this experimental procedure was that only one reading could be obtained at a time. Parsons and Cook (110) also used this method. Later on, using advanced technology, Bridgman (21,22) built an apparatus to study compressibility of liquids at high pressures. Besides leak problems, he encountered rupturing of steel at high pressures. In the final analysis he writes (22), "I discard the method with regret, for its simplicity and directness." After his earlier relatively less successful attempts, Bridgman (24) in 1928 built a cylinder piston assembly (Fig. II-5) where he could obtain a fit between cylinder walls and piston of the order of 0.00001 inches.

45 /7A C B Fig I 1.. Keyes and Beattic Equipment (8,73) Slide W\i re Piston -/ / Piezometer Wa ll Test Charging Port Space P, Fig. 1L, 5 Bridgman Piston Cell (24)

46 Position of the piston was determined by measuring resistance of a slide wire. Even such a well machined apparatus leaked due to uneven expansion of the cylinder with respect to the plunger at high temperatures. B-l(b) Constant Mass - Dry Method II. Bellows As early as 1930, Bridgman (23) prepared brass bellows (Fig. II-6) to measure compressibility of liquids up topressures of 12,000 kg/cm. Volume of the bellows was found by determining position of the top plate by the slide wire. The bellows was guided by a center post. In working with "Shim" brass, Bridgman (23) found that thickness of 0.002 inches was too large and that of 0.0012 inches too small in preparation of bellows. He eventually used 0.0015 inches (0.0038 cm) thick sheets in the manufacture of bellows. He also tried other materials of construction such as special grade brass recommended for deep drawing, phosphor bronze, nickel silver, soft iron, silver, platinum and copper. Bridgman (23) prepared his own bellows and has described his method of construction. The final form of bellows consisted of nine double sections with an unextended length of one inch. The bellows were flexible to the extent of 0.187 inches in both directions, giving 0.375 inches altogether or about 32% on the maximum volume. In his earlier attempts Bridgman (23) used an external guide for the bellows. Later on he introduced an internal guide. Total available volume of the bellows was about 5 cm3. Absence of hysteresis was proved by obtaining pressure values in a complete cycle of pressurization and depressurization, which formed a smooth curve. Volume of the bellows

47 was lineraly dependent on length of the bellows to better than 0.1%. Equipment was used in the temperature range of 0 to 95 C. Hysteresis effects due to temperature changes were within the experimental precision. Maximum temperature dependence of the constants of the apparatus amounted to a variation of 0.15%. Net maximum correction to isothermal values due to pressure effects was never more than 2% and that for the thermal expansion at constant pressures less than 6%. In his final analysis Bridgman (23) concluded that the bellows method was superior to his indirect-piston displacement method and undoubtedly the cylinder-piston method. Trade name of the bellows was "Sylphon". Cutler et al. (38) used an apparatus similar to "Sylphon" to study compressibility of liquids between 35 to 135 C and pressures up to 10,000 bars. Estimated cumulative error in calibration constants was +0.3%. Precision in volume was +1.6% around 350 bars and +0.4% around 10,000 bars. Precision in density was estimated to be about +0.1% around 350 bars and about +0.14% around 10,000 bars. In 1968 Bhada (15) fabricated a stainless steel bellows capable of about 1000% volume change. The same equipment is used in this investigation and is described later. B-2. Variable Mass Errors in mass balance of a test sample are often the limiting errors in the precision of PVT data. Burnett (27) developed a method, based on the following equation, which does not require measurements of mass. P1 VA = Z1 nl R T (11-27)

48 The Burnett apparatus consists of two cells of volumes VA and VB immersed in a temperature controlled bath (Fig. II-7) connected by an expansion valve. In an experiment a sample is confined initially in the cell having VA and after noting pressure P1 at temperature T of the thermostat, it is allowed to expand into the cell having volume VB, also at temperature T. Pressure P2 is noted after expansion and then the expansion valve is shut off so that chamber B can be evacuated. For the total system volume of VA and VB after expansion we have: P2 (VA + VB) = Z2 N1 RT (II-28) On dividing Eqn. II-28 by 11-27: P2 (VA + VB) Z2 P2 P1 (A- = Z — = 2 N (II-29) -1 VA z1 1 where N is an apparatus constant which depends only on volumes of two cells VA and VB. After a series of m successive expansions: Pm+) Nm Zm+ (II-30) 1 1 or P NM P1 Z /Z m+l N1 m+l/Zl 1 N, the apparatus constant, is a function of temperature and is determined as the limit of the ratio (P /Pm 1) as P goes to P1. This task may be performed graphically or numerically by fitting an equation to the isothermal data.

49 Wire Contact -_____ Top P'!te Bellows Guid - Bellows Centering Beam Hydraulic Fiuid In let - Fig 11 60 Bridgman Bellows Cell (23) Supply Ij ——'- - Vacuum Higjh PIressure Gas Cell Diaphira qi'n Ce1 T ie ste r Fig I. 7. Bur tt. Apprls, aUS (27)

50 Burnett's procedure requires precise pressure measurements at low values unless the isotherm is linear to high pressures. Also any error in determination of the cell constant N, is magnified in the calculations of Z due to the fact that N is raised m times. m+l Schneider (126) used the Burnett apparatus for high temperature studies with a modification that the chambers A & B in Fig. II-7 were maintained at separate temperatures. Using Eqn. II-24 appropriately he was able to determine second virial coefficients to a precision of about 0.5% around 0 C and about 1% around 600 C. Burnett apparatus has been described in detail by Bloomer (16), Mueller et al. (105) and Schneider (126). Experimental data processing has been described by Canfield (29), Pfefferle et al. (115) and Silberberg et al. (127). Estimated precision in Z was of the order of 2:1000 and in N, the cell constant, of the order of 1:10,000 according to Canfield (29). C. INTERMOLECULAR POTENTIAL FUNCTIONS A good representation of intermolecular potential energy is desirable for several reasons. On the molecular level, intermolecular distances are specified by the minimum in the potential energy; force constants for vibrating and rotating molecules are obtained from the second derivative of the potential energy with respect to intermolecular distance and higher derivatives determine anharmonicity constants. A potential energy function may be used to calculate bulk properties like the second virial coefficient, the Joule-Thomson coefficient,

51 coefficients of viscosity, thermal conductivity, self diffusion, the thermal diffusion factor in dilute gases and crystal properties at absolute zero. Several equations have been developed to fit bulk properties. In the following discussion we shall confine to the second virial coefficient, its relation to the intermolecular potential energy and various analytical expressions for the potential energy. The second virial coefficient, denoted by B(T), is defined by the virial equation of state: PV y= 1 + B(T) () + (II-27) RT V 2 where P = pressure of the substance under consideration V = specific volume R = gas constant T = absolute temperature B(T)= second virial coefficient C(T)= third virial coefficient Relationship between the second virial coefficient and the intermolecular potential energy, U(r), is derived through the use of statistical mechanics and is given by the following equation. a 2Tr T T B(T) -N JJJ{ 4| | [e -/kT-l]inel dOe Sine2dO2d(82-O )r2dr 0 0 0 0 (II-28)

52 where B(T) = second virial coefficient U = intermolecular potential energy k = Boltzman constant T = absolute temperature el,02 = polar angles ~1,~2 = azimuthal angles r = intermolecular distance N = Avagadro number Some general observations suggest the nature of the potential energy curve. The phenomenon of gases condensing to liquids, indicates that at large separations, the forces must be attractive. At the same time the effect that liquids resist compression suggests that the forces at small separations must be repulsive. Therefore the potential energy between two molecules will vary with respect to the separation distance as shown in Fig. II-8. U(r) d dm r Um Fig. II-8. General Representation of the Intermolecular Potential Energy

53 Next we must consider the shape and nature of the interacting molecules. As a simple case, let us consider the two molecules which are spherically symmetric in shape and the electronic charge distribution (Fig. II-9). r12 Fig. II-9. Interaction Between Spherically Symmetric Molecules In this case, the center of force may be assumed to coincide with their geometric centers and then the potential energy U12 is simply a function of r12. The integration in the Eqn. II-28 over the orientation angles can be performed for this case resulting into the following expression. 00 B(T) = -27TN (e r2 12 (11-29) 0 The significance of the symbols is described for the Eqn. II-28. As a little more difficult case, let us consider the two molecules, each having two centers of forces as in Fig. II-10. rBB' A - -rAB' rAA Fi.1-trac nBA'B Fig. II-10. Interaction Between Molecules Having Two Centers of Forces

54 The total potential energy is calculated by the rule of pairwise additivity of the individual pair potential energies. Since the distances r', r etc. are functions of orientations of both distances rAA, rAB,. molecules, the intermolecular potential energy U12 has angular dependence. Integration in the Eqn. II-28 is very involved in this case. The case of molecules possessing dipole moments is a particular variation of the case of molecules of two centers of forces (Fig. II-11). r'r2_B12X A A' Fig. II-11. Interaction Between Molecules Possessing Dipole Moments The potential energy between the dipoles then depends on the dipole moments, the distance r12 as shown in Fig. II-11 and orientation of both molecules. Similar qualitative picture can be obtained for complex cases of molecules possessing more than two centers of forces. The two molecules are considered totally interpenetrable if, at the least, their centers coincide completely resulting into zero intermolecular separation. Realistically no molecule is totally interpenetrable and partial penetrability can be assumed to be a rule. In such a case, the molecule is considered as having a hard core surrounded by a soft core. This is presented in Fig. II-12.

55 r 2 Fig. II-12. Interaction Between Partially Penetrable Molecules The potential energy now depends on an additional factor, the thickness, t, of the penetrable shell of the molecule. INTERMOLECULAR FORCES Intermolecular forces are arbitrarily divided into two categories as short range forces, and long range forces. Short range forces, frequently termed valence forces or chemical forces, arise due to overlapping of electron clouds of two molecules. These forces are highly repulsive. Calculations of these short range forces are based-on quantum mechanics and are very complicated. Only simple systems like H2+, H2 have been treated. Long range forces are generally considered to be made up of three parts: 1) electrostatic interaction, 2) interaction due to induction, and 3) dispersion forces. In the following discussion we shall summarize the results and the detailed treatment of these forces is given elsewhere (58,69).

56 ELECTROSTATIC CONTRIBUTION Various multipole interactions contribute to the total intermolecular potential energy. Coulombic law of electrostatic interaction gives formulae for various types of interactions. X X a bb aa a a Zb {a Yb Fig. II-13. Electrostatic Interaction Between Two Molecules With relation to Fig. II-13 the interactions are as follows: (CC) C Cb Uab = + a (II-30a) r (C,>) Capb CosO b Uab - (II-30b) (C,Q) = + (3Cos2 -1) (II-30c) Uab 3 b 4r Ua,3p)= _ ab [2CosOaCosOb-Sin eaSin ObCos( a-( ] where UabC'C) = energy of interaction between molecule a and molecule b, both possessing charges Ca and Cb, respectively C,Cb = charge of the molecule pa'pb = dipole moment of the molecule Qb = quadrupole moment of the molecule b ea,b = polar angles p 4 = azimuthel angles ab

57 The average potential energy Uab is obtained by averaging Uab over all angles with the use of Boltzman weighting factor exp. (-Uab/kT). For specifically symmetric potential functions the potential energy is given by the following expression. Uab = Uab e-Uab/kT dwadwb-31) Uab =........ I e dwadwb where dw = SinOdOde Boltzman factor accounts for the assumption that statistically molecules spend more time in those orientations for which the energy is minimum. For the dipole-dipole interaction given in Eqn. II-30d, average intermolecular potential energy for large separations is: P,~) 2 Pa2pb2 Uab 23kT 6 1a2b(II-32) where symbols are explained in Eqn. II-30. Dipoles considered in Eqn. II-32 are ideal and the treatment of real dipoles is given by Hirschfelder, Curtiss and Bird (58). INDUCTION CONTRIBUTION With respect to Fig. II-14, let us consider charged particle'a' inducing dipole moment in a neutral molecule'b' resulting into induction interaction.

58 +C + c +r c + b+ Fig. II-14. Induction Interaction Between Two Molecules If'a' possesses dipole moment pa, then the interaction between this dipole and the induced dipole is: (l, indHu) H~a2 b(3Cos20a+1) ~(~P,~~,indp) - ~a a ~(11-33) Uab 2r6 where ab = polarizability of the molecule b ea = polar angle Substituting this into Eqn. II-31, we obtain the average potential energy as: Ua(p, ind p) Ha b (II-34) Uab 6 r For cylindrically symmetric molecules the induction contribution to the potential energy is (58) as follows: 1 Ca 21 2 2 1 2 2 3 2 ZUab =8 1 Cb'Ca2 2a2 3ea Uab.ab + t +'''] - +a + ID8.. 2 4 6 8 2 4+ 6 8 r r r r r r (II-35) where Ca, Cb = charge of the molecule oa, cb = polarizability of the molecule pa, pb = dipole moment of the molecule 8a, 8b = quadrupole moment of the molecule

59 DISPERSION CONTRIBUTION For spherically symmetric molecules, the dispersion energy is independent of the orientation of the molecules and is given by the following equation. dis C C' C'' Uab 6 8.10 (-36) r r r dis where Uab = dispersion energy between molecules a and b C,C',C"= constants r = intermolecular distance First term in Eqn. II-36 is associated with interaction between two mutually induced dipoles and the constant C is given as: E Ea acab C 3 Ia Ib (II-37) 2 2(EI+EIb where EIa E = empirical constants which are often approximated to equal to ionization energy of the respective molecule. Other terms in the Eqn. II-36 describe interactions between higher induced moments. For asymmetrical molecules dispersion interaction depends on orientations (58). In summarizing the discussion on potential energy of interaction between two spherically symmetric polar molecules (58), for slightly polar molecules dispersion contribution amounts to about 99.9% and the rest is made up of electrostatic and induction contributions. For highly polar molecules, electrostatic contribution amounts to about 76%, dispersion contribution is about 20% and balance is made up by induction contribution.

For spherically symmetric non-polar molecules, long range forces arise totally due to dispersion effects and intermolecular potential energy is inversely proportional to sixth power of intermolecular separation. Asymmetric molecules show the same dependence on intermolecular distance. SECOND VIRIAL COEFFICIENT FOR MIXTURES Statistical mechanics gives a quadratic relationship between the second virial coefficient for mixture and its components as: m m B = Z Y. Y. B.. (II-38) mix i j=l i j ij where Bm. = mixture second virial coefficient mix Yi.,Y = mole fraction of ith and jth component m = total number of components B.. (i=j) = second virial coefficient of interaction between molecules of ith and jth component There are a few ways of calculating the second virial coefficient of a mixture. Usually the second virial coefficients for like molecules, Bii, are available through the experiment or can be calculated if the intermolecular potential energy parameters are known. Then the problem of evaluating the second virial coefficient for unlike molecules, Bij, is solved through averaging procedures such as follows: B.. (B.. + B..)/2 (II-39) 13 21 JJ

61 Alternately, potential energy parameters can be used strictly to obtain B.. For the sake of example let us consider a two parameter mix potential energy function such as Lennard-Jones (12-6) (85). The parameters are U and d. Therefore starting with these parameters for m m pure components, we can obtain corresponding second virial coefficients using Eqn. II-29. Now the pure component parameters can be averaged to obtain interaction parameters using such rules as follows: dmij = (d + djj) (II-40) 1/2 Umij =(Umr Xar U a ) (II-41) These averaged parameters are used to obtain interaction virial coefficients Bij and using all this information, Bmix can be evaluated from the Eqn. II-38. Thus mixture second virial coefficients can be calculated strictly from molecular parameters or from experimental component second virial coefficients. INTERMOLECULAR POTENTIAL FUNCTIONS The latest review of equations representing intermolecular potential energy is given by Fitts (50). Other excellent treatise is that of Hirschfelder, Curtiss and Bird (58). Varshni (137) reviewed potential energy functions for diatomic molecules. Mason and Spurling (95) have given another thorough treatment on this subject.

62 Following is a compilation on the analytical equations for potential energy. On several occasions the analytical expression cannot be integrated in Eqn. II-29, but with the use of fast electronic computers numerical integrations can be carried out. Wherever possible the final analytical expression for B(T) is given. The analytical equations are broadly classified into two categories as angle independent and angle dependent expressions. Angle dependency may be due to shape or the charge distribution. Altogether twenty potentials are discussed below. I. Angle-Independent Analytical Equations for Intermolecular Potential Energy 1. Hard Spheres Model: The molecules in this model are assumed to be perfectly rigid spheres with no interaction at large separations and infinite force of repulsion when they touch each other as shown in Fig. II-15. Mathematically this interaction is described as follows: U(r) = ~ for r < d (11-42) U(r) = O for r >d where d ='diameter of the molecules U d r Fig. II-15. Hard Sphere Interaction The second virial coefficient for this model is given by the following equation: 2 3 B = ~r Nd (11-43)

The second virial coefficient as expressed in Eqn. II-43 is independent of temperature and is always positive resulting into compressibility factor greater than unity. These two qualities of B for the hard sphere model are not in accord with the facts. 2. Point Centers of Repulsion: In this model interaction between two molecules is assumed to be of a repulsive nature at all intermolecular separations as shown in Fig. 11-16. The analytical expression for this interaction is as follows: U(r) = arc (11-44) where a = constant c = index of repulsion U(r) Fig. II-16. Interaction for Point Centers of Repulsion The value of c is usually taken between nine and 15. On inserting Equation 11-44 in Equation 11-29, we obtain the second virial coefficient as follows: B(T) = 2 a c (II-45) providing c >-3 Here B(T) is a function of temperature but it is not correct since it is positive for all temperatures.

64 3. The Sutherland Model: This model assumes the interaction to be an attractive for separations larger than the diameter of the molecules and infinitely repulsive for smaller separations as shown in Fig. II-17. The intermolecular potential energy is given by the following equation: U(r) = oo for r < d (II-46) -= for r > d r where a = parameter b = index of attraction U(r) d r Fig. II-17. The Sutherland Model The index of attraction, b, is taken as 6 to be consistent with London's Theory of dispersion forces. Using Equation II-46 in Equation II-29, the second virial coefficient is given by the following equation: 27rNd 1 3 ( B(T) = - - 6 (II-47) j=O d kT Eqn. II-47 involves two parameters d and a which can be determined from two values of B(T). This model correctly gives negative B at low temperatures and a constant positive value at high temperatures which is approximately in accord with the facts.

65 4. Lennard-Jones 12-6 Potential: Mie (103) first suggested that U(r) may be expressed as the sum of two terms, a negative term proportional to -m -n r and a positive term proportional to r with n m > o. Lennard Jones assigned the values of n=12 and m=6 giving the following expression: 12 6 U(r) = 4Um [( - ( (1-48) r r where various symbols are shown in Fig. II-18. U(r) d.. dm Um Fig. II-18. Lennard-Jones 12-6 Potential The minimum in energy, Um, occurs at dm. Substituting for U(r) from Eqn. II-48 in the equation II-29, the second virial coefficient is given as follows: 0o kVT-(2j+1)/4-(2j+l)/22_ 2 3 ] 4 — -._ (II-49) B(T) = Nd3 k 4j -49) j=0 As can be seen, there are two parameters d and Um in this potential which can be evaluated by two values of B(T). The results fit the experimental second virial coefficient fairly well over wide ranges of

66 temperature. The dimensionless second virial B*(T*) and dimensionless temperature T* are defined as follows. T* = kT/Um and B*(T*) = B(T)/(2/3TNd3) (II-50) Tables of B* as a function of T* are given by Hirschfelder, Curtiss and Bird (58) along with values of d and Um for several substances. 5. Dymond, Rigby and Smith Potential: The intermolecular potential energy as proposed by Dymond, Rigby and Smith (44) is given by the following equation: 28 d 24 18 U(r) = Um [0.331 (-) - 1.2584 (-) + 2.07151 (-) r r r - 1.74452 (d) - 0.39959 (-) 3 (II-51) r r where d and Um have the same significance as that for Lennard-Jones potential (Fig. II-18). The difference between this potential and the Lennard-Jones potential is given in Fig. II-19. 1 --- Lennard Jones (12-6) Potential \Up) \l - Dymond, Rigby and Smith Potential dm Um Fig. I-19. Dymond, Rigby and Smith Potential

67 It may be observed from Fig. II-19 that this potential has a broader bowl than that for Lennard-Jones (12-6) potential. Using equation II-51 in Equation 11-29, integration is done numerically and results are given in the form of tables of B* as a function of T* (both quantities defined in Equation 11-50) by Dymond, Rigby and Smith (44). The procedure to evaluate molecular parameters Um and d is the same as that used for calculating the parameters for Lennard-Jones (12-6) potential. The authors list molecular parameters for several substances. 6. Guggenheim and McGlashan: Using crystal data, Guggenheim and McGlashan (53) developed the intermolecular potential for argon which is given by the following equation: U(r) = co for r < d =r-dm 2 r-dm 3 r-dm 4 -Um+a b +C (II-52) dm dm dm for 3.6A < r < 4.15A - d 6 for r > 5.4A0 = - l(-) where Um, 1, a, b and dm are five characteristic constants and c is taken to be equal to b. This potential is a discontinuous one and in those regions (d < r < 3.6A0 and 4.15 < r < 5.4A ) the potential curve is made continuous by free hand drawing. The authors selected 1 in order to agree with the theoretical dispersion force constant. Other parameters Um, a, b and dm were determined from crystal properties while d was evaluated from the second virial coefficient data. The

68 second virial coefficient for this potential is evaluated by graphical integration. This potential predicts B for Argon at low temperatures to a high degree of accuracy but fails at high temperatures since repulsive energy is not in accord with the facts. Fender and Halsey (49) found that this potential fitted their low temperature second virial coefficients for Argon within 1%. The authors (54) applied their potential to Kr and Xe for which second virial data of Fender and Halsey (49) was used. 7. Square-Well Potential: In this model molecules are assumed to have a rigid core surrounded by a purely attractive core. The resulting potential is given in Fig. II-20 and expressed by the following equation: U(r) = o for r < d =-Um for d < r < ad = 0 for d > ad (II-53) where the symbols are explained in Fig. 11-20. U(r) d ad r Um -- Fig. II-20. Square-Well Potential

69 Equation II-53 involves three parameters namely Um, d and a. Using Equation II-53 in the equation 11-29, the second virial coefficient is given as follows: 2 3 3 Um/kT B(T) = rNd [1 - (a -1) (e - 1)] (II-54) The three parameters can be evaluated from three values of B(T). This potential has no interpenetration of molecules and therefore the values of B at high temperature are not in accord with the facts. Since there are three parameters, this potential predicts B for complex molecules better than two parameter potentials. The molecular parameters for this potential for several substances are compiled by Hirschfelder, Curtiss and Bird (58). 8. The Buckingham-Corner Potential: Buckingham (25) proposed a potential having exponential repulsion term and attractive portion made up of two terms. This potential is presented in Fig. II-21 and given by the following equation: U(r) = be -a -cr6 r-8 (II-55) where a, b, c and c' are parameters. U(r) dm r max Um Ptni Fig. II-21. Buckingham Potential

70 The potential energy goes through a maximum at separation less than dm (where potential energy is minimum) and goes to negative infinity as zero separation approaches. Since this behavior of the potential does not compare with the facts, Buckingham and Corner (26) modified this potential and the result is presented in Fig. II-22. The modified equation is as follows: r -6,-8 dm-13 U(r) = b exp. [ - ( - (cr - c r ) exp [-4( r —) dm r for r < dm (II-56a) =b exp [- a(L )]-(cr 6 + c'r 8) for r > dm (II-56b) where b = [- Um + (1+B) Cdm 6] ea (II-57a) c = Umadm /[a(l+B)-6-8B] (II-57b) c' =Bd2mC (II-57c) B = c'dm-8/cdm-6 (II-57d) U(r) dm Um Fig. II-22. Buckingham-Corner Potential

71 This potential function has four parameters Um, dm, a, and B. Parameter a determines the steepness of the exponential repulsion and is usually taken as 13.5. The second virial coefficient B(T) is tabulated as a function of F, (58), where the relationship between B(T) and F is given by the following equation: 3 kT B(T) = 27TNd mF (a, B, ) (II-58) Ur The molecular parameters for some noble gases are given by Hirschfelder, Curtiss and Bird (58). 9. Exp-6 Potential: Buckingham potential (Eqn. II-55) was modified to give the Exp-6 potential which is presented in Fig. II-23 and expressed as follows: Um 6 r dm U(r) =I6-[- exp ([ 1- ) -(-) ] for r > d (II-59) 1-6/a dm r - max = 00 00 ~ for r < dmax where dmax is the separation at which potential is maximum in the Eqn. II-55.

72 U(r) dm r Um Fig. 11-23. Exp-6 Potential This potential contains three parameters: Um, dm and t. Steepness of the repulsive section is given by a. Using Eqn. II-59 in Eqn. II-29, we obtain the second virial coefficient as: 2 3 kT B(T) = 2Nd mF (a, ) (II-60) The function F is tabulated by Hirschfelder, Curtiss and Bird (58), who have also compiled the values of the molecular parameters of this potential for several substances. 10. Carra and Konowalow Potential: The exp-6 potential was further improved by Carra and Konowalow (32). This potential is presented in Fig. II-24 and expressed as follows: Ur=U[+6 di [ exp ( [1 - dm) - 1] (II-61) L r C_+67

73 where Um, a and dm have the same significance as that given in the original Buckingham potential (Eqn. 11-55). | I - Buckingham Potential I l1-* -- Exp-6 Potential U(r) t 8 t I - x - Carra and Konowalow Potential dm r max dm Fig. II-24. Carra and Konowalow Potential This potential is sometimes referred to as the Buckingham —CarraKonowalow (BCK) potential. The three characteristic molecular parameters are Um, a and dm. The second virial coefficient is obtained by using Eqn. II-29 in conjunction with II-61 to give the following relationship: 2 3 kT B(T) = -Nd3mF (a, -) (II-62) 3 Ur where F for this potential is tabulated in Ref. 58. The molecular parameters of this potential for several substances are obtained by Main and Saxena (108).

74 11. Modified Buckingham-Carra-Konowalow Potential: Nain and Saksena (107) assumed a rigid spherical core inside a molecule and extended BCK potential to this molecular interaction. This potential is presented in Fig. II-25 and expressed mathematically as follows: a+6 dm-adm 6 6 r-adm U(r)=Um (-) { [a(1- ] -1 (II-63) a r-adm ao+6 dm-adm where parameter a is the ratio of core diameter to dm. \\ ---- BCK Potential U(r ) | | A Modified BCK Potential adm * dm _ I' - Um Fig. II-25. Modified Buckingham-Carra-Konowalow Potential Eqn. II-63 involves four parameters namely Um, dm, a and a. No second virial coefficient calculations have yet been made for this potential. 12. Morse Potential: Morse (104) proposed a potential in which both attractive and repulsive terms are exponential. The potential is presented in Fig. II-26 and mathematically expressed as follows:

75 2c U(r) = Um { exp [- (r-dm)-2 exp [- -(r-dm)] (II-64) U) U{x.do do dm where 1 1n (2 c) (II-65) Um, do and dm are molecular parameters. U(r) d dm Um Fig. II-26. Morse Potential The parameter c defines the curvature of the potential at dm. Small value of c gives a potential with a small curvature at dm, resulting in a wide potential well. Similarly large value of c will give a narrow potential well. Morse's potential has a finite value at the origin given by the following equation: U(O) = 4Umec(dc-l) (II-66) Second virial coefficient for this potential is obtained by inserting equation II-64 into equation II-29 and the result is as follows: 3 2(kT B(T) = 2XrNd F (c, -) (tI-67) Urn

76 The function F is calculated by Konowlow, Taylor and Hirschfelder (82). The molecular parameters of this potential for several substances are calculated by Konowalow and Guberman (81). This potential predicts second virial data over the entire temperature range better than Lennard-Jones 12-6 potential (124). 13. Singer Potential: Singer (128) proposed a potential made up of two Gaussian functions as follows: U(r) = A exp (-ar2)-B exp (-br2) (II-68) where A, B, a and b are the four characteristic parameters. Neither analytical expression nor tabulated values of B are available. Singer (128) obtained these parameters for Argon only using crystal properties and showed that this potential mostly overlaps Lennard-Jones (12-6) potential. 14. Boys and Shavitt Potential: Boys and Shavitt (18) introduced a potential containing unlimited numbers of adjustable parameters. The analytical expression for the potential energy is as follows: 4Um Z 2i 2 (r) = 2 23 i=O C2i [r exp A(l-r )-1] (11-69) (r +B ) They stipulated that intermolecular separation, r, should be measured so that U(1) = O and constants A and B2 be assigned values of 4 and 1/10. The constants C2i are then adjusted to fit experimental data. For C = 1 0

77 and C = 0, this potential agrees very well with Lennard-Jones (12-6) 2i potential (18). The second virial coefficient is given in terms of tabulated values for specific choices of constants CO, C2 and C4 by Boys and Shavitt (20). Munn (106) has done further work on this potential and has recommended a simple procedure to evaluate constants C0, C C4 and C6. Using appropriate number of constants, shape of the potential can be changed as desired. II. ANGLE-DEPENDENT POTENTIALS As mentioned earlier, this discussion is divided into three subsections as angle dependency can arise due to either shape or due to polarity or due to both shape aid polarity. a) Angle-Dependency due to Shape of the Molecules Qualitatively it is interesting to see how the second virial coefficient depends on the shape of a molecule. A simple way is to compare second virial coefficients of rigid convex bodies of several shapes. We must remember that in this case B is independent of temperature which is not in accord with the facts. Keesom (70) carried out first such calculations for rigid ellipsoids of revolution. The results were not very encouraging and after a gap of about forty years, Isihara and Hayashida (66,67) formulated a general theory for the second virial coefficient for rigid convex molecules of any shape. This theory was extended by Kihara (74, 76, 77, 78). The second virial coefficient for these rigid molecules can be written as follows:

78 B = b f (11-70) 2 3 where b = -rNd (II-71) o 3 f = shape factor The term bo corresponds to the second virial coefficient for rigid spheres of diameter d. The shape factor f is dependent upon the curvature of the molecules and surface to volume ratio of the molecules is given by the following equation (58). f = 1+ [(S / b ) (M/4)- (3/4)] (II-72) where where (1/2) [R R s (II-73) R1 2 ds = surface element for the integration S = the surface area of N molecules R1,R2 = principal radii of curvature of the surface at the surface element d s The shape factor, f, has been evaluated for variety of nonspherical shapes (65,66,67,75,76). 1. Kihara Potential: Kihara (74,76,77,78) visualized the molecules having a rigid convex core, superposed with a force field outside the rigid core. In this case the energy of interaction of the two molecules is taken as a function of the shortest distance between the surfaces of the two cores. Physical significance of this concept is that the centers of forces are uniformly distributed over the core surfaces and the forces have such a fast variation with distance that major contribution to the interaction energy is due to two closest centers of forces.

79 The equation for the potential is as follows: d 12 d 6 d m U = 4U [(- ) - ( ) ] (II-74) m r r where r= the shortest distance between the cores d = the intermolecular separation for which energy is m minimum U = the minimum potential energy m Second virial coefficient for this potential is given by the following equation (117, 119): UU M 2 U B 2 3 m 2 mF3 3( ModF2() + (S + 4) dm M S +v + (4 ) (II-75) o 47r where the functions Fl, F2 and F3 are available in the form of tables (35, 36). Factors M, SO and VO arise from size and shape of the core (58). The adjustable parameters of this model are d, U and the ones m m describing shape and size of the core. The usual procedure is to obtain the core shape and size parameters on the basis of molecular structure and then adjust d and U to fit experimental B(T) data. Another method m m is to leave size parameter adjustable, fixing only shape parameter, thereby giving us three parameters to work with. The method of evaluation of these parameters is described by Prausnitz and Keeler (118).

80 The core model is an extension of the shell model. This model has been fitted to heavy rare gases very well (95). Also it has been well fitted to the dipolar and quadrupolar gas data (95). 2. Corner Potential: Corner (37) approximated a long molecule by four centers of forces as shown in Fig. II-27. The potential energy for this interaction is given by the following equation: 12 6 4 4 dm dm U(r) = 4(Um) [r c (II-76) i=l j=l 1ij i where r.. = distance between point center i to the point center j dm = minimum distance between given two centers of forces c for which the potential energy is minimum Um = minimum potential energy corresponding to dmc c 2' 113 Fig. 11-27. Molecular Interaction for Corner Potential There are sixteen possible interactions in summation of Equation (II-76). Each interaction depends upon the orientation of both molecules which

81 are given in terms of OA, OB and 0. Using Equation (II-76) in Equation (II-29) and integrating over all angles, the second virial coefficient is given by the following equation: 2 Ndm 3 k kT ( kT B(T) = 3 [B*kTm) +, { 6Bl* k() + 4B2* (m)}] (1-77) 3 UM 1 Ur 2 Ur where B* = B/(2/3TrNd3) (II-78a) B*= T*k(dkB*/dT*k) (II-78b) k T* = kT/Um (II-78c) 29 1 53 1 3 + = 1 5 d 3- d-3 +.... (II-78d) 15 dm 15 dm The function fB in Equation (II-77) is tabulated (58). The parameters Um, and dm are sort of an average of those for all possible pairs of centers of forces. The quantity 1 is the characteristic length. There are three characteristic molecular parameters for this potential, namely, Um, dm and 1. These molecular parameters for several substances are given in reference (58). (b) Angle Dependency Due to Polarity of Molecules (1) Rigid Spheres with Imbedded point dipoles: If the molecules are considered to be rigid spheres of diameter d and having centers of dipole strength u, the potential energy is written as follows: U(r, 0, 02, 2- A1) = - for r < d 3 (11-79) - g(01' g2' $2- 21) for r > d where g(01' 02 ~2- 2 1) = 2CosGlCosO2 —SinelSine2Cos(~2-$1) (II-80)

82 This interaction is discussed before and presented in Figure 11-13. Substituting Equation (II-79) in Equation (II-29) we obtain the following expression for the second virial coefficient (70): B(T) = -'Nd [1- i (II-81a) i=l (2i)!(2i-1) d3kT 2 3 22 2 4 -'rrNd [1- ( ) - 7 ( 3.](II-81b) 2T 7 7 d kT d kT 27T ~TT 1 2 where G. = g2ksinelsine2ded2 (21) (II-81c) 0 0 0 where g is defined in Equation (II-80). Keesom (71) extended this work to calculate the second virial coefficient for rigid spheres having point quadrupole amounts. (2) Stockmayer Potential: Extending the Lennard-Jones (12-6) potential to dipole-dipole interaction, Stockmayer (132) proposed the following potential: 12 6 2'I,,='4U d d (11-82) U (rl> 102^~2v~l) I 4Um [(r) (r) ] 9 3 (II-82) r where g is defined in Equation (IV-54) and P is the dipole moment. Equation (II-82) was substituted in Equation (II-29) and the second virial coefficient is given as follows (59, 123): J F 2j-2i-1 2 1/4 1 2j i<j/2 (2i 4 ) 1[2 () r (3 - 2 1/2 m) ) _ _ E 2 B(T) = Na2 kT 4 j! (2i+1 3Gt2 / (II-83a) kT (j+l)2 Ur

83 p (j) 3i where G = 3b) i=O 2i+l (II-83b) i= +1 2 and t= 8-1/2 U (II-83c) m In the Equation (II-83a), d is the collision diameter and t is the reduced dipole energy. The equation(II-83a) can be simply written as: 2 3 B = rNd F(e,t) (II-84) where F(O,t) is tabulated (123) There are two parameters, Um and d to be determined for this potential. The method of determination of these molecular parameters along with their values for several substances are given in reference (58). (c) Angle-Dependency Due to Shape and Polarity Kihara Potential: O'Connell and Prausnitz (133) combined the dipoledipole interaction with Kihara potential to obtain the following equation: U(r) = o for r < d 12 6 2 = 4U [(-) - (-) + g] for r > d (IT85) m r r 3 r where d, Um, and r have the same significance as that explained in Equation (II-74) and g is defined by Equation (II-80). The second virial coefficient for this potential is as follows:

84 B(T) 2= Nd3F kT (II-86);Tr3 F (iii;m 8122U d3 m The function F in Equation (II-86) is evaluated by O'Connell and Prausnitz (109) for spherical molecules only. Suh and Storvick (134) extended this treatment to convex molecules. The expression for B(T) is: 2 3 3 2 B(T) = rNd F (z) + MNd F2(z) + (S+M /4T) NdF1(z) 3 c 3 2 21/2 2 + (V+MS/47)N - 36'rN (d+do) t 2H6(y) (II-87) where z = U /kT (II-88a) d = core diameter 0 t = 12/(8)1/2 U (d+do) (II-88b) m -U 1/2 (II-88c) y = 2 (k) H6(y) = y72 0 [(p r (2p+l (II-88d) The functions Fi are the same as that for the Kihara potential. Quantities M, S and V are derived from shape and size of the molecule. Suh and Storvick (134)have described the method of evaluation of the molecular parameters and have calculated them for several substances. Certain unsatisfactory features in this derivation were improved by Storvick and Spurling (133) and they obtained results for the spherical molecules only.

85 III. COMBINATION RULES FOR INTERMOLECULAR FORCES. The only exact rule for combination is that for the diameter of rigid sphere where interaction diameter is the arithmatic mean of the individual molecular diameters. Other rules must be regarded as empirical or semi-empirical. Therefore without explaining the theoretical connections, if any, the rules are simply listed below. For rigid spheres d2 = (dll+d12) (II-89) where the subscript 1 stands for one molecular species and subscript 2 stands for the second molecular species. The subscript 12 denotes the interaction between the molecule of species one with that of species two. The parameter d will denote the characteristic intermolecular separation for the particular potential. In the following discussion, parameter U will denote the characteristic potential energy for that particular potential: d2 = (d ll +d22 ) (II-89) and U 1/2 (Um U. U = 11 m22- (II-90) m12 (U1+U (Umll+Um22 ) Fender and Halsey (49) modified Equation (II-90) into the following expression: = mll m22 (-91) m12 (Umll+Um22)

86 Another rule for d12 is (95) 1/2 d12 = (dlld22) (II-92) Mason (94) proposed the following combination rules for the Exp-6 potential: 12 2( 11+ 22) (II-93) 1 dmi2 = 2 (dmll+dm22) (II-94) and Uml2 (U llU22)/2 (II-90) Nain and Saxena (108) proposed the following combination rules for the Buckingham-Carra-Konowalow potential: 12+6 (_ 1l+6 22+6 1/2 12 ll 22 e e e d 2 _ 11 22 m12 2 d2/ 1 + dm ) dmil 22 _1/2 __ doll dm22 2 a11 +22 m12 (UmllUm2222) a 1/2 d 2 2a (-97 m 12 For the Morse potential combination, rules were proposed by Saxena and Gambhir (124) as follows:

87 Uml2 (U mllU 22 (-90) C..C.~.C.C 1 2 11...22 (II-98) d /- d + - m1 dmll 2 d m11 d m22 d d 011 022 011 022 C 11..Cd22 d12 d ml2 21n2/(- + (II-99) 012 mL2 d d For the Stockmayer potential, combination rules for unlike polar molecules were given by Rowlinson (122) and they are as follows: d12 = (d + d22)/2 (II-89) 1U =(U U )1/2 a(II-90) Um12 = (UmllUm22 2211P22 w = 1 21 2U 2d (II-101) 12 1 olm/2um 3 m12 12 For the interaction between a polar and a nonpolar molecule, combinatory the following equations (122): 1/ d n = - (d+d ) 1/6 (11-102) np 2 n p (U =( U )1/2 2 (11-103) (Um)n, p (Ump mn) x2 U 1/2 4 U d3d3 mn

88 n,p = subscripts to denote nonpolar and polar molecule an = polarizability of the non-polar molecule n d,d = collision diameters of polar and nonpolar molecular species. p n For the Kihara potential, combinatory rules for the two parameters, d and U are the same as given in Equations (II-89) and (II-90), but m the interaction virial coefficient, B12, has a modified form in terms of individual shape and size factors (58) which is as follows: 2B d3 m12 2 m12 AB = 3 3 ( kT- ) + (M11+M22)d 2 2 kT m12 + (S11+S22+M llM 22/2jr)d12F1 - ) + M22s 11 +M11 22 (V11+V22 4+ (II-105) This concludes the basic review of literature on intermolecular potentials. For further reading, the work of Klein (79) on LennardJones, Kihara, Exp-6 and Square Well potential is recommended. IV. DIPOLE MOMENTS OF R-22 AND R-115 Smyth and McAlpine (129) reported the dipole moment of chlorodifluoromethane, R-22, to be 1.39 debye. Later on Fuoss (51) estimated that dipole moment of R-115 is 0.14 debye. Lately Giacomo and Smyth (52) reported a value for the dipole moment of R-115 to be 0.52 debye.

CHAPTER III EXPERIMENTAL WORK E.I. du Pont de Nemours and Company supplied twenty-two pounds of R-502, whose gas chromatographic analysis showed that it contained organic impurities less than 0.02 wt% and moisture 7 ppm by weight. The vapor phase contained 0.33 vol. % of air. The chromatographic analysis was carried out by the Du Pont Company. Experimental work to determine physical properties of R-502 was carried out in several phases. Vora (138) used static method to measure vapor pressure up to about 16 psia (-100 to -40 F). Hossain (61) using sealed tubes containing calibrated floats measured saturated liquid density from -165 to 180 F as well as critical temperature. PVT behavior was determined using a bellows PVT cell in the ranges of 0-2000 psia and 80 to 250 F. Equipment systems and operating procedures are described below and details are given in the Appendices. A. PVT BEHAVIOR OF R-502 A.1 Bellows PVT Cell Bellows PVT cell was designed by Bhada (15). Cell and auxiliary equipment are given schematically in Fig. III-1. The whole experimental set-up can be divided into the following sections: 1. Bellows PVT cell. 2. Pressure measurement system. 3. Temperature control system. 4. Temperature measurement system. 89

Vent Charge U 2 0-2000 0-500 0-100 V3 Cyl. V2 V5 V6 McLeod ~~ ff Cold D.~~ V., V7 Trap Gauge Recov. Vaccum Gauge,_.............P1 Cuyl. Pump Galvan. Null Indicator Bridge / 4-' C & CD. I (U Relay Vl 1~~~~~~~ Ln~~~~~~C VIV T- 8 Heater 2 Figure.-I Il. 1 System for PVT Measurements Using Bellows PVT Cell

91 5. Charging and recovery system. Details of the PVT cell are given in Fig. III-2. It consists of a bellows enclosed in a thick-walled cylindrical shell, all made of stainless steel 316. The bellows is suspended from the top and is provided with an inlet to admit the test sample. Space between bellows and the cylindrical shell is filled with a hydraulic fluid (mercury in present case). Appropriate ports are provided for bleeding and draining of the hydraulic fluid in the space between the bellows and the cylindrical shell. A hand operated hydraulic pump is used for forcing hydraulic fluid from the reservoir. Volume of the bellows is determined in terms of the level of the mercury in the reservoir which is measured on a glass gauge. The pressure measurement system consists of a PACE-diaphragm pressure transducer, null indicator, pressure gauges, dead weight tester and a supply of high pressure nitrogen gas. The pressure transducer, located in the bath in which PVT cell was submerged, received system pressure on one side of the diaphragm. Nitrogen pressure was applied to the other side of the diaphragm to balance the system pressure, so that differential pressure should not exceed 50 psi in normal operations. Balance of the pressure was indicated by a null indicator. The pressure transducer worked on the principle of magnetic reluctance. Nitrogen pressure was measured on an appropriate gauge. Three gauges of ranges 0-100, 0-500 and 0-2000 psi were accurated calibrated in situ by a dead weight tester before and after experimental runs.

92 - 2I Di 8IDl. CHARGING HOLE I-_ _D. CH, / / 761 DIA. HEAD 9A'-.// —k' - LLOWS; AP FOR VENT i i BELLOWS, I i 1. D.= 2" I I BELLOWS O. D4 iX, I I S g | -l Ico PINS I 7i i+o/ A 0' 65" Vicj. 111 2 Dde~aiI of thle L~l levis [W'Isl- CclI (15)

93 The temperature control system, consisting of a thermoregulator- relay and heater, gives an on-off type control of the temperature of the bath fluid in which PVT cell and the pressure transducer are immersed. A magnetically adjustable mercury contact thermoregulator, immersed partially in the bath fluid sends signals to the relay whether temperature of the bath fluid exceeds from that adjusted on the thermoregulator. Accordingly, the heater is switched off or turned on. At all temperatures of measurements above room temperature, cooling is due to heat lost to ambient and at room temperature measurements a cooling coil with tap water running through it, is used. The bath is well stirred. Bath temperature is measured by a platinum resistance thermometer. It was calibrated by the National Bureau of Standards. Resistance of the thermometer is measured by a wheatstone bridge connected to a galvanometer. The charging and recovery system consists of a vacuum pump, McLeod gauge, charging cylinder and a recovery cylinder. The vacuum pump is capable of pulling a vacuum as low as one micron. Weights of the cylinders are determined by a very accurate balance whose weights were calibrated. A-l.b Procedure of Operation The experimental procedure is divided into the following three sections. 1. Charging the PVT cell 2. Data observation 3. Recovery of the test sample from the PVT cell

94 Notations used in the following description are explained in Fig. III-1. Initially the bellows are compressed to their minimum volume, allowing air to escape through the vent valve V3. Then valve V3 is closed and the PVT cell is evacuated by means of the vacuum pump P1 to a vacuum of less than ten microns. The bath is kept at room temperature. In another operation, the charging cylinder is filled with liquid R-502 from the inverted supply cylinder. The charging cylinder is held inverted during the charging operation so that only liquid, having the given composition, is charged without getting any small impurities of vapor phase into the system. During charging operation valves V3, V4 and V7 are kept closed. The PVT cell and the lines are undeL vacuum at this stage. Then valve V6 is opened slowly and pressure is allowed to build in the PVT cell. Some pressure buildup can be absorbed by expanding the bellows to a desired volume. The pressure is continuously monitored through the pressure transducer. Nitrogen pressure must be manipulated to balance the pressure transducer diaphragm at all times. After the pressure reaches vapor pressure at the bath temperature, liquid mixture will trickle into the PVT cell. About fifteen minutes are given for the liquid to fill the PVT cell and then valves V1 and V6 are closed. Now valve V4 on the evacuated recovery cylinder is opened allowing liquid in the lines to flash into the cylinder. The recovery cylinder is held at -190 C by liquid nitrogen. At such low temperature, the mixture being solid, all liquid in the lines go into the recovery cylinder and freezes. To assure that all the residual amount of test sample in the lines is recovered, all the lines from the PVT cell to valve V7 are heated by an electric tape to about

95 200 F for about 20 minutes. The recovery cylinder is detached, and allowed to warm up to room temperature. From the weights before and after of the charging cylinder as well as recovery cylinder, mass of the charge can be determined. Now the temperature of the bath is controlled at the desired temperature by means of a Doty magnetic thermoregulator connected to a relay circuit which powers the heaters in the bath. The temperature fluctuation was of the order of +0.04 F over one full run. In observing the data we started with the largest volume depending on the pressure reading. The PVT cell is calibrated in terms of the level of mercury in the mercury reservoir. Then the cell is compressed by means of the hydraulic pump P2 to a desired volume. About half an hour is allowed for the test sample to reach thermal equilibrium with the bath and then pressure is recorded. This procedure is repeated as desired. Finally bellows is decompressed to bring the volume to the same as one start s out and again pressure is recorded. This provides a check to see whether the test sample has leaked. The same procedure of data observation is repeated with different amount of charges and different temperatures. In the recovery operation, all lines are evacuated to a vacuum of less than 10 microns. The preweighed evacuated recovery cylinder is positioned in its place. With the PVT cell at a temperature, usually higher than room temperature, valve V4 is opened. The recovery cylinder is held at -190 C using liquid nitrogen. The lines are heated and kept at a temperature less than the bath temperature so that no condensation of vapor can take place in the lines. The bellows is

96 slowly compressed to its smallest volume and then about 45 minutes time is allowed for all test sample to transfer to the recovery cylinder. Valve V4 is then closed. The recovery cylinder is allowed to warm up to room temperature and is weighed. From the weights of the charging cylinder before and after charging, the mass of the test sample is calculated which can be compared with the value obtained before in the charging procedure. Both values should agree within the precision of weighing, otherwise the data is discarded. A'lc. Experimental Precision Temperature were measured to +0.001 F using a platinum resistance thermometer. The on-off temperature contral gave a sinusoidal variation in the bath temperature (Appendix A). By recording the average resistance, estimated precision in the temperature value was +0.04 F at the worst. Pressure measurements were believed to be accurate to +0.17%. Volume calibrations were estimated to be accurate to +0.45% at the lowest bellows volume and +0.20% at the highest bellows volume. The accuracy of the whole weighing procedure was estimated to be +0.05%. The specific volumes obtained were estimated to be accurate to +0.5% at the lowest bellows volume and +0.25% at the highest bellows volume.

97 B. VAPOR PRESSURE OF R-502 Vapor pressure of R-502 was measured in two parts: 1) low-pressure experiment, and 2) high pressure experiment. Vora (138) measured low vapor pressure by the static method. For high vapor pressure measurements the PVT cell was used. Equipment and procedures of operation are discussed in general here and details are given in Appendix B. B-1. Low Vapor Pressure Measurements: B-la. ExPerimental System: Experimental system is similar to that used by Hou (62) and is presented schematically in Fig. III-3. It can be divided into the following sections: 1) The isoteniscope 2) Pressure measurement system 3) Temperature control system 4) Temperature measurement system 5) Charging system The isoteniscope is a glass tube of adequate capacity to hold a liquid sample. The isoteniscope is immersed in a constant temperature bath. The pressure measurement system consists of a mechanical vacuum pump, mercury diffusion pump, mercury U tube manometer and a cathetometer. One leg of the mercury U tube manometer is continuously exposed to a vacuum of about one micron created by a combination of mercury diffusion pump with the mechanical vacuum pump. The other leg of the mercury leg

PO - Drying Tube Heater Pt Resist. V8 2 V3 Therm McLeod V4 Gauge V2 g;Liq-N2 Cooled 4 j gv ~ ~ ~ ~ ~ ~ ~, AirV5 ~~~~~~~To Fill I I I~u u ~IE Hg Diffusion Sat. Liq. | A d ) Pump J Den, Bulbs C Ball Joint Mercury Isoteniscope > Barometric Charge Leg. Cyl. V, 1t[ l J z —-I Vaccum Pump Fig. 111.3 System for Low Vapor Pressure Measurements

is subjected to the vapor pressure of the liquid. The difference in the level of mercury in the two legs is measured by a cathetometer giving directly the vapor pressure of the liquid sample at the bath temperature. Temperature control system consists of a heater, supply of compressed air and a dewar filled with liquid nitrogen. Compressed air is cooled by the liquid nitrogen and is bubbled through the bath fluid. A constant rate of bubbling is adjusted. Also the heater is adjusted for constant heat input. When the rate of cooling is equal to the rate of heating, the bath attains a constant temperature. This constant temperature is measured by a platinum resistance thermometer as explained before. The bath fluid is well mixed by an air driven stirrer. Normal propanol was used as the bath fluid. The charging system consists of a charging cylinder, a drying tube and vacuum pumps. The drying tube is filled with P205 and the vacuum pumps are the same as those used for the pressure measurements. B-lb. Procedure of Operation: Operating procedure can be divided into two parts as follows: 1) Charging procedure 2) Observation of the data In terms of notation used in Fig. III-3, the procedure of operation can be explained as follows. With all valves except V1, V7, and V8 open, evacuation of the system is carried out to one micron vacuum. Then valve V4 is closed and V1 opened very minutely. Simultaneously the isoteniscope is cooled rapidly to -190 C by liquid nitrogen so that the test sample is collected in it. After assuring that an adequate amount of R-502 is condensed in the isoteniscope, valves V1 and V3 are closed off.

100 Now equipment is ready for the observations. Temperature of the bath is controlled at desired values by trial and error. Pressure is recorded from the manometer readings and corresponding temperature is measured by the resistance of the platinum resistance thermometer. Values of pressure were obtained at different temperatures. In one run the full range of 16 psia can be covered. The amount of test sample is normally vented to the atmosphere through valve V8 after the experiment. B-lc. Exerimental Precision: Temperature can be measured to the accuracy of +0.001 F by the platinum resistance thermometer. The temperature control was precise to +0.1 F. This amounts to a maximum error in the vapor pressure values of +0.03 psi. The cathetometer can read level differences of the magnitude of 0.001 cm. Precision in reading mercury levels was expected to be +0.1 mm giving differences in the levels accurate to +0.2 mm corresponding to a pressure of +0.005 psi. The total estimated precision in the vapor pressure values is +0.035 psi and the temperature values, +0.1 F. B.2 High Vapor Pressure Measurements An azeotropic mixture exerts constant pressure at a constant temperature in the two phase region. R-502 was compressed in the two phase region from dew point to bubble point with about 3 or 4 pressure data points at a temperature. The average of the data points was regarded as the vapor pressure of R-502 at the temperature. Details and precision of temperature and pressure measurements are the same as that given for PVT measurements.

101 C. SATURATED LIQUID DENSITY OF R'502 Hossain determined saturated liquid density of R-502 by the method used by Hou (62). The experimental system is presented schematically in Fig. III-4, and can be divided as: 1) Saturated liquid density bulb 2) Temperature control system 3) Temperature measurement system Saturated liquid bulb contains a liquid, whose density has to be determined, and a calibrated density float. The temperature at which density of the liquid equals density of the float is determined. The temperature control system is the same as that used for vapor pressure measurements for temperature below room temperature. For temperatures above room temperature, carefully controlled heat input through a knife heater was used. Temperature was continuously monitored by the platinum resistance thermometer which was shielded. According to the principle of Archimedes, the apparent weight of the float when totally submerged in the liquid is zero if the liquid has the same density as the float; consequently, the float has no tendency to either rise to the surface of the liquid or sink to the bottom. Experimentally, this point is difficult to detect, if not impossible. Temperature of the bath is allowed to rise very slowly and movement of the float is noticed. Initially density of the float being lower than that of the liquid, it floats on the top. The temperature at which the float starts sinking to the bottom is roughly noticed. Then the bath is allowed to cool and the heating rate is very carefully adjusted to determine precise temperature at which the float starts

Pt Res. Heater Thermo Liq.N2 2 l Cooled Air. Dw f Y: I I-~ I Dewar ~\,L~0.:-' I Safety -a)~~~~'- Box Density -. _ -- Float ____c _ Fig. 1 1.4 System for Saturated Liquid Density Measurements

103 sinking. Now the heating rate is reduced and the exact temperature at which the float starts rising is noted. The two temperatures should not differ more than 0.05 F. Temperature values are estimated to be precise to +0.05 F which amounts to an error of about +0.02% in density values. Possible errors in volumes of floats amount to about +0.01%. Float densities are expected to be precise to +0.06%. Total estimated precision in density values is +0.1% with temperature values accurate to +0.05 F. D. CRITICAL TEMPERATURE OF R-502 Critical temperature of R-502 was determined by the constant volume method. A saturated liquid density bulb containing a float whose density is close to the critical density was used in observing the disappearance and reappearance of the meniscus between the vapor and liquid phase. Experimental system is the same as that used in determining saturated liquid densities of R-502. An ethylene glycol bath equipped with an electric heater is used to control temperature of R-502 in the bulb. After making sure that the bulb is not likely to crack, a shielded platinum resistance thermometer is used to measure temperature. The average of temperatures of meniscus disappearance and reappearance is taken as the critical temperature of R-502. The critical temperature is estimated to be precise within +0.03 F.

CHAPTER IV EXPERIMENTAL'RESULT S All experimental data of R-502 is given in Appendix E. In this chapter the data is analyzed graphically as well as algebraically. Details of algebraic correlations are given in Appendices F, G and H. Vapor Pressure of R-502: The vapor pressure data covering the range of -150 to +180 F corresponding to the pressure range of 0.4 to 590 psia is presented as a semilog plot of P vs. 1/T in Fig. IV-1. This data was correlated by Martin and Downing (90) using the following equation: lnP = A + - + ClnT + DT + E(F-T) ln(F-T) (IV-l) ~~T ~ FT where P = psia T = F + 459.67 A = 24.51091456 B = -8453.14404297 C = -0.36983496 D = 0.0040211239 E = 533.7385 F = 654.0 Equation (IV-1) is compared with the experimental data and other vapor pressure values in Tables IV-3 through IV-7. These comparisons are summarized in the following table. 104

1000:: o VORA (138) o LOFFLER (86) A BADYLKES (5,6,7) I00 - 10 UO 1.0 0. - 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 28 2.9 3.0 (I/T) IV1 Vapor Pressure of -502'() Fig. IV.1 Vapor Pressure of R-502.

106 TABLE IV-1 Summary of Comparison of Equation (IV-l)'WithVapor Pressure Data Average Source Average Absolute % Dev. This Work -0.22 1.28 Badylkes (5,6,7) +0.35 0.35 Loeffler <86) +3.55 3.55 Downing (42) -0.12 0.57 Du Pont (47) -0.24 0.69 Examination of Tables IV-3 through IV-7 points out that Equation (IV-1) predicts well the experimental data of this work and that of Downing (42). The vapor pressure values of Badylkes (5,6,7) and Du Pont (47) being based on the experimental data of Downing (42) consequently are predicted by Equation (IV-l) very well. Loffler's values (86) seem to lie unusually lower to the values of this investigation and the discrepancy cannot be analyzed since details of his work are not available. Saturated Liquid Density of R-502 The experimental saturated liquid density measurements covering the temperature range of -165 to 179 F are presented in Fig. IV-2. This figure also includes saturated vapor densities (90) and the rectilinear diameter for R-502 as well as R-22 and R-115. The data points are fitted to the following equation by Martin and Downing (90). Details of the algebraic correlation are given in Appendix H.

220 200 - 180 - 160\ 140 120 100 40 -I60- 40 - aFig. R-2. Saturated liquid and vapor density plot for R-22, R-115 and R-502 W R- 1 15 R-22 -- Benning and McHamess (14) ~ -40 - 11- Du Pont (46) -60 C ~ Mears (98) -80 - R- 115 * University of Michigan (136) Downing (41) 10This Work R-502 DuPont, T-502,(47) -140 - Badylkes (5,6,7) 1 LoLffler (86) C 10 20 30 40 50 60 70 80 DENSITY (lbs/cu ft.) Fig. IV-2. Saturated liquid and vapor density plot for R-22, R-115 and R-502.

108 dSL = A + B(1-TR)/3 + C(1-TR)2/3 + D(1-TR) + E(1-TR)4/3 (IV-2) where d = density of saturated liquid T = T/T = (F+459.67)/639.56 T c A = 35.0 B = 53.48437 C = 63.86417 D = -70.08066 E = 48.47901 Equation (IV-2) is compared with the experimental data of this investigation and the saturated liquid density values reported by others in Table IV-8 through Table IV-11. These comparisons are summarized in Table IV-2. TABLE IV-2 Summary of Comparison of Equation (IV-2) and Saturated LiquidDDens i tyValues Average Average Source % Dev. Absolute % Dev. Hossain (61) +0.075 0.11 Badylkes (5,6,7) +1.20 1.20 Loffler (86) +0.47 0.47 Du Pont (47) +1.96 1.96 Examination of Tables IV-8 through IV-ll points out that values of this work agree very well with the saturated liquid density values reported by Loffler (86) over almost the entire range except near the critical point. Comparison of Equation (IV-2) with the works of Badylkes (5,6,7)

109 and Du Pont (47) is relatively poor. The discrepancy between the values of this investigation and Du Pont (47) cannot be analyzed since details of the work are not available. Critical Constants: The average of a number of observations of the temperature at which the meniscus of liquid R-502 in an appropriate liquid density bulk disappeared and reappeared gave the critical temperature as 179.89 F or Tc = 639.56 R. Substituting this value in Equation (IV-1), Martin and Downing (90) calculated the critical pressure as 591 psia. Martin and Downing (90) reported a critical density of 35.0 lbs/cu.ft. This was confirmed by plotting a rectilinear diameter of the saturated liquid and vapor density values for R-502 (Fig. IV-2). Rectilinear Diameter: A plot of saturated liquid and vapor density values for R-502 gives the rectilinear diameter (Fig. IV-2). Vapor density values given by Martin and Downing (90) were used. Rectilinear Diameter for R-502 can be described by the following equation: d +d sl SV = A(1-TR) + d (IV-3) 2 R c where dl = saturated liquid density dS = saturated vapor density d = critical density = 35.0 lbs/cu.ft. TR - T/Tc = (F+459.67)/639.56 A = 31.544 Eqn. (IV-3) is compared with the rectilinear diameter points in Table IV-12.

110 PVT Behavior of R-502: PVT behavior of R-502 was determined over the temperature range of 80 to 250 F, up to 2000 psia and up to two times the critical density. It is presented as a PV plot in Fig. IV-3. The experimental data is converted into compressibility fact Z and is presented as a function of reduced pressure in Fig. IV-4. The compressibility factor is defined as: PV Z =RT (IV-4) where P = pressure V = specific volume T = absolute temperature R = gas constant Molecular weight of R-502 was taken as 111.641. No disagreements were found between the compressibility factors of this investigation and the generalized compressibility factors prepared from PVT investigations of several refrigerants. PVT data is correlated with the following equation: TR A + B2TR + C2ekT A + B3TR + C3ekT R R + 2_ 2_ _2__+ 3 3Rb/Vc 3 z= z (V-b/V) 2 c R c Zc (VR-b/V) Z (Vb/Vc) A4 + B4TR + C4e-kTR A5 + B5TR A6 + B6TR + 4 4 a V 1 a )V a+V aVRv z (VR-b/V) 1 R +cl R) e2R e2R e (1+cle ) e 2e ) (IV-5)

111 1700 1500 1300 _ 1100 03 w _ 900 100 0 0.05 0.10 0.95 0.20 0.25 0.30 0.35 0.40 VOLUME (Cu.Ft/Lh) Fig.. PVT behavior of R-02 Fig. IV-3. PVT behavior of R-502

1.0 *I ~ 0.9 0.76 0188; 00.7 128 0. 0.6 2_. 62 —0 0.0 0.2 0.4 0.6 0~.86 1.1.... 18 20 22 24 2.6 280. Red0 Reduced Ps IF 1.08 Temperature o Or~~~~~~~~~~~~~~~~~~~~~~~~~~T 0.2 ~ ~ ~~09 0.1 rosIiI21 — Fron 13,1411 o r 0.:30 - - — Ciia ~~~~~~~~~~oin r, 0.0 0.2 0.4 0.6 0.8.0 1.2 i.4 1.6- 2.0 2.2 2.4T210 Reduced Pr enssur, Pr o I i I \F.o I C e i i o1 0._,....j, Cit~o Pin Reduced~~~~~Al Preossrr O~~~~~~~i. IV4Cmrsiblt Fatr ofs R-502.1

113 where P = P/P = (psia)/591.0 R C VR = V/V = (lbs/cu.ft.)/0.028571 C TR = T/T = (F+459.57)/639.56 Z = P V /RT = (591.0)(0.028571)/(0.0961248)(639.56) C CC C = 0.27466 a1 = 16.00 B3 = 0.198065x10 a2 = 22.00 C3 = 0.815044 b = 0.118328 A = 0.132335x10 4 C1 = 3.5x10 B4 = 0.197201x10-2 -i A2 = -0.409519 C4 = 0.654305x10 B2 = 0.146538 A = 0.793470x105 C2 = 0.224995x10 i B 0.957628x105 A3 = 0.211483x10 A6 = 0.256235x107 B6 = 0.248641x107 Equation (IV-5) is compared with the experimental data in Table IV-13. The experimental data was taken at approximately four reduced temperatures namely TR = 0.8, 1.0, 1.04 and 1.1. At reduced temperature 0.8 we are dealing with low pressures and the isotherm is fairly short since it is limited by the two phase region. At the critical temperature, the isotherm goes through inflertion at the critical point. The difficult shape of the isotherm is more apparent in the compressibility chart where TR = 1 curve starts out with Z = 1 and curves steeply down to Z and then immediately goes up as PR increases. Similar behavior is observed with the isotherm of 1.04 TR because it is still close to the critical temperature and exhibits a deep well. As we go to higher temperatures, say 1.1 TR, the bowl in the isotherm curve becomes shallow.

114 Therefore, merit of an equation of state may be quickly judged by observing how it fairs at these four isotherms. From Table IV-13 it is apparent that appreciable deviations are observed at low temperature, but they are still within the total experimental precision. At the critical temperature, fit is very good all the way up to two times the critical density. The deviations reported in Table IV-13 are pressure deviations rather than volume deviations. Pressure deviations are a very severe test of the test data particularly in the high pressure, high density regions. The fit is again good around TR = 1.04 where data goes up to 1.9 times the critical density. Equation (IV-5) compares with the data very well at TR = 1.1 up to 1.6 times the critical density. Thus in overall, Equation (IV-5) predicts the PVT behavior of R-502 well and within the precision of experimental measurements (Appendices A and B).

115 TABLE IV-3 IV-3. Comparison of Equation IV-1 and Experimental Vapor Pressure Data for R-502 Obtained in This Work t P P Percent F psia psiaeq Deviation psia -151,12 C,4C0 0.404 -1.11 12'- 12o C7 1 0CS lo 08 4.50 -118,68 1.712 1*(45 3.90 -217 14 1.* 71 1,746 -1 55 -1C9, 65 2. 296 2.313 -0, 72 -1C9.60 2.307 2. 317 -0,42 -109.51 2,329 2,325 0,19 -109.19 2. 445 2. 352 3.80 -108,83 20 398 2,383 0.63 -1I03 45 2o 958 2,68l 2.26 -98*03 3,481 3,490 -0.25 -97.37 3.523 3.569 -1. -2 -88.389 40 E51 4, 729 2,51 -884r9 4. 911 4.790 2.46 -78,45 6 452 6. 562 -1o 70 -75,95 6.890 6.867 0 33 -71. 57 8o 322 8. 057 3 18 -67.71 8.916 9* 010 -1.05 -65.82 9,338 9.508 -1, 82 -560<o loCE (6C 12 146 -2.41 -55o19 1 2. 304 12. 737 -3.52 -54.85 12, 901 12,853 0.37 -49o 71 140 265 i4. 713 -3.14 -43. 02 16 725 17,445 -4.31 9 8.c 4 6.2 24t 38u 22 6,2 71 -0.84 S9.48 226. i5 30 22. t31 CC9 9$S 5 225.3 50 22 6.62 9 -0.5Z ICOo 52 32. 050 2320471 -0.18

116 TABLE IV-3 (contd.) t P P Percent F ps ia psseq Deviation psia 100.54 2 33,.0 63 32 0.23 102.71 240o 780 239'o.198 0.66 i10,O5 2 6 0o30 4265 447 C.44 1209.9 302.770 301o000 0.58 13 o.04 3 4 3 5 08 0 33 7C3 -0.19 130,0 5 336, 620 3. 743 0.26 130, 33 339 630 0 E3 o~62 0.82 139.5i1 379iCO 37 i5e 161 1C04 147, 2o 41 4. 900 41. C 97 1 16 14i9-P22 4t24 200. S3 38 1.15 1 503 4 3 1.0:0 424.888 1,90 1 50i).42 430 -3'00 425 CS1 1. 21 15 2. 41 43, 3 60 434. 749 0.48 1 52.5 C 435~ 550 4 3 5.191 00 8 163 2 7 47 1]. C 49 Co 963 1.24 1 t4.a C- 499 C, a0 4c,6 E 16 0, 26 52 7. 450 526 4 72 0. i A 1 79 65 58 8 5 8 o 3 99 -0, 10 179.74 5R- 9. 340 5c3, 99C, -0.11 179, 75 589, 340 590. C6o -0.12

117 TABLE IV-4 IV-4. Comparison of Equation IV-1 and Vapor Pressure Values for R-502 reported by Badylkes (5,6,7) t P P Percent F psia psia Deviation -112.00 2.121 2. 120 0.02 -103o00 2.942 2.937 0 16 -94,00 4. 01 4 3.998 0.39 -85.00 5, 382 5.355 0.50 -76 00 7.106 7.066 0, 56 -67.00 9.250 9. 194 0.60 -5 8. 00 i 1, 880 11809 0, 60 -49. 00 15 070 14.986 0. 56 -40, 00 18'. 900 i 8.802 0, 52 -31. 00 23.450 23*344 0.45 -22,o 0 28.810 28, 698 0, 39 -13.00 35.07C 34.954 0.33 -4o 00 42.320 42 207 0, 27 5 00 50. 660 50.553 0*21 14,00 60 1 0 60.08.9 0.15 23, 00 70. 990 70 913 0. 11 32.00 83.190 83.126 0.08 41*00 96*880 96.828 0,05 50000 112.190 112.121 0.0 59.00 i29.210 129. i08 0.08 68. 00 148.0 i0 147,893 0. 14 77.00 168~ 900 168. 583 0.19 86, 0 0 1 91.29 0.27 95.00 217.000 2160 128 0.40 1 04. 00 244.500 243. 225 O. 52

118 TABLE IV- 5 IV-5. Comparison of Equation IV-1 and Vapor Pressure Values for R-502 Reported by Loeffler (86) t P Peq Percent eq F psia psia Deviation -112 00 2. 146 2,120 1, 19 -103.00 3 000 2* 937 2.09 -94.00 4.100 3.998 2.48 -85o 00 5. 526 5,355 3.09 -76.00 7.320 7.066 3.47 -67000 9550 9. 194 3.72 -58,00 12.290 11.809 3.91 -4 9 00 15,580 i4. 986 3.82 -40. 0 19. 550 18. 802 3.82 -31.00 24* 400 23. 344 4.33 -22.00 29*980 28.698 4. 28 - 1 30 00 36,45C 34. 954 4,10 -4* 00 43.940 42,207 3.94 5. 00 52.610 50 553 30911 14,00 62,460 60, 089 30 80 23*00 73.770 70*913 3.87 32 00 86 410 83*126 3, 80 41.00 100C 500 9C6 828 3.65 50.00 116. 200 112,121 3051 59 00 133. 700 129S108 3.43 68.00 153 100 147. 893 3.40 -7.00 174,600 168 583 3, 45 8600 19 8, 000 191.289 3.39 95,00 223, 700 216.128 3* 38 104,00 251. 900... 2943 225 3.44 113.00 282, 500 272. 719 3,46 122.00 315800 304, 766 3t49 131.00 352.1 CCO 339. 550 3056

119 TABLE IV-5 (contd.) t P P Percent F psia pseq Deviation psia 140.00 391.700 377.297 3.68 149 00 434 400 41 8*292 3 71 158a00 480c 900 462, S25 3*74 167,00 531 100 511 759 3.64 176.00 535~ 80C 5653710 3*43 180090 617.300 597.80~ 3.16

120 TABLE IV-6 IV-6. Comparison of Equation IV-1 and Vapor Pressure Values for R-502 Reported by Downing (42). t P P Percent F pssia eq Deviation psia -20.00 29. 800 30* 007 -0 69 -10.00 3 7600 37.257 0 91 -1 0 00 36, 900 3 7. 257 - 0*97 0,0 46.000 4 5 776 0* 49 10.00 56b. C0 55 697 0*54 20*00 67* 500 67,156 0, 51 30 8 0 80A00 80.287 -0.23 40 00. 95a200 95. 229 -0. 03 40.00 95*700 95,229 0.49 50o 00 111.600 112. 121 -0.47 60. O00 130. 800 1=1. 105 -0*23 70.0'0 150o 7C0 152.322 -1.08 80.00 176,0 I0 175*92 2 0.10 90.00 201o 100 2C2.C58 -0.48 1 003 00 2.30. 800 230. E95 -0*04 110. 00 260,500 262.612 -0.81 I.0000 265.000 262.:612 0 90 130.00 332~700 335, 544 -0.85 i'50.00 4199700 423. C63 -0.80

121 TABLE IV-7 IV-7. Comparison of Equation IV-1 and Vapor Pressure Values for R-502 Reported by Du Pont (47) t P P Percent F psia eq Deviation psia -1COa00 3.230 3 261 -G.97 -80o00 6.280 6,258 0O 35 -60.00 Lii280 11i182 0,887 -40. 00 18 970 1 8 802 0* 88 -20 00 30. 220 30. 007 0o71 0.0 450 940 45 776 0 36 20o00 670 140 67 156 -0 02 40.00 94O 900C 95 229 -0.35 60. 00 1 30300 131.105 -0. 62 80.00 i74. 6C0 175 922 -0.76 100.00 229.100 23C, 895 -0*78 120.u0 295~ 000 297o 415 -0o 82 140*00 373 800 377 297 - 0 94 A 60.00 4670 300 473. 389 - 1 30

122 TABLE IV- 8 IV-8. Comparison of Equation IV-2 and Experimential Saturated Liquid Density Data for R-502 Obtained in This Work t d d Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation -161.8.0 104. 220 104.023 0.19 -67.32 9 4.410 914.410 0.0 32.00 32.560 82.564 -0O 00 50.55 79.680 79.979 -0.38 60.25 78.500 78.555 -0.07 63.79 78.020 78.020 0.00 64.83 77.940 77.861 0. 10 102.01 71.580 71.592 -0.02 116.25 63.760 68.760 0.00 157.86 57.290 57.293 -0{.00 16.78 52. 240 52. 136 0.20 176.22 46.270 46.270 0.00 179.03 41.250 41.452 -0.49

123 TABLE IV-9 IV-9. Comparison of Equation IV-2 and Saturated Liquid Density Values for R-502 Reported by Badylkes (5,6,7) t d d e Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation -112.00 100. 530 99.087 1.44 -103. G0 99.090 98.166 0.93 -94.00 98.160 97.236 0.94 -85.00 97. 240 96.294 0.97 -76.00 96.190 95.341 0. 88 -67.00 95.160 94.375 0.82 -58.00 94.160 93.396 0.81 -49.00 93. 170 92.403 0.82 -40.00 92..080 91.394 0.75 -31.00 91. 130 90.367 0.84 -22.00 90.080 89.323 0.84 -1 3.00 89.050 88.258 0.89 -4. 00 88.050 87.172 1.03 5.00 86.950 86.062 1.02 14.00 85.870 84.926 1.10 23.00 84.820 83.761 1.25 32.00 83.680 82.554 1.33 4 1.00 82.470 81.331 1.38 50. 0 8 1. 13 0 80.059 1.38 59.00 80.030 78.741 1.61 68.00 78.620 77.373 1.59 77.00 77. 360 75.947 1.83 86.00 75.850 74.453 1.84 95.00 74., 320 72.881 1.94 104.00 72.510 71.215 179

124 TABLE IV-10 IV-10. Comparison of Equation IV-2 and Saturated Liquid Density Values for R-502 Reported by Loeffler (86) t d deq Percent F lbs/cu.ft. lbs/cu.ft. Deviation -112.00 99.720 99.087 0.64 -10 3.00 98.780 98.166 0.62 -94.00 97.850 97.236 0.63 -85.00 96.790 96.294 0.51 -76.00 95.890 95.341 0.57 -67.00 94.870 94. 375 0.52 -58.00 93. 880 93.396 0.52 -49.00 92.760 92.403 0.39 -40.09 91.800 91.394 0.44 - 31.00 90.740 90.367 0.41 -22.00 89.570 89.323 0.28 -.13.00 88.550 88.258 0.33 -4. 00 87.430 87.172 0.29 5.00 86.230 86.062 0.19 14.00 85.0 0 84.926 0.15 23.00 83.910 83.761 0.18 32.00 82.680 82.564 0.14 41.00 81.390 81.331 0.07 50.00 0. 140 80.)59 0. 10 59.00 78.q20 78.741 0.10 68.00 77.450 77.45 77.373 0. 10 77.00 75. 950 75. 947 O. 00 86.00 74.500 74.453 0.06 95.00 72. 9 30 72.881 0.07 104.00 71.260 71.215 0.06 113.00 69.520 69.435 9. 12 122.00 57.630 67.516 0.17 131.00 65.640 65.4118 0.34

125 TABLE IV-10 (contd.) t d d Porcent eq F lbs/cu. ft. lbs/cu. ft. Deviation 140.00 63.380 63.083 0.47 149.00 60.850 60.416 0.71 158.00 57.860 57.233 1.08 167.00 54.100 53.138 1.78 176.00 48. 210 46..518 3.51

126 TABLE IV-11 IV-11. Comparison of Equation IV-2 and Saturated Liquid Density Values for R-502 Reported by Du Pont (47) t d d Percent F lbs/cu.ft. lbs/cu.ft. Deviation -100. 00 98.490 97.857 0.64 -1O0.00 96.550 95.766 9.R1 -n60. 00 94. 520 93.615 0.96 -40.00 92.400 91.394 1. 0 -20.00 90.180 89.088 1.21 0.0 87.840 86. 682 1.32 20.00 85.390 84.152 1.45 14)0.00 82.800 81.470 1.61 60.). o 80. 40 78.592 1.81 30.00 77.070 75.457 2.03 100.09 73.800 71.968 2. 48 120.00 70.080 67.956 3.03 140.00 65.590 63.083 3.82 160.00 59. 9 59.490 56.430 5. 14

127 TABLE IV-12 IV-12. Comparison of Equation TV-3 and Rectilinear Diameter Values for - -502 t d d Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation 479.67 42,886 42.886 0*0 489 67 42 3S3 42. 393 0.00 499*67 41. 898 41. 900 -0.00 509. 67 41.389 41.406 -0.04 519.67 40o 880 400913 -0.08 529.67 40. 368 40*420 -0, 13 53 9 67 39. E75 39.927 -0, 13 549067 39.375 39.433 -'0.15 559.67 38,878 38,940 -0.16 5t9.67 380403 38.447 -0. 11 579, 67 37. 34 37 954 -0, 05 589.67 370 473 37.461 0*03 599o 67 360 992 36.967 0* 07 609.07 36*478 36.474 0,01 619, 67 3 5970 35.981 -0o03 629,67 35*44C 35.488 -0.13

128 TABLE IV-13 IV-13. Comparison of Equation IV-5 and PVT Data of R-502 V T=(F+459.67) Pexp V/0.028571 T/639.56) Pexp/591.0 Pl/591.0 %Dev. cuft/lb R psia 0~582420 541,140 81.950 20.38500o 0 *846 0,139 0.138 0.82 0.466240 541.130 99.620 16. 38645 0. 846 0.169 0.168 0.52 0. 4C4380 541.140 116.940 14. 153512 0.846 0.198 (0190 4 11 0.3C7140 541.140 141. 2S0 10. 750001 0.846 0.239 0.239 0.16 0O248410 541.140 166.230 8.694480 0O846 0.281 0*282 -0.22 0.216550 541. 130 178.8C0 7.579364 0.846 0.303 0.312 -3.10 0.577660 639.490 100,030 20. 218403 1.000 0.169 0.169 0.05 0.461C20 639.490 123.530 16.135942 1.000 0.209 0.209 0.19 0.358770 639.640 154. 190 12. 557138 1.000 0.261 0.262 -0.48 0.345300 639.500 160.530 12.085681 1.000 0.272 0.271 0.15 0.287570 639.620 188.540 10.065101 1*000 0*319 0.319 0.06 0. 279680 639.500 193.430 9.788947 1.000 0.327 0*327 0.23 0.225160 639,530 232.430 7.880718 1.000 0.393 0.393 0.13 0. 172130 639.610 288.490 6 024640 1.000 0.488 0.488 0.01 0.139340 639.610 338.240 4.876973 1.000 0.572 0.572 0.00 0. 114880 639.630 393.490 3.901859 1.000 0.666 0.668 -0.26 0.054600 639. 590 555.36C 1. 911029 1.000 0.940 0.941 -0.18 0.049090 639.600 569.260 1.718176 100U 0,963 0.966 -0.26 0.045340 639.600 576.260 1l 586924 1.000 0.975 0O979 -0. 44 0.042200 639.600 581.760 1.477022 1.000 0.984 0.988 -0.41 0.031760 639. 620 586.260 1.321620 1.000 0.992 0,997 -0.50 0.037560 639.580 586.770 1.314620 1.000 0.993 0,997 -0.41 o.023180 639.570 590.280 0.811312 1.000 0.999 1.006 -0*68 0.022820 639.540 594*270 0.798712 1.000 1.006 1*007 -0.18 0.02i370 639.600 603.260 0. 747961 1,000 i.021 1.029 -0,78 0.020370 639. 560 624.270 0.71296i 1.000 1.,056 1,061 -0.40 0.01)880 639.570 634.260 09695810 1.000 1.073 A.086 -1020 0.018300 639.6 00 729.610 0b 6'0510 1.000 1.235 1.246 -0.90

129 TABLE IV-13 (contd.) 0,011680 639., 530 806, 470 0. 618809 1*000 1.365 1,362 0.16 0.016980 639,560 930.270 0. 5943C9 1.000 1.574 1.566 0.53 0.01 6430 6390550 1066.270 0. 575059 1.000 1.808 1.799 0.49 0,015960 639.560 1224.270 0, 558608.0o00 2.072 2.070 0.07 0.015510 639, 540 1418,290 0.542858 1.000 2.400 2.410 -0.44 0,015180 639.570 1602.290 0. 531308 1.000 2.711 2.725 -0.52 0,014830 639.580 1837.790 0. 519058 1*000 3,110 3*130 -0.67 0.014660 639, 5 80 1975*290 0.5131 C8 1,000 3*342 3.358 -0.48 0.037610 664,060 7C7.740 1. 316370 1.038 1.198 1.199 -0-09 0,028910. 664 0 40 751.740 1.011865 1.038 1.272 1.281 -0 71 0 025060 664, 0 50 782. 540 0. 87711 3 1.038 1*324 1.339 -1.12 0.022280 664.*040 834.040 0.7798i2 1.038 1*411 1*416 -0*35 0.0O 20380 664*030 909.740 0,713311 1.038 1*539 1.543 -0.26 0.018730 664.030 1C51.640 0. 655560 1.038 1.779 1.788 -0.50 0.017050 664,040 1366.820 0o596759 1.038 2*313 2.326 -0.56 U, 016240 664.060 165G 220 0.568409 1,038 2.792' 2*776 0.58 0,01 5630 664.050 1962.320 0. 547058 i038 3*320 3*241 2.39 01 C8940 666.150 433.400 3.812957 1.042 0.733 0*734 -0.(03 0.086400 666.130 503.160 3, 024045 1.042 0.851 0.853 -0.17 0 9063970 666,i40 593.460 2.238964 1.042 1.004 1.005 -0.04 0.043500 666.150 689.260 1. 522523 1.042 1.166 1.167 -0.04 0,033780 6h6. 140 736.960 1. 182318 1.042 1.247 1.250 -0.27 0* 1 C7400 708.990 488.710 3. 759056 1. 109 0O827 0.83 1 -0.47 O, Ce7960 708.960 563.510 3.078646 1.109 0.953 0.959 -0.60 0.071.050 708,970 649.010 2.486787 1.109 1.098 1,105 -0.62 0. 055680 708.960 752. 010 1. 948829 1.109 1.272 1.277 -0, 36 0.040880 709,040 882. 5 10 1 43G821 1.109 1*493 1.501 -0.50 0,033170 703.950 977.000 1* 160967 1.108 1*653 1.666 -0 79 0.038760' 712, 500 924,600 1,356620 1.114 1.564 1.568 -0.21 0,032100 712.540 10i6.600 1. 1235i7 1.114 1*720 1.731 -0*62

130 TABLE IV-13 (contd.) O.026050 712.560 1151.600 0.911764 1.114 1.949 1.961 -0.66 0.022850 712.570 1289.300 0.799762 1.114 2.162 2.172 0.44 0020830 712.,580 1445.900 0.729061 1.114 2.447 2.432 0.60 0.019480 712.570 1613.3C0 0.681810 1.114 2.730 2.747 -0.64 0.018680 712.590 1759.0C0o 0. 653810 1.114 2.976 3.025 -1.65 0.017670 712.610 1956o2 GC 0.625459 1*114 3.310 3.401 -2. 75

CHAPTER V PREDICTION OF THE PROPERTIES OF R-502 One of the objectives of this work is to devise methods to predict the properties of R-502 from those of its components. Since this is just one mixture, the methods we use will need more testing before they can be regarded as rules. The following discussion is divided into PVT behavior, vapor pressure, saturated liquid density, critical constants and intermolecular potentials. PVT Behavior The experimental determinations of PVT behavior for R-22 have been made by Michels (99) and Zander (140). The data is presented as a P-T plot in Fig. V-1. Their values are in mutual agreement as can be seen from a few isochores which are close to each other. The PVT data is correlated with the following equation: -kTR -kTR T A +B T + A2+BT+C BT+C e TR 2 2R 2 A3+B3TR+C 3e P _,. +, + c (VR-b/V Z 2 2 C 3 (VR-b/V3 ) -kT ~A +B T +C eA+B5T A6+BT + 4 4R 4 + 5 + 6 R(V-1) 4 4 alV alV a2V a2V c R c e (l+cle ) e (l+c2e ) where the constants are given in Table V-1. Input conditions required to solve the constants in Eqn. (V-1) are given in Table V-2. Eqn. (V-1) is compared with the experimental data in Tables V-14 through V-16. The correlation covered the entire range of Michel's data with the following deviations in pressure values. 131

TABLE V-i Values of Constants in Eqn. (V-i) for R-22, R-115 and R-502 Constant R-22 R-115 R 502* R 502** 456.0 59379 591.0 P (psia) 721.906 T (R) 664.5 635.56 638.23 639.56 C V (ft3/lb) 0.030525 0.02681 0.028622 0.028571 C 0.069468 0.0961248 0.0961248 R 0.124098 0.2672 0.2769 0.2770 0.2747 a1 16.00 16.00 16.00 16.00 a2 22.00 22.00 22.00 22.00 b/V 0.108523 0.12640 0.122732 0.118328 C c x106 3.5 3.5 3.5 3.5 c x106 1.4 1.4 1.4 1.4 2 -0.405920 -0.400673 -0.409519 A 2 -0.417902 B2 0.153671 0.142469 0.141223 0.146538 C2 -2.22487 -2.24052 -2.32088 -2.24995 C2 -2.227-2 A3 0.191762x10' -0.426782x102 -0.752109x10 0.211483x102

TABLE V-1 (contd.) Constant R-22 R-115 R-502* R-502** B3 0.370338x10-2 0.265288x10 0.280848x10- 0.198065x10 C3 0.795797 0.808223 0.842313 0.815044 A -0.146404xl102 0.235928xl0-2 0.299498x102 0.132335x10-2 B4 0.710054xlO-3 -0.305903xi0-2 -0.0353417x102 -0.197201x10-2 -1 -0.676293x1 -0.654305x10-1 C4 -0.633150x10 -0.644044x10 -0.676293x10 -0.654305 A5 -0.357334x104 -0.121940x106 -0.156243x106 -0.79347x105 B5 0.199891x105 0.138356x106 0.172659x106 0.957628x105 A6 0.103874x10 0.367427x10 0.445685x107 0.256235x10 B6 -0.962803x107 -0.359833x107 -0.438091x10 -0.248641x10 k 3.0 3.0 3.0 3.0 * Values for mixing rules **Values for best PVT correlation

134 TABLE V-2 Input Conditions to Solve Constants in Eqn. V-1 for R-22, R-115 and R-502 Factor R-22 R-115 R-502* R-502** f2(Tc) -0.375 -0.375 -0.375 -0.375 f3(Tc) 0.0625 0.0625 0.0625 0.0625 f4(T ) -0.003906 -0.003906 -0.003906 -0.003906 lnf5(T ) 9.706 9.706 9.706 9.706 lnf (T ) 11.2377 11.2377 11.2377 11.2377 a1 16.00 16.00 16.00 16.00 a2 22.00 22.00 22.00 22.00 c x106 3.5 3.5 3.5 3.5 c2x106 1.4 1.4 1.4 1.4 2p b/V 0.108523 0.1264 0.122732 0.118328 c k 3.0 3.0 3.0 3.0 + H+~~~~~~~~~ ~ ~ ~~ (dPR/dTR) 3.91 3.95 3.93 3.92 o 4,J 1.SV 4 1c (dPR/dTR) p 7.40 7.55 7.45 7.45 o0 o c O,o (dPR/dTR).'4.10 14.40 14.20 14.10 c 0 1.4 Pc r u JW a) a) (dP /dTR (dPRRT1.8 p 23.80 23.80 23.80 23.80 r) -4 c 2 2 o (d PR/ dT PC 0.0 0.0 0.0 0.0 0 0 W a)': r 2 2 (d P /dT 0.0 0.0 0.0 0.0 m (.j d2R 2)8 8PcH a)'4 a(c 1.8T -0.740 -0.730 -0.736 -0.735 c TB TC 2.3 2.3 2.3 2.3 + ~

1)55 2300 2300 2200~ ~ _ 3 I In 2200 2200 IGOl 0 210 0)QIDI /, 133 oD t 1900 / / 1900 I 41975 1800 -/51800 1900 4195 10 1700 / / 3955 1700 - 1700 1600 — 1600 34120 33274 1500 -11500 1400 29778 1400 /29.778 27784 26782 1300 26782 1300 23.536 1200 I 22483 - 1200 ~_ 1100 J — t 2,6o o 21.600 1100~~~~~~~~~ 19.352 1100 f./) _~ I~ I IIiIIII I18.262 wu 17.355 a: D 1000 1000 C,) ClU~~~~~~~~~~~) 15.482 a900 I13.422 900 13.198 12.262 11.920 800 11.861 800 10687 10.080 LBS/CU FT 9.801 700 944 700 8301 8.295 600 8195 - 600 7016 6.667 500 - 500 -" 5826 5.150 400 - 4847 400 4661 / 4A135 300,,-,~ —-~' I __ 3.575 -300 30030 3. 005 2.527 200 2- 200 ~_~_./ ~~2.070 1.610 100 o Michels (99) j 100 Zander (140) I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 500 550 600 650 700 750 800 850 900 TEMPERATURE (R) Fig. V-1. PVT behavior of chlorodifluoromethane (R-22)

136 Average percent deviation = -0.04% Average absolute percent deviation = 0.11% Standard percent deviation = 0.18% Equation (V-1) also covers the entire isothermal PVT data reported by Zander with above deviations of 0.08, 0.23 and 0.51%, respectively. Zander's isometric data goes up to 2.34 times the critical density. This equation goes up to 1.8 times the critical density with the majority of deviations under 1% and a maximum deviation of -2.42%. Thus, we believe that the fit is extremely good. PVT behavior of R-115 was determined by The University of Michigan (136) and Mears et al. (98). The data is presented as a P-T plot in Fig. V-2. Their data is in mutual agreement considering the experimental precision. The PVT data is fitted with Eqn. (V-1) and the constants are given in Table V-1. Also the input conditions required to evaluate these constants are given in Table V-2. Eqn. (V-1) is compared with experimental data in Tables V-17 and V-18. The correlation covered the entire range of experimental data reported in both investigations and the fit is summarized in Table V-3. TABLE V-3 Summary of Comparison of Eqn. (V-1) with the Experimental PVT Data for R-115 Average Average Standard Max. Source % Dev. Ab.% Dev..% Dev..% Dev. Univ. of Mich. (136) -0.26 0.61 0.76 -2.49 Mears et al. (98) 0.18 0.29 0.41 1.03

(51I-H) aueqaojon$eau@dojoo3o Jo aohemqaq mLm'F-A'OTl (Jo) 3anltiV3cJdW31 068 0t78 06L O0t 069 Obt9 06 Ot 06t7! I,,,,, 0 — L3'no/S9-1 09 OL6Z' 0 001 C696~ (86) sloaVU o (9i1) Uo6!O!lAI.o,i!SfaA!U1 ~ Ogg~3' V,Z. ~"~/. _;j~~ 1 ~~~-00~,,,,,,, ~~~~OOgl! ~~~~~~~~~~~3L~~~~~~~~~~~~~~~~~~~f ~d~~~~~~~~~~~~~~)~~U c -00Z rM - ~~ ~ ~ ~~~~~~~~-006 -0001 b tn -0011 /6 /i c C 0031 -0021

138 Mears et al. (98) reported that their pressure values are precise to +0.2%, temperatures to +0.05% and the volume figures are accurate to +0.1%. To predict the PVT behavior of R-502 using Eqn. (V-l) given the constants for R-22 and R-115, there are two choices. The first method would be to combine the constants in Eqn. (V-1) for R-22 and R-115 as given in Table V-1, with some combining rule and then predict the PVT behavior of R-502. It was theorized that since the constants are all dimensionless, we may be able to combine them linearly on mole fraction basis. This was done and using true critical constants for the mixture, we obtained a poor fit. A more serious drawback to this method was that the equation of state for the mixture R-502 did not behave in accordance with the generalized facts, such as,the critical isochore was not linear but the isochore around 1.4 pc was. The second method was to devise a method to combine input conditions (Table V-2) for R-22 and R-115, thereby the equation of state will have the right behavior in all regions. Again it was theorized that since all the input conditions are dimensionless, we may be able to combine them linearly on a mole fraction basis. Using the input conditions thus combined and true critical values for R-502, we obtained an extremely good fit. This clearly indicated that if only true critical constants for the mixture can be predicted, the PVT behavior of the mixture could be predicted very confidently. Later on a review on prediction of true or pseudocritical constants is presented and finally the methods are recommended for our mixture R-502. These methods are as follows.

139 In order to calculate critical volume, it was found best to combine component critical volumes linearly on mole fraction basis as proposed by Kay (63). V = XlV + x2V = 0.028622 ft3 /lb (V-2) cm lcl 2c2 R-502 is an azeotropic minimum boiling mixture, a fact which can be asserted if the normal boiling point of the mixture is known. Thus, given the normal boiling point of the mixture, the Li, Chen and Murphy method (85b) is recommended to calculate the critical temperature. bm bl b2 L X1T+- x + (V-3) cm cl c2 where T boiling point of the mixture bm T = critical temperature of the mixture cm TblTb2 = boiling points of the components TclTc2 = critical temperatures of the mixture..'. T = 638.23 R (V-4) cm To calculate the critical pressure, a new method is proposed in which the reciprocals of component critical pressures are combined on mole fraction basis and it is expressed by the following equation: 1= f +-2 (V-5) c P P P cm ~ cl c2

140 where P = critical pressure of the mixture cm PclP 2 = component critical pressures Using Eqn. (V-5), we obtain: P = 593.79 psia (V-6) cm Now the critical constants being predicted, the input conditions for R-22 and R-115 are combined linearly on mole fraction basis, and are listed in Table V-2. Using these input conditions and predicted critical values, constants in Eqn. (V-1) are evaluated and listed in Table V-1. This equation is compared with the experimental PVT data of R-502 in Table V-19. The results in Table V-19 may be compared with those in Table IV-13 along with the input conditions listed in Table V-2. The input conditions for the best correlation of Table IV-13 and those of this correlation are almost the same except for the critical values. The predicted critical temperature differs from the true value by 1.33 R or by about 0.2%. True critical pressure differs from the predicted value by 2.79 psia or by 0.47%. The predicted critical volume exceeds the true value by 0.000051 cu.ft./lb or by about 0.18%. Since the predicted critical pressure is high, the pressure values around the critical point on the real critical isotherm (T = 639.56), are high. Again, this same effect is carried to the compressed liquid region where higher pressures are predicted. Around TR = 1.04 and 1.11,

141 pressures are predicted within 2% except at the highest densities. Comparison of the last run at TR = 1.116 was a little poor. Thus, the comparisons can be summarized as follows. Using the method of prediction described above, we would obtain pressure values within 3% up to densities of 1.4 P and temperatures of 1.11 TR except near the critical region. This analysis may be compared with the best correlation given in Table IV-13. Input conditions for both comparisons are almost the same except for the critical constants. It may be added that if we use the exact input conditions for the best correlation with the predicted critical constants, comparisons do not improve. Finally, other predicted critical constants were used and no superior correlation was found. Vapor Pressure Vapor pressure values are correlated by the Martin, Kapoor and Shinn equation (93) which is as follows: B E(F-T) lnP = A + - + ClnT + DT + ( ln(F-T) (V-7) T FT where p = pressure, psia T = absolute temperature, R A,B,C,D,E,F = constants of the equation Method of evaluating these constants is illustrated with respect to R-115 data in Appendix G. Martin and Hou (91) reported that reduced pressures can be expressed as a function of 1/TR and a parameter M.

142 Therefore, Eqn. (V-7) was transformed into reduced form as follows;,B E(F-TR) Let lnPR = A + + C'lnTR + DTR + FT ln(F-TR) (V-8) where PR = P/P = reduced pressure R c T = T/T = reduced temperature R c A',BlC',D',E',F' = constants of the equation The relation between the constants of Eqn. (V-8) and Eqn. (V-7) are given below: A' = A-lnP E lnT + ClnT (V-9) c F c c B' = (B + ElnT )/TC (V-10) C' = C (V-1l) D' = DT (V-12) c E' = E/T (V-13) F' = F/TC (V-14) These reduced constants may then be combined according to M factors to obtain vapor pressure of the mixture. Factor M is defined by the following equation: M = M' + 4 (V-15) M where TB (V-16) M' =BlnP T -T c c B

143 TB = boiling temperature, R T = critical temperature, R P = critical pressure in atmospheres The combining rule for the mixture may be expressed as follows: IM-Nh 1 m 21 Gm = G1 IM, + G2 NM_ 2 (V-17) where G = a typical constant in Eqn. (V-8) for the mixture m G1 G2 = component constants M = factor M for the mixture m M1, M2 = factor M for the components This is the theory used in predicting vapor pressure of R-502. Vapor pressure of R-22 has been determined by several investigators (12,17,46,80,83,140). All the available data is plotted in Fig. V-3 and correlated by Eqn. (V-7) by Martin (46) which were reduced using Eqns. (V-9) through (V-14) and are listed in Table V-4. Comparisons of Eqn. (V-8) with the available vapor pressure values are given in Tables V-20 through V-24. A summary of these comparisons is given in Table V-5.

000 i I I I I I I. I I I I I I Fig. 9.3 VAPOR PRESSURE OF CHLORODIFLUOROMETHANE-(R-22) o ZANDER (140) o BOOTH AND SWINEHART (17) v BENNING AND McMARNESS(12) A DU PONT BULLETIN F-22 (46) I001 4 DU PONT BULLETIN X-57B (42) 10'0 Cl_ w 0. 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 (I/T)x103 (R')

145 TABLE V-4 Constants in the Vapor Pressure Eqn. (V-8) and Properties of R-22, R-115 and R-502 Constant R-22 R-115 R-502* R-502** T (R) 664.5 635.56 638.23 639.56 c TB(R) 418.33 421.99 409.92 409.92 M 7.222 7.376 7.243 7.201 P (psia) 721.906 456.0 593.79 591.0 c A' 7.0302613 5.8980259 6.8758664 15.245786 B' -10.33303 -11.436969 -10.483569 -7.825343 C' -7.8610306 -10.497277 -8.2205167 0.36983496 D' 3.3522815 5.5504768 -3.6520337 -2.5717487 E' 0.46023576 0.15040074 0.41798577 0.83454005 F' 1.02 1.02 1.02 1.02 * Values given by the prediction method ** Values obtained for best data correlation

146 TABLE V-5 Summary of Comparisons of Eqn. (V-8) with the Vapor Pressure Values for R-22 Source Average Av. Absolute Max %.Dev. % Dev. % Dev. Booth and Swinehart (17) -1.69 1.90 -4.47 Benning and McHarness (12) 0.35 0.49 0.99 Du Pont (46) 0.05 0.05 0.11 Downing (42) 0.59 0.59 0.89 Zander (140) 0.12 0.19 -0.47 Values reported by Zander (140) agree very well with the values reported by Du Pont (46). The poorest agreement is found with the data of Booth and Swinehart (17). The reasons for these diagreements can be determined if the impurities in the sample are accurately determined. Eqn. (V-8) predicts data of Benning and McHarness (12) within +0.5% which is within their experimental precision. Thus the fit with Eqn. (V-8) is considered good. Vapor pressure of R-115 was determined by several investigators (4,87,98,136) and the available values are presented in Fig. V-4. The data is correlated with Eqn. (V-7) and the constants are reduced for use in Eqn. (V-8). The reduced constants are listed in Table V-4. The correlating equation (V-8) is compared with the reported vapor pressure values in Tables V-25 through V-28, and the summary of these comparisons is given in Table V-6.

1000 Fig. v.4. VAPOR PRESSURE OF CHLOROPENTAFLUOROETHANE (R- I15) o UNIVERSITY OF MICHIGAN (136) o MEARS (938) - ASTON (4) a DU PONT BULLETIN RT-31 (45) 100 L'L IO. t: - co GOI II 0.0 16.5 1.6.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 (l/T)x 103 (/R)

148 TABLE V-6 Summary of Comparisons of Eqn. (V-8) with the Vapor Pressure Values for R-115 Average Av. Absolute Max. Source % Dev. % Dev. % Dev. Univ. of Mich. (136) -0.51 0.70 -1.69 Mears et al. (98) +0.19 0.56 1.48 Aston et al. (4) 0.75 0.75 1.09 Downing (42) -1.16 1.16 -1.35 The sample of R-115 used in the vapor pressure determinations at The University of Michigan (136) contained about 0.0032% air in the vapor. The experimental precision is not reported. Aston et al. (4) used about 99.99% pure R-115 and the experimental precision is undetermined. Mears et al. (98) used 99.9 mol% pure R-115 and report that pressure measurements were precise to +0.2% and temperature measurements were good to +0.05. The correlating Eqn. (V-8) does predict vapor pressure values of Mears et al. (98) within the experimental precision. It is believed that the values reported by Downing are synthetic and therefore may be off as much as about 1.2%. Thus, the correlating Eqn. (V-8) is believed to be consistent with the experimental values. Vapor pressure values for R-502 have been determined in this investigation and are discussed with the values reported by others in Chapter IV. Using the method of prediction, described earlier, constants of Eqn. (V-8) are evaluated on the basis of factor M and are listed in Table V-4. The method of prediction is compared with the vapor pressure

149 values in Tables V-29 through V-33 and are summarized in Table V-7. TABLE V-7 Summary of Comparisons of Eqn. (V-8) with the Vapor Pressure Values for R-502 Source Average Av. Absolute Max. % Dev. % Dev. % Dev. This Work -1.57 2.21 7.54 Badylkes (5,6,7) -0.14 0.74 1.74 Loffler (86) 2.47 2.47 3.93 Downing (42) -1.35 1.39 -3.78 Du Pont (47) -1.24 1.56 -4.48 Table V-7 must be compared with Table IV-1 where summary of the best correlation made by Martin and Downing (90) is given. In each case the average deviations are poorer for our method of prediction. The merit of this methlod may be seen by studying Tables V-29 through V-33 which point out that vapor pressure values are predicted within 1% in the middle ranges but as we go towards critical value and to low pressures, the deviations increase. The reason for these differences was traced to Eqn. (V-8) where after combining the constants, at TR = 1, Eqn. (V-8) for R-502 predicted a reduced pressure of 1.028. Besides the low predicted critical temperature along with high critical pressure prediction of higher pressures near the critical point. If the mixture equation is normalized to predict PR = i at TR = 1, the low pressure values would automatically fall into line since the vapor pressure line will move up accordingly.

150 Other methods of prediction were tried without success. Saturated Liquid Density Saturated liquid density values are correlated by the Martin-Hou equation (92) which is given below: 1/3 2/3 4/3 ds = A + B(1-TR) + C(1-TR) + D(1-TR) + E(1-TR) (V-18) where ds = density of the saturated liquid A = d = critical density TR = T/TC = reduced temperature BC,D,E = constants of the equation The method of evaluation of these constants is illustrated with the data for R-115 in Appendix H. Equation (V-18) can be written in the reduced form as follows: d 1/3 2/3 4/3 d = 1 + B'(1-TR) + C'(1-TR) + D'(1-TR) + E' (1-TR) c (V-19) where B' = B/dc C' = C/dc D' = D/d. E' = E/dc Eqn. (V-19) may now be used to predict the mixture saturated liquid densities by combining the reduced parameters linearly on mole fraction basis.

151 TABLE V-8 Constants in the Saturated Liquid Density Eqn. V-19 For R-22, R-115 and R-502 Constant R-22 R-115 R-502* R-502** T (R) 664.5 635.56 638.23 639.56 d (lbs/cuft) 32.76 37.3 34.938 35.0 c B' 1.667717 1.761663 1.702477 1.528125 C' 1.121762 1.066756 1.101410 1.824690 D' -0.680481 -1.270241 -0.898692 -2.002303 E' 0.624948 1.168901 0.826210 1.385114 * Values given by the prediction method **Values obtained for best data correlation

152 Saturated liquid density values for R-22 have been reported in the literature (14,46,140) and constants in correlating Eqn. (V-18) have been reported by Du Pont (46). The data is presented in Fig. IV-2 with the location of the rectilinear diameter. Fig. IV-2 confirms the value of the critical density of R-22 to be 32.76 lbs/cu.ft. Constants in Eqn. (V-18) are reduced for use in Eqn. (V-19) and are listed in Table V-8. The comparisons of the correlating Eqn. (V-19) with the reported saturated liquid density values are given in Tables V-34 to V-36 and are summarized in Table V-9. TABLE V-9 Summary of Comparisons of Eqn. (V-19) with the Saturated Liquid Density Values for R-22 Average Av. Absolute Max. Source % Dev. % Dev. % Dev. Benning and McHarness (14) -0.004 0.044 -0.08 Du Pont (46) -0.003 0.003 -0.02 Zander (140) -0.16 0.17 -0.29 Benning and McHarness (14) report a precision in temperature measurement of +0.1 C amounting to an error of about +0.01%. The precision of density measurements was not given. Since Eqn. (V-19) given by Du Pont (46) was based on this data, the agreement is obvious. Besides values reported by Du Pont (46) are calculated from Eqn. (V-19) and hence the fine agreement is obtained as indicated in Table V-9. Zander's (140) saturated liquid density values are consistently lower except near the

153 critical. He reports a precision in the density measurement of +0.01%. Thus, Eqn. (V-19) does not predict Zander's (140) data within his experimental precision but is off by about -0.06%. Saturated liquid density of R-115 was determined at The University of Michigan (136) and by Mears et al. (98). The data is plotted in Fig. IV-2. The rectilinear diameter confirms the value of critical density of 37.3 lbs/cu.ft. The experimental data is correlated by Eqn. (V-18) and constants are reduced for use in Eqn. (V-19) which are listed in Table V-8. Comparisons of Eqn. (V-19) with the experimental saturated liquid density values are presented in Table V-37 and Table V-38, and a summary is presented in Table V-10. TABLE V-10 Summary of Comparisons of Eqn. (V-19) with the Saturated Liquid Density Values for R-115 Average Av. Absolute Max. Source % Dev. % Dev. % Dev. Univ. of Mich. (136) -0.004 0.25 0.547 Mears et al. (98) -0.05 0.27 0.716 Mears et al. (98) report a volume precision of +0.1% and temperature precision of +0. 05%. Experimental precision of The University of Michigan (136) values is believed to be less than +0.1% for density values.

154 Saturated liquid density of R-502 is determined in this work and along with other values is discussed in Chapter IV. Using the method of prediction, as described above, constants in Eqn. (V-19) were evaluated and are listed in Table V-8. The comparisons of Eqn. (V-19) with saturated liquid density values are presented in Tables V-39 through V-42 and are summarized in Table V-ll. TABLE V-11 Summary of Comparisons of Eqn. (V-19) with the Saturated Liquid Density Values for R-502 Source Average Av. Absolute Max. % Dev. % Dev. % Dev. This Work 0.29 0.44 2.9 Badylkes (5,6,7) 1.06 1.06 1.95 Loffler (86) 0.51 0.51 6.13 Du Pont (47) 1.91 1.91 5.51 Table V-ll may be compared with Table IV-2. Values reported by Du Pont (47) and Badylkes (5,6,7) are predicted better than before while the values of this work and Loffler are predicted with little larger deviations. To see the fit, one must examine the comparison of Tables V-39 through V-42. Eqn. (V-19) predicts the experimental data of this work within 0.2% for most of the points up to a reduced temperature of 0.96. The difficulty occurs near the critical point because of the fact that predicted critical density is lower than the true value and likewise predicted critical temperature is lower than the true value. Similar

155 observations can be made on the saturated liquid density values reported by others. Thus, this method of prediction of saturated liquid density values may be used with confidence up to 0.97 TR. To complete the data analysis equations for the rectilinear diameters of R-22 and R-115 are also formulated. The equations are given below and compared with the rectilinear diameter values in Tables V-43 and V-44. For R-22 d = 32.76 + 30.129 (1-T/664.5) (V-20) For R-115 d = 37.30 + 32.834 (1-T/639.56) (V-21) Critical Constants In our analysis of prediction of properties of the mixture R-502 from the properties of its components, we found that if true critical constants are used then the constants of analytical equations, describing certain property, may be combined simply on mole fraction basis. Several methods are available in the literature for the prediction of critical constants. Some methods are formulated to predict pseudocritical constants which can be used in general correlations. Other methods predict the true critical constants. A few of these methods are described in Appendix J. They are all summarized in Table V-12. Some methods simply use the component critical constants and the mole or mass fractions in the mixture. Other methods employ extra parameters such as accentric factor, molal average boiling points, etc. Our mixture is a minimum boiling point azeotrope and this fact could be determined only if the normal boiling point of the azeotrope is measured and compared with the component boiling points. Thus, it is

156 TABLE V-12 Summary of Mixing Rules for Critical Constants of R-502 P T V Z Method Reference cm cm cm cm psia R ft3/lb I. Kay-Mole fraction 623.52 653.8 0.028622 0.2705 II. Kay-Mass fraction 585.76 649.69 0.028622 0.2721 III. Geometric Mean Av. 616.4 653.7 0.02827 0.2708 IV. Lorentz Cube Root Av. 618.6 653.85 0.028388 0.2708 V. Chueh & Prausnitz - Simplified (34a) 647.81 0.028622 VI. Chueh & Prausnitz (34b) - 651.70 0.029590 - VII. Ekiner & Thodos (47a) 661.2 - VIII. Grieves & Thodos (52a) - 650.78 - IX. Leland-Mueller (84a) 600.0 655.0 0.028388 0.2705 X. Joffe-Method A (67a) 598.2 645.53 - - 583.7 639.56* - - 578.4 639.98 - - XI. Joffe-Method B (67a) 597.4 649.98 - - 587.8 639.56* - - XII. Li (85a) - 650.6 - - XIII. Kreglewski & Kay (82a) 528.56 639.56* - - XIV. Li,Chen & Murphy (85b) - 638.23 - XV. This Work 593.79 True Values 591.0 639.56 0.028571 0.2747 *True values of T were substituted in the equations. cm

157 believed that having a knowledge of the normal boiling point of the mixture is necessary, and as proven below, a sufficient condition to be able to predict the critical constants of the mixture. Based on this reasoning, we recommend the Li, Chen and Murphy (85b) method for the prediction of critical temperature. From Table V-12 it may be observed that this method is extremely superior to other methods of prediction and predicts the true critical temperature of R-502 within 1.33 F. Averaging the molal critical volumes on mole fraction yields, the critical volume for the mixture is within 0.000051 ft3/lb or within 0.18%. Other methods deviate by larger amounts. In order to predict the critical pressure of the mixture, we were looking for a simple method. Mass fraction averaging gives a fairly good value of the critical pressure. Then Joffe's (67a) methods are best for this prediction. In order to use Joffe's method (67a) we have to use the critical, temperatures predicted by his method which differ from the true value by about 6 R for his simple method and by about 10 R for his second method. But considering all the combinations of T and cm P predicted by different methods, Joffe's method-A (67a) is simple cm and the best. We were not happy with the fact that to use Joffe's (67a) method A, even though the critical pressure is predicted within the precision of its determinations, the predicted critical temperature differed from the true value by a large amount. Further investigations proved successful and we are proposing a new and simple method for the prediction of critical temperature which is described by Eqn. (V-5) given below:

158 1 xi x 2.1 - i (V-5) P P P cm cl c2 The reasoning behind formulating Eqn. (V-5) was based on the fact that we do need the boiling point of the mixture to predict its critical temperature. Eqn. (V-3) describes the method of prediction of critical temperature: Bm Tbl b2 = x1 + x 2T (V-3) cm cl c2 Let us substitute the pressures corresponding to temperatures in Eqn. (V-3). At the boiling points pressure is atmospheric (14.7 psia). At the critical temperatures the pressures are critical. Therefore, Eqn. (V-3) becomes: 14.7 14.7 14.7 P + x iX2.... (v-22) cm cl c2 Cancelling the common factor 14.7 in Eqn. (V-22) we obtain our new method of prediction of critical pressure of a mixture. As stated above, this method predicts a critical value for the mixture of 593.79 psia which is within 2.79 psia of the true value or within 0.47%. In summary, we have three methods which predict the critical constants of R-502 very well compared to other methods.

159 Intermolecular Potential Energy A general nature of the potential energy of interaction between two molecules is presented in Fig. II-8. Several methods to describe this curve are reviewed in Chapter II. Most of the methods can be characterized by the number of adjustable parameters they contain and the higher this number, the more difficult the method. We were looking for a simple method containing a few parameters which can be handled mathematically and still be realistic. Our investigation started with the two parameter Lennard-Jones (12-6) potential and ended up with multiparameter method of Boys and Sharitt (18,19,20) where computers have to be used. In the simplest method due to Lennard-Jones (12-6) the two parameters are determined by either trial and error method or graphically, involving extensive calculations. Therefore a new method is proposed to obtain two characteristic parameters d and U. This method is described in detail in Appendix K. Only important features are discussed here. The second virial coefficient is given in terms of the intermolecular potential energy by the following equation: -U /kT B = 21TN J(e -1) r 2dr (V-23) 0 As discussed in Appendix K, a new equation is proposed for the intermolecular potential energy: d 12 d 6 U =4U [(r-) - ) for d < r < oo (V-24) m r o

160 and -U/kT 12 e = Cr for 0 < r < do (V-25) Further, an assumption is made that in the region beyond do we may express the exponential term in terms of quadratic expansion as follows: -U/kT e 1 - U/kT + 1/2 (U/kT) (V-26) Final expression for the second virial coefficient is given below: 3 U U 1 2 m 16 m 2 B = 8fN do 15 9 kT 315 kT The parameters d and U are the characteristic parameters. 0 m In correlating PVT data we used several input conditions out of which three pertained to the second virial coefficient. The second virial coefficient at the Boyle temperature is zero. Two values of generalized second virial coefficient at TR = 1.0 and TR = 0.8 are used as other input conditions. Given B = 0, Eqn. (V-27) can be easily solved for U /k and from a value of B at TR = 1.0, second parameter d can be determined. To see the reasonableness of this procedure o values of U and d could be used to predict B at T = 0.8. Using this m o R procedure, the parameters Um and do for R-22 and R-115 were evaluated and they are listed in Table V-13.

161 Order of magnitude of these parameters is comparable to generalized correlations (Table V-13). Thus our approximations are reasonable. Going further to predict the second virial coefficients for R-502, we combined the component parameters as follows: d = (d + d )/2 (V-28) 012 01 ~2 U = (U U )l/2 (IV-29) m12 ml m2 Using the relationship between the second virial coefficient of mixtures with those of components, the mixture values were predicted and they are summarized in Table K-1. From the input condition to the equation of state for R-502, at the Boyle temperature a value of B!2 was calculated to be- 3.58 cc/gmole. Using the parameters calculated by Eqns. (V-28) and (V-29), the predicted value was +3.02 cc/gmole or within a 0.6 cc/gmole. At another temperature (TR = 1 for R-502), value of B12 was calculated to be -241.09 and the predicted value is -251.53 cc/gmole. Similarly a disagreement of about 10 cc/gmole was obtained at TR = 0.8 for R-502. These disagreements may be compared with the experimentally determined second virial coefficients by two different sources, where differences as high as 10 cc/gmole are usually observed. Thus using the component parameters evaluated by this new method, then using well known combining rules we have been able to predict the second virial coefficient for the mixture reasonably well.

162 TABLE V-13 Summary of Intermolecular Potential Energy Parameters Parameter R-22 R-115 R-502 U /k (K) -239.3 * -228.9 * -230.33 * 0 d (A) 5.24* 5.98 * 5.51 * 0 d (A) 5.88 6.71 6.18 16 Um(erg)xlO 330.3 316.0 318.0 Vc(cc/g) 1.906 1.674 1.784 V /dm 1.346 1.421 1..401 T (K) 369.17 353.09 355.31 kT /U 1.543 1.543 1.543 c m P d3/U 0.3063 0.3005 0.3024 c m m P V /kT 0.2672 0.2769 0.2747 cc c k = 1.38044 xlO16 erg/deg 1 atm = 1.0133x106 dynes/sq.cm. *These characteristic parameters can be used in the Lennard-Jones potential energy equation II-48, even though they were derived specifically for equations V-24 and V-25.

163 If the Boyle temperature is not used, two values of B will give a quadratic in UM/k which can be easily solved exactly and then do could be determined. This is the advantage of this method. Also considering R-502 to be a pure substance, parameters d and Um were evaluated and are given in Table V-13. Generalized parameters are also calculated. In summary, we have been able to predict the PVT behavior, vapor pressure, saturated liquid density using simple combination rules for equation constants and critical constants. Using a new analytical method of determining the intermolecular potential energy parameters, we were able to predict the second virial coefficient of the mixture from the component values.

164'2TABLE.V- 14 V-14. Comparison of E]qn. V-1 and PVT Data for R-22 Reported by Michiels (99) V/0.030525 T/664.5 ep /721. 906 P /721.906 %Dev. exp calc 20a 34823 9 0.791 0, 13( O 0130 -0 08 20.33 4'29 0 0.08 U. 133 0 i33 -0.02 20o34' 39 0.821 0. 136 0*136 0.01 20.3452J3 9 0, 848 O, 14 2 0, 12 0.04 20,348239 0.875 0Do 147 0 147 0. 0o 20o 34-8239 0.91i O. 14 0,154 0,05 20.348239 0o.943 0. 161 0.161 0o04 20034u8239 05 973 0 167 0o 157 0. 03 20o 3482 3 9 i.000 0. 173 0o173 0.03 20.348239 1.011 0,175 00175 0. 01 20, 3482'39 1o042 0.181 0,181 0.00 20. 348239 1*079 0 188 0.188 0. 01 20.348239 1 146 0.201 0,202 -0o03 15 828337 0,791 0. 161 0.161 -0.*17 i5,828 3 37 0,808 0, 166 0 166 -Oo 08 159 828337 0.a821 O0 169 0,169 -0,05 15o828337 0.848 Go 177 0.177 0.01 15.o822)337 0,875 0.184 o0 184 0.04 15.82 o 8335 7 0.911 0. 194 0.o194 0. 05 15.832 >3 7 O,943 0o203 0203 0 15, t;2 i.3 2 7 C 973 0.o 21i1 0210 0.03 i 5 8 2 837 000 0 118 0,218 0218 O.00 15. t33 7 1,011 0. 20. 2Z0 -0. O0 152 82 83 i7 1.042 0o.229 0.229 -0. 01 13o, 28'3 7 1, C79 00.38 0, 3 83 - O. 0 15; 82t 337 i146 0, 2'6i 0.25: -0.05?~.9o,":473 0,808 () 195 0, 1963 -0o l9 2.9'?3't7 3 0.82Z 0, 00 0. 200 -0n.' 0

165 TABLE V-14 (contd.) 12 963473 0.848 0. 210 0.210 -0.02 12.963473 0. 875 0.212 O, 219 0* 03 12, 93473 0O 911 0.231 0.231 OO4 12o963473 0.943 0 242 0.242 0. 03 12.963473 0. 973 0.252.0 252 0.3 12.963473 1000 Oo 26 1 0.261 0.01 12.,963473 1.011 0.264 0. 264 0O00 12. 963473 1.042 0. 275 0,275 -0*02 i2 9 634 73 1,070 0 286 0, 287 -0. 02 12 963473 1.146 0.308 0,308 -0, 07 10.o 902211 0.821 0,o230 0.231 -0.21 10. 902211 0.848 0.242.0. 2 42 -0o08 10.902211 0.875 0o 253 0 2 53 -0.01 10, 902211 C, 943 0. 281 0 281 0, 03 10.902211 0.911 0,268 0*268 0.02 10. 902211 0.973 0O 293 0.293 0O02 10.902211 1.000 0, 304 0.304 0,01 10, 902211 10-i1 O, 308 0.308 -0. 01 10. 902211 1. 042 0,321 0. 321 -0.02 10.902211 1.079 0,335 0.335 -0.03 10. 902211 1,146 0361 0o362 -0 08 9, 162981 0.848 0, 277 0,277 -0 18 9.162981 0,875 0.291 0,291 -0, 06 9.162981 0. 911 0.3C9 0,309 -0.003 9.162981 0. 943 0, 326 0.325 0.01 9. i 62981 0. 973 0.340 O0 340 0. 01 9 162981 1.000 0.354 0.354 -0O00 9.1 62 98i 10. 0.359 0o359 O 359 - O0o O 9. 162981 i, 02 0. 374 0, 74 -0. 02 9. 62 981 le079 0) 3 91 0.391. - 0 05

166 TABLE V-14 (contd.) 9. 162 96l 1. 146 0O 423 0.424 -0.10 7.922686 C.875 0O 325 0.326 -0.14 7.922686 0,911 0.347 0,347 -0.03 70922o86 0 943 00366 0. 366 -0.00 7.92268u 0.973 0.384 0.384 0 00 7 922686 1.000 0*400 0.400. -0.00 7,922686 1.011 0, 406 0.406 -U.01 7.922686b 1042 0.424 0.424 -00 03 7o 922686 1. 079 0. 444 0.444 -o 06 7.922686 1,146 0.482 0*482 -01il 7.028337 00 911 0.380 0.380 -0. 09 7 028337 0 943 0, 402 0.402 -0,02 7, 028337 1.000 0,441 0.441 -0. 02 7 02833 7 1. 011 O 448 0*44 8 -0. 02 7. 02833 7 1.042 0. 468 0*468 -0. 04 7.028337 1 079 0.492 0.492 -0. 07 7,028337 1,146 Oo, 535 0.536 -0.09 6.759378 0.875 0.365 0.366 -0.28 6,759378 0.911 0.391 0*391 -0,10 6a759378 0.943 0.414 0*415 -0.03 6,7593 78 0, 973 0 436 0*436 -0,05 6,759378 1.000 00455 0*455 -0.01 6,759378 1, 011 0,462 0 *462 -Oo 02 60759378 1*042 0,484 0.484 -0,03 6,759376 1.079 0. 5C8 0 509 -0.06 6*759378 1,146 0.554 0.554 -0,1i 5. 6232 6 0 0.911 0,444 0.445 -0,22 5,623260 0*943 0. 474 0*475 -0.09 5.623260 0.973 0, 501 0. 501 -0.03 5, 62326,0) 1. 000 O0 525 0 525 -0.03

167 TABLE V-14 (contd.) 5.623260 o.011 0.34 0.534 -)0.03 5, 623260 1.042 0.560 0. 561 -0.05 5, 623260 1. 79 0. 591 0. 592 -0, 07 5.623260 1.146 0,648 0.648 -0.11 4.669615 0. 911 0.499 0 *501 -0.43 4.669615 0*943 0.537 0.538 -0. 19 4o 669615 0.973 0.571 0*571 -0.08 4,669615 1.000 Oo 601 0.601 -0,05 4.669615 1.0 11 O 612 0.613 -0.04 4.66 9615 1. 042 0. 646 0. 66 -0; 04 4.,669615 1.079 0.684 0. 685 -0. 08 4.669015 1. 146 0.755 0. 755 -0. 12 3.997379 0.943 0. 589 0.591 -0 31 3. 937379 0.973 0.631 0.631 -00 13 3. 997379 1o 000 Oo 668 0o668 -0. 06 3 9$7379- 1.011 0 b661- 0*682 -0. 00 3,9S7379 1.042 Oo 722 0.722 -0*04 30 997379 1*079 0, 709 0.769 -0.06 3.997379 1. 146 0.853 0.854 -0.12 3. 946601 0.973 0.637 0.636 0.06 30 946601 1i000 0, 673 0. 674 -0O 09 3.946601 1i011 0.687 0.687 -0.08 3 946601 1. 042 0,728 0.729 -0. 06 3. 94660i 1. 079 0 776 0o 776 -0. 09 3. 94660 1 1.146 08. 6l 00863 -0, l1 3 o 46 287 0. 943 0 635 0.638 -3049 3.46])287 0,973 0. t685 0.686 -0. 20 3, 469287 1000 0, 729 0.*730 -0o03 3,469287 1.011 0. 745 0. 746 -0.06 3,469287 1.042 0?794 0. 794 -Oo 04

168 TABLE V-14 (contd.) 3.469287 1*079 C. 850 0.850 -'0.05 3. 469287 10 146 0,951 0.952 -0. 10 3 2501 23 0.973 0.709 0.710 -0.24 3.250123 1. 00 0 757 0. 758 -0.09 3.250123 1.011 0.775 0.775 -0.06 3*250123 1.042 0.828 0,828 -0.03 3. 250123 1.079 0. 888 c.868 -0.03 3e 250123 1.146 0. 997 0, 998 -0.10 3.065356 0.973 0.730 0, 731 -0.25 3. 065356 1.000 0.782 0O782 -0. 09 3o065356 1.011 0. 801 0.801 -0.06 3.065356 1.042 0o858 0.858 -0,.00 3*065356 1.079 0 923 0.923 -0.02 3o065356 1*146 1.04 1 1 041 -0.09 2*748239 0.973 0 766 0*769 -0. 36 2*748239 1*000 0, 826 0*827 -0.10 2.748239 1.011 0*849 0.849 -0*05 2.748239 1.042 0O 914 0.914 0.03 2.748239 1*079 0. 989 0.989 0,03 2,74823 9 1.146 1.124 1,124 -0.05 2,671712 0.973 0.775 0.778 -0.37 2.671712 1,000 0 838 0.838 -00.09 2.67i712 1.011 0.861 0.861 -0.03 2.67i712 1.042 0.929 0.928 0O05 2,671712 1.079 1.006 1.006 0 07 2,6717i2 1.146 1. 146 1.146 -0.02 2.482228 0.973 0, 796 0.800 -0.50 2*482228 1.000 0, 866 0,866 -0.10 2.482228 1.01i 0. 891 0.891 -0.03 2.482228 1.042 0.966 0.965 0. 08

169 TABLE V-14 (contd.).*482228 1. 079 lo C51 1050 0.08 2,482228 1.146 1.204 1.204 -0 00 2. 193284 0.973. 826 0 831 -0.61 2.1932834 1.000 0. 908 0.909 -0.08 2.193284 1i011 O.c38 0*938 0. 03 2.193284 1. 042 o 026 1*024 O. 17 2.193284 1.079 1e 126 1.123 0.22 2.193284 1 146 1.305. 1.304 O0 12 1 793939 1.000 Os 962 0.962 -0, 05 1.793939 1.011 1. 001 1000 0*13 1 793939 1.042 1. 115 lo ll, 0.37 1.793939 1.079 l 244 1. 239 0.42 1i793)39 11i46 1.475 1.472 0( 24 1.457101 1.000 Oe 993 0.993 -0.02 1.457101 1*011 1 C44 1*042 0*24 1.457101 1.042 1. 191 1*185 0.51 1. 457101 1.079 1.360 1.352 0. 54 1.457101 1,146 1*662 1.657 0.35 1 179099 1.000 Io003 1,002 O.* O 1.179099 1.011 1. 067 1.065 0.21 1,179099 1,042 1.t25 1.252 0.30 1,179099 1.079 1.475 1.470 0.30 1e 179099 1,146 1. E75 1.871 0.20 0. 9601 31 1 000 1 o 003 1. 004 - 0 05 0. 9601-31.* 01! lo C81 1i 085 -03 7 0.960131 1.042 1. 320 i.326 -0.61 0. 960i31 1.079 1. 606 1.614 -0.51 0,960131 1,146 2. 142 20145 -0* 13 0)780C'75 1.000 iO C13 1, 013 0.00 0.780475 1o0 t1 1, 118 l1123 -0.49

170 TABLE V-14 (contd.) 0. 780475 1.042 1.445 1. 455 -0.70 0.780475 1.079 1.843 1.848 -0.27 0,780475 1.146 2. 603 2.586 0.67

171 TABLE V-15 V-15. Comparison of Eqn. V-1 and Isometric PVT Data for R-22 Reported by Zander (140) Density Temp. Pressure V/0.030525 T/664.5 Pexp/721.906 Pcalc/721.06 %Dev. d t P g/cc C bars 1.2490 18c 17 76o 23 0 420146 0,789 1.531 3.114 -103. 35 1.2490 19.97 90.25 0. 420146 0,7?4. 813 3.406 -87.85 1.2490 24 62 128.21 0.420146 0.80(7 2.576 4.168 -61.82 1.2490 29.99 168.50 0 420146 0,821 3.385 4.941 -45.95 1.2490 35.14 208.37 0O 42C146 0,835 4*186 5,672 -35.46 1.2350 14.20 15.73 0,4249C9 0.776 0.316 1.666 -427.13 1.2350 20.28 61.33 0.4249C9 0.795 1.232 2.641 -114.33 1.2350 24,89 96.04 0 4249C9 0.807 1.930 3.345 -73,37 1.2350 29.98 134,08 0.424909 0.821 2.694 4 089 - 51. 79 1.2350 35.08 172.38 0.424909 0.835 3.463 4.800 -38.59 1.2350 39.83 207.84 0*424909 0.848 4-176 5,433 -30,10 1.2180 19. 83 24.02 0.43C839 0.794 0.483 1, 673 -246. 79 1.2180 24.64 58.37 0.430839 0.807 1.173 2.386 -103*43 1.2180 29.81 95.24 0.43C839 0,821 1.913 3. 120 -63.07 1.2180 34. 87 131.31 0 43C839 0.834. 638 3.809 -44. 40 1.2180 40,02 168,00 0.43C839 0.848 3,375 4.482 -32.78 1.2180 44.85 202.01 0.43C839 0.861 4.059 5.086 -25.32 1.2020 24.71 27. 33 0.436574 0.807 0.549 1.615 -194.02 1*2020 29*78 61.72 0.436574 0*821 1.240 2.313 -86.55 1.2020 33.97 90,21 0*436574 0,832 1*812 2.871 -58,41 1.2020 40,03 131.28 0*436574 0.848 2.638 3,047 -38.27 1.2020 45.01 165. 18 0 436574 0.862 3. 319 4.259 -28. 34 1. 2 020 4984 19 7 62 0.436574 0.875 3.970 4,831 -21 69 1.1820 29*87 28.74 0.4439ti 0.821 0.577 1.434 -148.30 1. 1820 36.27 69.52 0o443961 0.838 1.397 2.248 -60.96 1.1820 40 18 94.63 0.4439 l 0.849 i.901 2.729 -43.55 1,1820 45.1.6 126.54 0. 443961 0. 362 2 542 3,324 -30.77 1.1820 55, 24 191.23 Cr 443961 0 3)0 3. 842 4.472 - 16.41

172 TABLE V-15 (contd.) 1.1570 34.89 23.01 0.453554 0.8 34 0.462 1.096 -137.09 1.1570 40. 0o 53* 69 0.453554 0.848 1.079 1.707 -58.21 1.1570 45.04 83.74 0.453554 0.86Z 1.682 2.279 -35,44 1.1570 509 18 114, 13 0,453554 0,876 2,293 2.853 -24. 43 1,1570 55.30 144. 4 0. 453554 0,890 2.906 3.410 -17.34 le.1570 65.10 203.22 0.453554 0.916 4.083 4.435 -8.63 1. 1360 40.00 25,02 0.461939 0.848 0.503 0.984 -95.69 1.1360 44.99 52.81 0.461939 0.862 1.061 1.535 -44.65 1*1360 50.07 81.61 0.461939 0.876 1.640 2.083 -27.03 1.1360 60.20 138.05 0.461939 0.903 2.774 3.139 -13.19 1,1360 65.14 164*44 0,461939 0.916 3.304 3.638 -10.12 1 1360 70.22 192.81 0.461939 0.930 3,874 4*140 -6.87 1.1160 45.02 28. 54 0.47CZ17 0. 862 0.573 0.936 -63.30 1.1160 50.08 55.1C 0.470217 0.876 1.107 1.462 -32.02 1.1160 55. 13 81.83 0.470217 0.889 1.644 1,976 -20,17 1.1160 60.09 107. 62 0.470217 0.903 2.162 2.471 -14.30 1.1160 70.15 161.14 0.470217 0.930 3.237 3.450 -6.e55 1.1160 75.19 187 56 0.47C217 0.944 3.768 3.927 -4.21 1.0950 49.95 31.64 0*479235 - 0875 0.636 0.892 -40.38 1.0950 55009 56.85 0.479235 0.889 1.142 1*394 -22*07 1.0950 60,11 81.81 0.479235 0.903 1.644 1,877 -14*18 1.0950 65.18 106.86 0.4792335 0.916 2,147 2.357 -9,77 1.0950 71. 36 137.51 0.479235 0.933 2*763 2.932 -6.13 1.0950 75,14 156.43 0.479235 0.943 3.143 3.279 -4.34 1.0950 85.04 205.87 0.479235 0.970 4.136 4.171 -0.84 1.0730 55.13 3. 01 0. 489061 C0.889 0.723 0.890 -22.97 1,0730'65.07 81.80 0.489061 0.916 1.643 1.797 -9.32 1.0730 71.44 111. 86 0.489G61 U0933 ~ 2247 2.367 -5.30 1.0730 80.30 153.24 0.489061 0.957 3.079 3.146 -2.18 1.0730 90*21 199,73 0.489061 0.9134 4.013 4,000 0.32

173 TABLE V-15 (contd.) 1.0470 60.09 36,11 0.5012C6 0.903 0*725 0.832 -14.74 1. 0470 t5.10 59.00 0,501206 0.916 1.185 1.2ol -6.40 1.0470 75.42 101.52 0. 5012C6 0,944 2 040 2.133 -4.57 1.0470 95.02 i86. 52 0.5012C6 0.997 3.747 3.749 -0.04 1.0160 65.12 35.92 0 516498 0.916 0.722 0.763 -5.65 1.0160 75.44 75.88 0,516498 0,944 1.525 1.573 -3.18 1. 0160 85. 10 113.93 0.516498 O.970 2.289 2.324 -1. 52 1.0160 95.03 153.14 0, 516498 0,997 3.077 3.088 -0,37 1.0160 105.06 192.65 0.516498 1.024 3.871 3.853 0,45 0, 9880 70. 09 39,12 0. 531136 0.930 0*786 0 789 -0 38 0.9880 e5.26 93,85 0,531136 0.971 1*885 1.892 -0.33 0.9880 100.32 148.51 0.531136 1,012 2.984 2,977 0.22 0.9880 115 23 203.64 0. 53116 1,052 4.091 4*044 1.15 0.9580 74.87 41*55 0,547769 0.943 0 835 0,821 1.65 O 95 80 90.01 91.09 0.547769 0,984 1.83 0 1.835 -0 24 0.9580 100.38 125 90 C, 547769 1*012 2.529 2,527 0,08 0.9580 120. i7 192 69 0.547769 1.065 3.871 3,847 0.63'0,9330 80.06 46,66 0.o562446 0.957 0.938 0.950 -1,33 0,9330 89.94 76.11 0*562446 0.984 1.529 1.566 -2.42 0 9330 100.13 107.39j 0. 562446 1.011 2.158 2.203 -2.08 0.9330 115.10 153.88 0. 5C2446 1.052 3. 092 3.139 -152 *0*9330 129.95 200.54 0*562446 1.092 4.029 4,069 -0*98 0.9010 84. 85 51, 69 U0 582422 C,970 1.039 10019 1,84 0 9010 100.03 93,63 0.562422 1.011 1.881 1.882 -0.07 0.9010 120.21 149,80 0.582422 1*066 3o010 3.038 -0,93 0,8680 89.77 55, 33 U, 6C4565 0.. 983 1.112 1. 111 0.05 0.8680 105.16 93,65 0.604565 1.025 1.882 1.904 -1.19 0,8680 120. 10 132.47 0,604565 1,065 2.661 2.681 -0.73 0 8680 140,09 184.98 0 6C4565 1.119 3.716 3 729 -0.35 0.8160 89.96 47,43 0. 643091 0,984 0.953 0.944 0.91

174 TABLE V-15 (contd.) 0.8160 93.30 54.24 0.:43091 0.993 1.090 1.089 0.04 0.8160 105.06 79.19 0.643C91 1.024 1.591 1.604 -0.81 0.8160 120.09 112. 2e 0 643091 1 065 2.263 2.269 -0.24 0.8160 14010 158.OC 0.643091 1.119 3.174 3.165 0.29 0.7340 98.32 55,91 0.714935 1.006 1.123 1.126 -0.23 0.7340 105.19 67. 53 0.714935 1.025 1.357 1.360 -0.23 0.7340 119.97 93.32 0.714935 1.065 1.875 1.869 0.34 0.7340 139.98 129.44 0.714935 1.119 2.601 2.567 1.29 0.6910 100.08 56*30 0.759425 1.011 1.131 1,138 -0.62 0.6910 119.99 86.90 0.759425 1.065 1.746 1.744 0.11 0O6910 129.94 102.30 0.759425 1.092 2,055 2.050 0.24 0.6910 139.98 118.52 0.759425 1.119 2,381 2.362 0.83 0.6240 104. 80 60*28 0. 84C965 1.024 1.211 1. 225 -1 11 0.6240 114.94 73.09 0.84C965 1.051 1.468 1.484 -1.07 0.6240 129.80 93.18 0. 840965 1.092 1.,872 1.867 0.27 0.6240 139.94 105.76 0, 84C965 1.119 2.125 2.130 -0,24 0O5330 105.02 58.60 0,84545 1.024 1.177 1.184 -0. 59 0o 5330 120.21 74. OB 0.8 84545 1.066 1.488 1.495 -0.46 0.5330 139.96 94.65 0.984545 1.119 1.902 1.900 0.11 0.4770 110.41 62.48 1.100131 1.039 1.Z55 1.255 -0.01 0.4770 120.20 71.15 1.100131 1.066 1.429 1.429 0.05 0.4770 139.96 88.54 1.100131 1.119 1.779 1.777 0.12 0.4290 104,92 56.76 1,223222 1.024 1.140 1.138 0.20 0.4290 119.98 68.46 1* 223222 1.065 1.375 1.371 0.31 0.4290 139.98 83.78 1,223222 ll11 1.683 1.678 0.33 0.3770 99.90 52.14 1.391943 1.011 1.048 1,046 0.12 0.3770 109.92 58.92 1.391943 1.038 1.184 1 179 0940 0.3770 125.04 68.90 1.391943 1.079 1.384 1,377 0.52 0.3770 140.00 78.74 1.391943 1.119 1.582 1.571 0.70 0.3460 99.66 51,34 1. 16654 1.010 1.032 1,031 0.05

175 TABLE V-15 (contd.) 0.3460 110,07 57. 67 1. 516654 1.038 1.159 1.155 0.33 0.3460 i25.02 66.59 1.516654 1,.079 1*338 1.331 0.53 0.3460 139,81 75.17 1,516654 1.119 1.510 1.502 0.51 0.3100 99.62 50.29 1.692782 1.010 1. Oi 1.010 0.09 0.3100 110, 00 55.83 1.692782 1.038 1.122 1.117 0.38 00 3100 124. 86 63.51 1.692782 1.078 1.276 1.270 0.50 0.3100 139.96 71.12 1.692782 1.119 1.429 1.422 0.49 0.2780 95, 08 46,76 1. E87635 0.997 0.939 0.941 -0.15 0.2780 110 11 53.77 1. E87635 1.038 1.080 1.077 0.27 0.2'780 124.92 60.41 1.E87635 1.078 1.214 1.209 0.35 0.2780 139.99 67.14 1.887635 1.119 1.349 1. 342 0*54 0. 2480 89,69 42,75 2. 115977 0.983 0.859 0.868 -1.09 0.2480 104.90 48.77 2*115977 1,024 0.980 0.989 -0.92 0.2480 125.03 56.93 2.115977 1.079 1.144 1.145 -0.07 0.2480 140.03 62.56 2.115977- 1.119 1.257 1. 259 -0.12 0. 2150 89. 61 41.05 2.440755 0.983 0.825 0.829 -0. 48 0, 2150 104.97 46.36 2. 440755 1.024 0,931 0.930 0.11 0.2150 1150 7 49.49 2.440755 1.052 0.994 0.996 -0.18 0.2150 125003 52.66 2.44C755 1.079 1,058 1.060 -0.19 0.2150 139.82 57.28 2.446755 1.119 1.151 1.154 -0.24 0. 1900 84.57 37.54 2, 761907 0.969 0.754 0. 759 -0. 61 0. 1900 94.82 40.55 2. 761907 0.997 0,815 0.818 -0.35 0, 1900 1090 88 44.79 2.761907 1.038 0.900 0.902 -0.27 0.1900 125.00 48,92 2.761907 1.079 0.983 0.986 -0.27 0.1900 139.89 53.18 2.761907 1.119 1.069 1.066 0*21 0.1570 75*88 32,43 3.342436 0.945 0.652 0.654 -0. 32 0.1570 94.7i 36.85 3. 342436 0996 0.740 0.739 0.19 0.15 70 110,17 40.30 3, 342436 1.038 0.810 0.807 0.27 001570 124.92 43.50 3. 342436 1.078 0.874 0.o72 0.29 0.1570 140.09 46.38 3.342436 1.119 0.932 0,936 -0.47

176 TABLE V-15 (contd.) 0.1323 70.02 28. 51 3. S66458 0.930 0.573 0. 575 -0.43 0.1323 85.15 31. 39 3.966458 0.971 0.631 0.631 -0009 0.1323 99.95 34.12 3. 66458 1.011 0*685 0*685 0.08 0,1323 119.81 37.34 3. 466458 1.064 0.750 0.755 -0.69 0,1323 140,22 41,13 3' 66458 1.120 0.826 0.826 0.02 0.1068 62 07 239 9 4* 913506 0 908 0.482. 0483 -0*26. 0. 1068 79.94 26. 68 4.913506 0. Sd6 0.536 0.534 0.31 0.1068 99.85 29.42 4.S135C6 1.010 0.591 0.590 0.19 0.1068 119. 90 32.23 4. c13506 1L065 0*648 0*645 0.43 0.1068 139.91 34.90 4.913506 1.119 0.701 0.698 0.43 0.0825 55.10 19.40 6.360757 0.889 0.390 0.392 -0.61 0.0825 69.89 20.98 6.360757 0*929 0.422 0.423 -0.41 0.0825 84.89 22.54 6.360757 0.970 0.453 0.454 -0.35 0.0825 110.13 25.06 6.366757 1.038 0.504 0.506 -0.40 0.0825 124.92 26.51 6.36C757 1.078 0.533 0.535 -0.42

17,7 TABLE V-16 V-16. Comparison of Eqn. V-1 and Isothermal PVT Data for R-22 Reported by Zander (140) Compress. Temp. Pressure Factor V/0.030525 T/664.5 Pexp /721.906 P /721 96 %Dev. t P Zca c bars 30,00 ~0.75 0. 628000 11 785273 C.821 0.216 0.217 -0.35 30.00 6.34 0.'906900 21.883774 0.821 0.127 0.127 -0.01 30.00 5.93 0.913500 23.56267S 0.821 0.119 0.119 0.0U 30.00 3. 33 0.953600 43. 749172 0,821 0.067 0.067 0.07 30.00 3.11 0.956900 47 106568 0.821 0.062 0.062 0,07 50.00 17.97 0.753200 6, E33082 08,75 0,361 0.363 -0,47 50.00 14.31 0.813200 9.267264 0.875 0.287 0.289 -0.46 50,00 10,42 0. 873300 13, 662027 0, 575 0,209 0.209 -0.04 50,00 7.94 0*906200 18.597977 0.875 0.160 0O160 -0.00 50,00 559 0. 935900 27 311513 0.875 0.112 0*112 0,03 50.00 4*18 0,952900 37*182627 0.875 0084 0.084 0.05 50.00 2 89 0.967900 54* 59 7C9 0,875 0.058 0.058 0,04 70,00 28.50 0.651300 3, c562S2 0*930 0*573 0,576 -0,59 70.00 24.00 0 730600 5.27C710 0.930 0.482 0 483 -0,24 70,00 17, 84 0. 815300 7, 910128 0,930 0.359 0,359 -0.06 70,00 14,12 0O859500 10.537371 0*930 0O284 0.284 -0.00 70,00 9,91 0.905200 15,814748 0.930 0.199 0.199 0.03 70.00 7063 0.928600 21. CC7764 0.930 0,153 0.153 0.06 70.00 5.22 0.952300 31.613223 0.930 0.105 0. 105 0.06 70.00 3096 0, 964200 42. il36~7 Q*930 G,080 0.080 0.06 100.00 58.69 0.225400 0.72303j. 1.011 1*179 1.172 0.64 100.00 55.29 O 235800 0 8 02904 1,011i 1.l11 1 113 - 0. 19 100.00 53.31 0.308000 1o C67635 1e01i 1.071 1.072 -0*06 100.00 b2, 94 0 339800 i. 208362 1.011 1i 064 1.063 0.10 100. 00 51. 11 O0 431700 i 590255 1.01i 1,027 1,027 0.02 100,03 50.88 0.442400 1.(31C70 1.0.1 1.022 1.021 0.14 100.00 49.63 0.47-)500 1,i'790 1.0 i. 0.997 0.996 0. 12 100.00 45+.09 OT 5 731 00 2. 39 3049 li. Oi 0.O06 0.905 0.60

178 TABLE V-16 (contd.) 1 00. 00 44.52 0.582600 2.463865 1.011 0.894 0.894 0. 05 100.00 42,37 0. 616000 2. 737186 1.011 0.851 0.851 0.07 100.00 36.27 0.694000 3.601920 1.011 C.729 0.729 0.01 100,00 35.63 0(701700 3, 70E124 1,011 0.716. 0*716 0.03 100.00 33.26 C0.727800 4. 119140 1.011 0.668 0.668 0.04 100.00 27.29 0.785600 5.42C554 1.011 0.548 0.549 -0.15 100.00 26. 74 0.792500 5. 58C651 1.01i 0.537 0.537 0.02 100.00 24,66 0.812000 6.199837 1.0il 0.495 0.495 0.07 100.00 19.71 0.854300 8.158639 1.011 0.396 0.396 0.03 100.00 19.24 0.858200 8. 396b73 1.011 0.387 0.386 0.03 100.00 17.59 0.871700 9,331626 1.011 0.353 0353 U0.03 100.00 13. 82 0, 901500 12.281170 1.011 0 278 0.278 0.04 100,00 13.47 0,904200 12; 64C833 1.011 0.271 0.270 0.04 100.00 9,26 0.935800 19.C23209 1.011 0.186 0.186 0.05 125. 00 350.16 0.854500 0.490220 1.079 7.035 6.796 3.40 125.00 247.82 0.b50400 0.527217 1.079 4.979 4.893 1.73 125.00 186.16 0. 519300 0. 56C373 1.079 3.740 3.812 -1.92 125.00 97.46 0.357900 0. 737732 1.079 1.958 1.961 -0.14 125.00 90.29 0.356600 0.7933S1 1.079 1.814 1.821 -0.41 125.00 86,07 0.361300 O. 843240 1.079 1.729 1.740 -0.61 125.00 75.04 0.414800 1.110445 1.079 1.508 1.507 0.02 125.00 72.97 0. 433800 1.194303 1.079 1.466 1.462 0,25 125.00 71.31 0.450600 1.26 SI25 1.079 1.433 1.427 0.38 125.00 63,91 0 5317C0 1.671178 1079 1.284 1.278 0.48 125, 00 61. 85 0, 5534CC 1.797429 1*079 1.243 1 238 0.39 125.00 60,10 0.571500 1.91G364 1.019 1.207 1 203 0.33 125.00 51.92 0.650200 2.515596 1.C79 1.043 1.042 0.13 125.00. 49.74 0.669800 2.705320 1.079 0.999 0.998 0.12 125.00 47.77 0.683600 2. E752d 1.C79 0.960 0.961 -0.17 125.0 0 39.80 0 75010C 3. 786007 1.079 0.800 0.800 -0.01

179 TABLE V-16 (contd.) 125.00 37.77 0.7s5600 4.C71391 1.079 0.759 0.759 0.01 125.00 36.10 0.777600 4*326835 1.079 0.-725 0725 -0.02 125.00 29.14 0.826500 5.6~EC79 1.079 0.585 0.586 -0.02 125.00 27,46 0.837700 6.128206 1.079 0.552 0.552 -0.02 125.00 26. 11 0.846600 6. 512786 1.079 0.525 0.525 -0.01 125.00 20. b65 0.881600 8.575824 1.079 0.415 0.415 0.00 125.00 19.38 c. 889600 9.219750 1.079 0*.389 0.389 0.02 125,00 18.36 0.895900 9, E04531 1.079 0.369 0,369 0.02 125.00 i4.32 C. 920300 12.902 62 1 079 0.288 0.288 0.04 125,00 13,40 0.925800 13.876914 1.079 0.269 0.269 0.05 125.00 12.66 C.930100 14.756137 1.079 0. 254 0,254 0.05 125.00 9.79 0.94670C 19.4297S4 1.C79 0.197 0.197 0.06 125,00 9.14 C.950400 20. E833;3 1.079 0.184 0.184 0.06 150,00 348,13 0.851200 0.522015 1.146 6.994 6.930 0.91 150. 00 198, 74 0. 5740C0 0.616623 1. 146 3. 993 4.024 -0.78 150,00 128.51 0.472900 0.785643 1.146 2.582 2.566 0.63 150.00 109,58 0,476400 0,928183 1.146 2.202 2.200 0.06 150.00 93.25 0.516500 1.182574 1.146 1.873 1.868 0.31 150.00 8488 0, 5554CC 1.396991 1.146 1,705 1.696 0.54 150.00 73.90 0.616000 1.779604 1.146 1.485 1.479 0.41 150.00 66,83 0.658100 2.102359 1.146 1.343 1.339 0.31 150.00 57,03 0.715500 2*678688 1.146 1.146 1.144 0.15 150, 00 50,70 0,751400 3 164C8i 1.146 1.019 1.018 0,07.50.00 42,25 0.797800 4.031345 1i].46 0.849 0.849 0.02 150.00 37,01 0.825400 4*761826 1. I46 0.744 0.744 -0.01 150.00 30.26 0.860100 6. C67381 1. i46' 0o.8 0.608 0.00 150.00 26.22 0.880300 7, 168431 i. 140 0.527 0.527 0.02 150,00 21015 0, 904900 9, 1325C8 1,146 0a425 0ot42 0.03 150.00 18.19 0.919000 10.767568 1.146 0.365 0.365 Oo4 1s 0.00 12.43 0.945600 i6.2350 8 1.146 0.250 0250 0. 04

180 TABLE.V-16 (contd.) 150.00 8.42 0.963700 24.434134 1. 146 0.169 0.169 0.05 150.00 5.66 0.975800 36.778997 1l146 0.114 ~ 0.114 0.04 200.00 346.80 0.877400 0.603971 1.282 6.968 6e940 0.40 200.00 257.87 0.741600 0.66654' 1.282 5, 181 5.101 i 53 200.00 170. 27 0. 648500 0.909221 1.282 3.421 3.395 0.75 200,00 149.34 0,646600 1.033611 1.282 3.000 2.990 0.35 200.00 117.85 0.675700 1.368743 1.282 2.368 2.362 0.25 200.00 106.74 0.695800 1, 556162 1.282 2.145 2.141 0.17 200.00 86.26 0.74450C 2. C60501 1.282 1.733 1.733 0.00 200.00 768 12 0,766600 2.342602 1.282 1.570 1,571 -0.08 200.00 62.50 0.812000 3. 101611 1.282 1.256 1.258 -0.19 200.00 56.25 0.830600 3.526163 1.282 1.130 1.132 -0.21 200.00 44.34 0. 867300 4* 6655C8 1.282 0.891 0.893 -0.19 200.00 39.64 0.881800 5.309812 1. 282 0.797 0.796 -0.17 200.00 30.85 0.908600 7.025827 1.282 0.620 0.621 -0.14 200 00 27.45 0. 918900 7. 991701 1.282 0.551 Oo552 -0.13 200,00 21.16 0*937800 10.582156 1.282 0.425 0*425 -0.10 200900 18. 75 0,945000 12. C29804 1.282 0.377 0,377 -0.09 200*00 12*69 0, 963000 i8 111712 1.282 09255 0.255 -0.06

181 TABLE V-17 V-17. Comparison of Eqn. V-1 and PVT Data for R-i15 Reported by the University of Michigan (136) Density Temp. Pressure ad T Pexp V/0.02681 T/635.56 exp/456.0 P /45calc/ Dev. lbs/cuft R psia 1.1350 470.30 34.40 32 863009 0.740 0.075 0.075 0.38 1, 1350 492.20 36.40 32. 83009 0. 774 0.080 0.079 0.67 1.1350 531.20 39.60 32.863009 0.836 0.087 0.087 0.28 1o 1350 51.30 4 390 32. 6300C9 0,915 0*096 0096 0,40 1.1350 621.80 47.30 32.663009 0.978 0.104 0,103 0.39 1.1350 668.10 51,30 32.863009 1.051 0.112 0.112 0.66 1*1350 715.20 55.10 32. E830C9 1.125 0.121 0,.120 0.45 1.1350 757.90.58.70 32. e3C09 1.192 0.129 0.128 0.58 1.2970 492.20 39.90 28,758300 0.774 0.087 0.090 -2.49 1.2970 535.50 44.50 28. 758300 0.843 0.098 0.099 -1.49 1.2970 579,30 49 10 28.758300 0.911 0.108 0.108 -0,68 1,2970 620.00 52. 7C 28,758300 0.976 0.116 0.117 -1.25 1.2970 668.80 57.40 28. 7583 G0 1,052 0.126 0.127 -1.10 1a 29 70 717. 00 62.10 2 8. 758300 1.128 0 1 6 0.1 3 7 -0.81 1.2970 761*20 66,30 28. 75E3C0 1.198 0. 145 0.146 -0.72 2.9650 534,50 94.00 12.57S938 0.841 0.206 0.207 -0.27 2.9650 569,70 102. 0 12. 579938 0.896 0.225 0.226 -0.23 2.9650 611.00 112.80 12.579938 0.961 0.247 0.247 0.06 2* 9650 661 90 124. 70 12.579938 1.041 0*273 0 273 -0. 01 20 9650 745, 70 142* 30 12. 57S938 1.173 0.312 0.316 -1.20 5. 8850 571.60 179, 40 6 338065 0.899 0.393 0.392 0.36 5.8850 614 10 2010 70 6.338065 0.966 0.442 0.442 O.li 5. 8850 651.30 220. 70 6.338065 1.025 0.464 0,484 -o,07 5. 8850 668, 90 230.00 6 338065 1.052 0.504 0. 504 0.05 5.8850 718.20 253.90 6.338C65 1.130 0o.57 0.559 -0,.34 5.8850 764,40 276,50 6.338065 1.203 0.606 0,609 -0.41 7,0000 575.50 202.90 5. 328502 0.906 0.445 0.447 -0.50 7.0000 593.70 214.60 5. 328562 0.934 0.471 0.474 -0.67

182 TABLE V-17 (contd.) 7.0000 608.50 223* 80 5.328502 0.957 0,491 0.495 -0.87 7.0000 646,10 247.80 5.32E5C2 1.017 0.543 0.548 -0.89 7, 0000 670,20 26 3 20 5.328502 10055 0.577 0.582 -0. 78 7.0000 701.30 282. 50 5.328502 1. 103 0.620 0.624 -0.76 7.0000 730,20 299*90 5. 28502 1.149 0.658 0.663 -0.83 7. 0000 754, 10 31 4 40 5.328502 1.187 0.689 0.695 - 0. 79. 16,6750 619.80 373.00 2*236852 0.975 0.818 0.826 -0.93 16.6750 o46,20 430.10 2.236852 1.017 0.943 0.938 0.58 16. 6750 718. 00 564.30 2. 236852 1. 130 1.237 1*232 0.45 16.6750 802.70 714.20 2.236852 1.263 1.566 1*564 0*15 16* 6750 886.90 866 30 2.236852 1 395 1.900 1*883 0.90 23,0420 638.90 455.60 1.618762 1.005 0.999 0.997 0.19 23.0420 645. 60 475.60 1 618762 1.016 1. 043 1,040 0*26 23.0420 696.90 623.60 1.618762 1. 097 1.368 1*364 0.23 23.0420 766.90 822.10 1.618762 1.207 1.803 1.793 0.53 23.0420 7 86. b0 876.40 1.616762 1.238 1.922 1.912 0.53 23.0420 837.60 1016.90 1. 618762 1.318 2,230 2.215 0.68 27.7210 639.10 465.90 1.345533 1.006 1.022 1.024 -0.27 27.7210 674.40 595.80 1.345533 1.061 1.307 1.311 -0.32 27.7210 743.00 843.30 1. 345533 1.169 1.849 1.856 -0.35 27.7210 E13. 90 1099.70 1.345533 1.281 2.412 2.407 0. 18 27.7210 862.80 1274. 10 1. 345533 1.35E 2.794 2.782 0.42 37.50t40 642.00 487.70 O. 94548 1.010 1.070 1.077 -0,71 37, 5040 663 50 601.10 0.994548 ~ 1 044 1.318 1 334 -1.22 37. 5040 688,00 735. 4 0 0.994548 1.083 1.613 1.627 -0.91 37. 5040 737.40 1008*30 0.994548'1. 160 2.211 2.219 -0.34 37.5040 790.70 1307.00 0. 994548 1.244 2.866 2.857 0.33 42. O010 633.50 439.00 0. E87872 0.997 0.963 0.972 -0.99 42.0100 641. 70 487.00 0, 87872 1.010 1.068 1.085 -1.62 42.0100 663.70 0 626.00 GC.87872 1.044 1.373 1*390 -1.24

183 TABLE V-17 (contd.) 42. 0100 ee8.60 790,00 0.887872 1.083 1.732 1*736 -0.23 42,0100 713.10 948,00 0. 887872 1.122 2.079 2.079 -0.01 42.0100 747,80 1180.00 0.8871872 1,177 2.588 2.567 0.80

184 TABLE V-18 V-1.8. Conmparison of Eqn. V-1 and PVT Data for R-115 Reported by Mcat s et al. (98) Volume Temp. Pressure V T P V/0.02681 T/635.56 P /456.0 P /45.0 Dev. exp exp cac45. cuft/lb R psia 0. 018107 634.842 502.309 0. 675392 0.999 1.102 1.100 0.16 0.018112 644..022 598.274 0. 675571 1.013 1.312 1.314 -0.15 0,018117 653.112 654,533 0.675751 1.028 1,523 1,527 -0.25 0. 018i22 661. 896 79u.057 00675930 1.041 1.733 1.733 -0.04 0.018126 671.670 894.692 0.676109 1.057 1.962 1.964 -0.09 0, 018131 680e 526 993*156 0.676288 1.071 2,178 2 173 0.22 0.026568 635.508 459.103 0. 990981 1.000 1.007 0.999 0,73 0. 026575 644.616 507,453 0,991220 1*014 1 113 10109 0,36 0.026583 653. 688 555.656 0O991519 1.029 1.219 1.218 0.07 0.026587 661.014 595.482 0. 991698 1.040 1.306 1.306 0.02 0 026597' 671*688 653,678 0.992057 1,057 1.434 1.434 -0.01 0.026603 f80.688 702.616 0 992296 1*071 1.541 1,541 -0.04 0,026611 689.688 751.259 0* 992595 1.085 1,647 1.649 -0.11 0.026618 698. 688 800.491 0-992834 1.099 1*755 1 757 -0.09 0.026626 707.634 849.282 0,993132 1,113 1,862 1.864 -0.08 0,026640 725e706 949,068 0.993670 1.142 2.081 2.080 0,06 0,027773 63 5. 58 459. 544 1,035912 1,000 1.008 1.000 0.73 0. 027779 644*634 504*367 1* 036151 1.014 1.106 1 103 0.26 0.027787 653.688 551.394 1,C36450 1.029 1.209 1.206 0.27 0.027795 662.670 597.098 1.C36748 1.043 1.309 1.308 0. 13 0,027803 671.706 643,538 1. C37047 1.057 1.411 1.410 0.09 0.027818 689.634 735.241 1.037585 1.085 1,612 1.613 -0,01 0. 027824 7017, 598 827826 1. 037824 1.113 1*815 1.815 0.00 0.027837 725.598 920.117 1.038302 1.142 2.018 2O018 -0,01 0. 02 7861 743.688 1013, 5d3 1*039198 1.170 2.223 2*220 0.10 0.030486 635.688 456.0i7 1. 137125 1.000 1.000 1.001 -0.11 0.030496 644. 42 458.047 1,13T7484 10014 1*092 1.093 -0.05 0.03050 53. oj88 539.196 1.137842 1.029 1.ld2 1,183 -0.04

185 TABLE V-18 (contd.) 0,030522 671.688 621.200 1.13644C 1.057 1.362 1,364 -0.11 0.030538 689. 706 703.057 1. 139037 1.085 1.542 1.544 -0.13 0.030552 707.688 783.444 1.139575 i.113 1.718 1.723 -0.26 0.030570 725.688 863.684 1.140232 1.142 1.894 1.901 -0.35 0.030586 743.778 943.777.1. 14C829 1.170 2.070 2,079 -0.45 0.030602 756.378 1001.091 1.141427 1.190 2.195 2*202 -0,32 0.037664 635.688 451.608 1.404856 1*000 00990 0.994 -0.32 0,037687 653*706 517.593 1.4C56S3 1.029 1.135 1.132 0.24 0,037706 671.688 580,345 1.406410 1,057 1.273 1.270 0.25 0.037727 689.724 641.333 1.407186 1.085 1.406 1.406 0.05 0.037744 707.706 702.175 1.407844 1.114 1.540 1,540 -0.03 0.037765 725.742 762.428 1.4C8620 1.142 1.672 1.674 -0O 13 0.037786 743 742 821.947 1.4C93S7 1.170 1.803 1.807 -0.23 0.037805 761.688 880.731 1.410114 1.198 1.931 1.938 -0.33 0.049262 630.054 418.395 1. 837432 0.991 0.918 0.920 -0.27 0.049270 635.670 433.238 1.837731 1.000 0.950 0.951 -0.07 0.049298 653.940 480.265 1.838806 1.029 1.053 1.050 0.31 0.049326 671.688 523.471 1. 63S822 1.057 1.148 1.145 0.26 0.049351 689.580 567.413 1.840778 1.085 1.244 1.239 0.39 0.049375 707.616 609.002 1.841674 1.113 1.336 1.334 0.14 0.049403 725.580 651.180 1.842690 1.i42 1.428 1.426 0,11 0.049428 743.706 693.063 1.843646 1.170 1.520 1.519 0.06 0*049455 761.616 733,183 1.844662 1.198 1.608 1.609 -0.10 0,049481 779.724 774,626 1.845618 i-227 1.699 1,700 -0.09 0.049495 788.778 794.613 1*846155 1.241 1.743 1*745 -0.15 0.049508 7970778 814.011 1.864633 1.255 1.785 1.790 -0O26 0 070414 617.832 351,528 2.62c405 0.972 0.771 0.772 -0.15 0.070452 635,688 380.332 2.627839 1.000 0*834 0,834 0.05 0.070494 653.688 409.284 2.629393 1.029 0.898 0*895 0.31 00 070532 671. 8o 437, 941 2Z630327 1.057 0.9o0 0.956 0.50

186 TABLE V-18 (contd.) 0.070569 689.790 463.218 2.632201 1.085 1.016 1i.015 0.11 0.070603 707.544 490.112 2.633455 1.113 1.075 1.072 0.22 0.070643 725.616 515.977 2.634949 1.142 1.132 1.131 0.08 0.070680 743* 7,2 541.695 2.636323 1. 17'0 1. 188 1.188 -0.02 0.070718 761. 688 568.000 2.637757 1.198 1.246 1.245 0.08 0.070755 779.706 593.571 2.639132 1.227 1.302 1.30i 0.08 0. C70794 797.706 618.995 2.64C566 1.255 1.357 1.356 0.10 0.107293 600.012 266.438 4.001985 G.944 0.584 0.582 0.47 0,107397 635.562 300.827 4.C05868 1.000 0.660 0.653 0,95 0.107530 671i634 333.599 4,010828 1.057 0.732 0.724 1.02 0.107639 707.598 365.343 4.014890 1.113 0.801 0.793 1.03 0O 107698 725.670 380.332 4. C17101 1.142 0.834 0.827 0. 86 0.107698 725.580 380.165 4, C17101 1.142 0.834 0.827 0.84 0.107755 747,162 397.821 4.019192 1 176 0.d72 0.867 0.64 0.107871 779.688 426.478 4.023554 1.227 0.935 0.926 0.96 0.107964 808.668 450.432 4. C27019 1.272 0.988 0.979 0.93 0,107330 587.610 252.477 4.003359 0.925 0.554 0.556 -0.37 0,107343 591.372 257.474 4,003837 0.930 0,565 0.564 0.20 0.107399 609.192 274.374 4. 005928 0.959 0.6.02 0.600 0.27 0.107461 62E. 3C8 292.156 4.0CE258 0.989 0.641 0.639 0.33 0.107577 665. 172 325.222 4.C12560 1.047 0.713 0.711 0.27 0.107706 7C5.006 360.640 4. C17400 1 109 0*791 0*788 0.41 0. 107815 738.612 389.150 4.021463 1.162 0.853 0.850 0.34 0.107936 775. 278 420.159 4 C25944 1.220 0.921 0 918 0.40 0.160676 564. 102 181,643 56 593149 0.888 0.398 0.398 0398 04 0.160849 597.906 202.364 5.999601 0.941 0.444 0.441 0.71 0.161006 634.662 223.085 6.005457 0.999 U.t89 0.436 0.74 0.161205 673.362 243.660 6. C12866 1.059 0.534 0.532 0.50 0.161368 709.308 262.764 6. C18960 1.116 0.576 0.574 0.46 0.e 161543t. 744.948 282. 310 6 C25472 1.172 0e619 0.614 0*78

187 TABLE V-18 (contd.) 0.161716 779.544 300.239 6.031925 1.2z7 0.b58 0.653 0.79 0,161855 806*094 313.760 6.C37123 1.268 0.688 0.683 0.79

188 TABLE V-19 V-19. Comparison of Eqn. V-1 and PVT Data of R-502 V T P V/0.028622 T/638.23 Xp/593,79 P /593.79 % Dev. cuft/lb R exp exp calc cuft/ib Rpsia 0.582420 541.140 81.950 20.3486e3 0.848 0.138 0.137 0.71 0.466240 5416130. 9S.620 16.289567 0.848 0.168 0.167 0.39 0.404380 541.140 116,940 14. 128293 0.848 0.197 0.189 3.9b 0.3C714u 541.140. 141.290 10. 73090o 0.848 0.238 0.238 -C.04 0.248410 541.140 166.23 0 E. 67898B 0u848 0.280 0.281 -0.47 0,21t550 541.130 17e.800 7*565858 0.848 0.301 0.311 -3.39 0.577660 6397.490 l0C.030 20,182377 1.002 0.168 0.169 -0.06 0.461020 639.490 123.530 i6*107190 1.002 0.208 0.208 0.06 0.358770 634.640 154*190 12.534763 1.002 0.260 0.261 -0.65 0.345300 639.500 16. 530 12. 064146 1.002 0.270 0.270 -0.02 0.287570 63s.620 168.540 10.047167 1. 002 0.318 0.318 -0.14 0.27(680 639.500 193.430 9.771504 1.002 0.326 0.326 0.02 0.225160 o3c.530 232,430 7. F66676 1.002 0.391 0.392 -0.13 0. 172130 639.610 288.490 6.013905 1.002 0.486 0.487 -G.33 0.139340 639.610 338.24C 4. 86283 1.002 0.570 0.572 -0.43 0,111480 639*630 393.490 3.894906 1.002 0.663 0.668 -0.79 0. 054600. 39. 590 555.3o0 1. 907624 1.002 0,935 0.947 -1.2S 0.049090 639.600 5o9.260 1.715114 1.002 0.959 0.973 -1.49 0. 045 40 639,0600 576.260 1. 58d40 9 1.002 C. 970 0.988 -1.77 0.042200 63S.600 5el8.7C 1.474390 1.002 0.980 0.998 -1.84 0.037760 639. 620 586.260 1.319265 1.002 0.987 1.008 -2.0 0. 037560 639). 5 80 586.770 1.312277 1.002 09o.a8.U008 -2. 00 0.02318i 63. 570 590. 2EC C. 809867 1.002 0.994 1 026 -3.25 0.0 22820 639.540 594.270 0. 7S972 1.002 1.001 1.029 -2.80 00. -21'70 3g. 600 b03.260 0,. 746628 1.002 1.016 1.054 -3.73 0.020370 639.560 624.270 0.71160o 1.002 1.051 1.090 -3,64 C. 019l8o 63 Q.570 634.260 C. 694571 1.002 1.068 1.118 -4,62 i).01 0300 639.600 729. 610 0. C393c6 1.002 1.229 1.288 -4.80

189 TABLE V-19 (contd.) 0. 017380() 639.5)0 80c *47J 0.617707 1.00U2 1s358 140U9 -3.77 0. 01;080 039,560 930.270 0. 593251 1.002 1.567 1.618 -3*25 0. 016430 63'),550 i06Sf.27U 0 574034 1.002 1.799 1,853 -2 91. 01i5'7600 639,560 1224.27C 0.557013 1,002 2.062 2,123 -2*98 0,01.C510 6;3i5.540 1418. 20 0. 541 S1 1.002 2*389 2.459 -2.94 0. 015180 63- 570 1 t07229 0 0, 53)361 1.002 2*698 2*766 -2.51 0,014830 639. 5EO0 1837*790 ), 518133 1,002 3*095 3.158 -2.05 0, 0 14660 639.5eo 1975.290 0. 512193 1.002 3.327 3,377 -1.53 0 03 7610 664.060 707, 740 1.314024 1.040 1 192 1.2i2 - i 65 0 028910 664. 040 751* 740 1. 01C062 1 040 1 266 1.298 -2 50 0.025060 664.0/50 782.540 0. 75550 1.040 1.318 1.356 -2.88 0.022280 664.040 634,040 0.778422 1.040 1.405 1.436 -2.23 0,020380 664.030 9C9S740 0. 712040 1.040 1.532 1.577 -2.96 0.018730 664.030 1051.640 0O654392 1.040 1*771 1*854 -4*68 0.01 1050 664.040 1366*820 e O 595696 1.040 2.302 2.423 -5.27 0.016240 664.060 1650.220 0.567390 1.040 2.779 2.857 -2 79 0.015630 664*050 1962.320 0. 546063 1.040 3,305 3*268 1*10 0,1 C8940 666 150 433.4CC 3. 8061363 1.0U44 0.730 0.734 -0.57 0*086400 66c6130 503. lt0 3, 01i 657 1.044 0.847 0.855 -0 t6 0,063970 666.140 593.460 2,23499'4 1.U44 0.999 1.009 -0.98 0.043500 uo6,.150 685.260 1. 51.9810 1.044 1*161 1,177 -1o42 0. 033780 666. 1 40 73bo960 1.180211 104 4 1.241 1.265 -1 95 0.1 07/4, 00 708e990 488, 710 3. 752356 1.111 0,823 0,831 -1.63 O007 O 500 700.960 563o510 3. 073161 1.111 0.949 0.961 -1.27 0.071050 7C8, 970 649.6C10 2.48235o 1.111 1.093 1.109 -1i4o 0.055 68 0 703.960 752.010 1.9453557 1.111 1 266 1.285 -1.45 O.04083 0l) 7C ~*040 662.510 1, 42t272 1.il1 1.486 1e.5i -1.95 0.033170 70839503 S77,CCO 1. 158899 1,111 1.645 1.685 -2.41 0.038760 712.500 924.660C 1,354z'03 1,116 1.557 1.584 -1.71 00o 32100 712.540 1 016.600) 1. 12151i i.l11 1,712 1.750 -2.24

190 TABLE V-19 (contd.).O2tU0'5 712.5o0 1151.6CC 6.910139 1.116 1.939 1,978 -1.58 O.022d50 712.570 ib89.3Co 0. 7'337 1l116 2.171 2.185 -0.61 0, 020P30 712.580 1445*CCC 0.727762 1.116 2,435 2.465 -1.25 0. 01 80 712,570 1613.300 C. 660595 1.116 2.717 2.827 -4.05 Ol.01d680 712.590 1759S.C00 0. 52645 1.117 2,962 3.148 -6.27 0.017670 712. o10 i956.2C0 0.624345 1.117 3.294 3.569 -8,34

191 TABLE V-20 V-20. Comparison of Ean. V-8 and Vapor Pressure Values for R-22 Reported by Booth and Swinehart (17) t P P Percent t psia paeq Deviation F psia psia 72. 63 138.000 141,788 -2.75 88~ 52 1754 90C 179. 209 -1o 17 88070 177.400 i79. 672 -1 28 104.18 21 8. 500 222. 900 -2 O01 105o 38 225.000 228o381 -1l50 i22o54 286. 000 28 3, 578 0.85 140.54 353. 900 354 143 -0*07 148o46 376f 700 38g.030 -3.27 159.06 435,60C 439.700 - *94 1 60o 70 45 Oo 000 447L 96d 0.45 177o 98 531. COO 54 20 3 8 -2.19 i77,0)8 528.600 542. 638 -2.66 185o 72 576, 500 58c,699 -2 32 195.I80 6bo 200 85d 55a 1 -00 202 10 671 500 7014c,5 -4,47 20 2. 4 6 8 8 C CC 705,476 -2.27 203 54 697 200 12.1 -2, 15 2'4~ 80 706o b,0 72 i. 15 - o i 205, 3 4 7iC7 960 725 703 -2 5

192 TABLE V-21 V-21. Comparison of Eqn. V-8 and Vapor Pressure Values for R-22 Reported by Benning and McHarness (12) t P P Percent F psia eq Deviation psia -78,27 5.100 5 053 0. 91 -41 i 9 14 800 14,752 0,33 23.00 61. 700 61.088 0.99 77o 27 152,400 1510 c72 0.28 i68*62 488. 900 489o 598 -0.14 198, 68 674, 800 676*765 -0.29

193 TABLE V-22 V —22. Comparison of Eqn. V-8 and Vapor Pressure Values for R-22 Reported by Du Pont (46) t P P Percent F psia psieq Deviation F PSl& psia — 1550O0 O209 Go209 011il -135t 00 0,'566 Co565 0.09 115*00 1,3.5 1 344 0oCS -950 00 2,373 2.871 0. 07 -7 50 0 5, 61l 5.607 0.06 -550 0 10.166 IC.*160 0.06 -3 5. 0C 1 7,290 17o 28 1 0o 05 — 15O00 27.865 27, E52 0. 05 10.00 47 464 47.445 0 04 30.00 69 591 69o566 0o 04 50,00 980 727 S8a 694 Oa 03 70.00 136.120 i36 C81 0,03 90 00 18 39 09-0 1 83~ C42 0.03 1i0. 00 241i040 240 79 0.03 1 30 00 31 lo 500 3i1,41? 0.03 150 0 J 0 396o 190 396o 10~ 0 02 7.070,00 497, 260 47 149 0002 i90: J00 o17 590 61t 7oO) O02 204, 81 721, 910 721.69i. 0,03

194 TABLE V-23 V-23. Comparison of Eqn. V-8 and Vapor Pressure Values for R-22 Reported by Downing (42) t P Peq Percent F psia psia Deviation -50 00 11 o 700 11. 667 00 28 -40o00 15.300 15, 214 0.56 -30o 00 19.700 1 S 563 0.70 -20o 00 250 CGC 24. 833 0.67 -10.00 31.300 31.148 0*48 000 38 ~ 800 38.640 0, 41 1 01 00 47.600 47.445 0*32 20.00 58. 000 57.705 0. 51 30 00 69. 900 ) 69 566 0.o 48 40,00 83* 700 83. 177 0. 62 5000 99.400 18 694 0O71 600 00 1 7.200 116 2 75 0 79 70,00 137.200 136.C8i 0.82 8000O 159,700 15E.,279 0.89

TABLE V-24 V-24. Comparison of Eqn. V-8 and Vapor Pressure Values for R-22 Reported by Zander (140) t P P Percent eq F psia psia Deviation -93.69 3.000. 007 -0*25 -79.46 4o880 4o 663 0*34 -79.39 4, 890 4. 74 0.32 -J8 5 9 92 9198 034 -41.43 14o 7 20 14.o 660 0,41 -380 12 1 60 020 15o967 0.33 -40 07 35. 520 3 5.440 0. 22 13. 76 51o200 51fo 125 0, i5 32401X 72,240 72 156 0. 12 68e00 L32, 000 13 1 934 0, 05 76. 98 L51o 500 151. 313 Oo 12 85*50 L71* 700 171. 570 0* 08 104. 16 223o000 222.840 0.07 104w2 5 223* 300 223o 111 0.08 122 7 2 284. 500 284 228 0,10 140 20 353~ 0.Q 3529706 0O11 149o,31 393*3CG0 392.9 22 0.io 158,o 20 U 435o 9 43'35t412 O, 1 1 67.23 482 9C(C 482. t083 0 }. 7 185.O00 530.60)0 55. 305 0, 2i i94j25 646 t0 4 j i90) O.s 199.2 7 7700 6 80 90 2 -.? t 7 201k. i. 3 709o, 200 70t;.47,,C'

196 TABLE V-25 V-25. Comparison of LEn. V-8 and Vapor Pressure Values for R-115 Reported by the University of Michigan (136) t P Pe Percent psieqa Deviation F psia psia!35o 54 0, 551 0. 546 0o 87 -1i13.71 1,30 1. 377 0,26 -46.80. i 1.682 11.766 -0, 72 -3o80 31o645 32.154 -1,61 10o 65 42. 335 43.051 -1i69 62c9i 106,020 106 o 896 -0,83 03733 152o370 153-548 -0.77 11.3o27 216.150 218.030 -0*87 140 56 302 860 305.573 -0 90 168.82 41S 860 421, c77 -0.50 72.o 4 436*090 43*531~2 -0.74 175 89 4 3 000 456.000 -0.66

197 TABLE V-26 V-26. Comparison of Eqn. V-8 and Vapor Precssure Values for R-115 Reported by Mears et al. (98) t P P Percent F- psia ieq Deviation ~F psia~ psia -89.07 3 2t38 3.366 0.93 -59 46 8 zt460 8. 349 1.31 -39.50 14,370 1 4.187 1.27 -21o59 2].,750 21.793 -0.20 -3 59 32 33 323303 2.295 0. 11 i402 46, 590 45. 953 1.37 30.76 63.050 62. 24 0. 68 31.85 64 810 630 848 1248 49.68 87. 150 86 5=33 0. 71 67.21 115 Sq0C 114.222 1045 85,10 148.100 148. 758 -0.44 85.93 150,500 150. 528 -0.02 94o 96 170.3800 170. 803 -0. 00 102.67 188 600 189, t54 -0*56 103,87 192o500 192o 721 -0 11 109, 25 2C5. 700 206. 23 -0. 59 112.94 217 500 217o 102 0.18 12l, 7 5 243. 400 242. 903 0o20 i28. 0 5 2(0, 60 262. 704 -0.8 13 0o, 9 8 273.200J 27 2, 312 0. 2 134 63 283. 3CC 284.647 -0.48' 3C 938 304,100 303.z 7t 0.20 145 38 321. 8() 23~424 -0. 5 0 147,6 3 32 100 3 2. C i -0 24 14902 338. 300 337.421 0. 26 156] 9 2, 3c8 /o(4jC 3b9.3 93 -0.2 7 1 5,, 04 372 000 37 4,i 09 -0, 4 162.32 391. 1. (0 392. 567 -0o3u

198 TABLE V-27 V-27. Comparison of Eqn. V-8 and Vapor Pressure Values for R-115 Reported by Aston et al. (4) t P P Percent tF pseia pseq Deviation F psia psia -i394 58 00453 (0.45 3 0.20 -130, D9 0 685 C 682 0.45 -116o38 1,247 1o 238 0.66 - 85.17 3 9872 3 830 1. 09 -68.85 6*434 6 367 1.o 03 -54.07 9 786 90 69 1 0*9 7 -39o74 14.21 1.9 102 0. 82 -38,62 140623 14. 504 0.82

199 TABLE V-2.8 V-28. Comparison of Eqn. V-8 and Vapor Pressure Values for R-115 Reported by Downing (42) t P P Percent F psia psieq Deviation F psia psia -50000 10.700 lC 8.13 -1.06 -40 00 1 3o 900 14,010 -0.79 *-30 00 17 700 17* 905 -lo 16 -20.00 22. 400 22*596 -0 6b8 -10.' 00 270 28. 188 -1*03 0 o0 3-4 400 34 7 8 7 -1.13 100 0 42.000 4 2. 507 -1*21 20 00 50,800 51o465 -1.31 30.00 61. 000 61.781 -1.28 40 00 72 600 73*579 -1, 35 50.00 85, 900 E6 S88 -. 27 60*00 o00. 800 102o 140 -1.33 70o 00 117.700 11 o 170 -1.25 80,00 136. 600 138. 2.i9 - i9

200 TABLE V-29 V-29. Comparison of Eqn. V-8 and Vapor Pressure Values for R-502 of This Work t P P Percent eq F psia psia Deviation -151.12 0.400 0.381 4.78 -129088 1. Cc7 1.015 7.54 -118.68 1.712 1.6(9 6.01 - 117* 14 1.7i9 1.709 0*57 -109.65 2.2S6 2.277 0.86 -1 C9.60 2.3C7 2*281 1.15 -109.51 2* 32S 2.288 1.74 - 109. 9 2.445 2.316 5.28 -108.83 2.3c8 2 34 7 2.14 -103 45 2.958 2*856 3. 44 -980 03 3 481 3.457 0.69 -97.37 3.523 3.537 -0.40 -80 889 4.8.1 4.702 3.06 -8. 49 4. 9 4 1 4. 764 2.99 -7bo.45 6.4 52 6.546 -1.46 776* 95 b 6.890 6.85,4 0.53 -71, 57 8.322 8.052 3.25 -6- 7 71 83 916 9.0 11 -1 06 -65.82 9, 338 9. 512 -1.87 -56.95 11.860 i2.169 -2,60 -55. 1 12.304 12,764 -3. 73 - 54 85 12.901? 12. 880 0. 1 6 -49,71 1.2 5 14.753 -3.42 -4 30 2 16 72 5 17.503 -4.65 983.46 2'24.3,C 2 30. 204 -2.60 9 8. 48 2 2 6,5 3 C 230. 2 6 5 -1.65 938. 58 225.3 5C 23(0. 574 -2.32 1Co.52 232.050 236.619 -1.97

201]. TABLE V-29 (contd.) 1ouoa54 233, CC'236.6l8 -1,55 102. 71 240.780 243,583 -1* 164 110. 85 266 63C 270 5 18 -lo 57 120 98 302. 7 iC 307 830 - 1. 67 i 30o 04 33is0EC 344070 -2 o 6 8 130 ) 05 330, 62C 344 i 11 -2 23 1. 3 3 9 o 9630 345.o 2 1 1 39o 1 379o 1 CC 385.369 -1. 65 i470 26 414.900 It21. S 76 -1. 71 149o 22 424o2 C0 431.660 -1 o 76 150o 38 4 4330 O37 476 -i * 01 150o42 43C,300 437.677 -1I 71 152o 41 4t36 3 60 447 807 -2 51 1;52. 50 435 5 5 5C 4 4/8 269 -2 e 92 163 27 S47,1 0 5C6 598 -9. 91 1 64 6r) 4 9 4 0 5 1 4 5 8 C -2. 93 169o 55 52704 5 54 3,v56 -3.06 179.65 5 8.8CO 6C o,500 -3 535 179a 79/t.v5 7 9+ o 3 4 0 9 1 4 - 536 179 4 7 5 58 9. 34 6C9l83 -3o 3 7

202 TABLE V-30 V-30. Comparison of -Ecn. V-8 and Vapor Pressure Values for R-502 Reported by Badylkes (5,6,7) t P P eq Percent F psia psia Deviation -112.00 2.121 2. 08 1.74 - i03 00 2o 942 2.902 1 35 - )4. 00 4,014 I/ 3 $ 36 i5 *- 85o(C0 5,382 5.332 US2 -76 00 71 o0 C6 7. 054 0.73 -67o00 9.250 91917 0,58 -58,00 11.880 11. 329 0.43 -49 0CO 15, 07C t15027 0.28 -40.00 8. 18oCC 18. O3 0*16 -31 00 23,450 23.440 0.04 -22o03 2681C 2e. d23 -0. 06 -3,00 35*07C 35,126 -0.16 -4 GO 42.,320 420429 -0.26 5.00 50.66C 50. 837 -0.35 14 00 6 0,180) 60.452 -0.45 23,00 70 o9 0 71.381 -0.55 32. C3O 3. 190 83.729 -0.65 4,I0.ce EC 97.610 -0.75 50. )d g00 112191) 3 0i 3 7 -0.84 59 0 C 12 i i i30. 3,47 -) 94 o68~) [14381 CO i49, b2 -1. 01 77,00 i8. 90C 170. 78 -1.12 86, 00 191.8CC 1 94. 11 - 21 95,00 2!70 CO0 2 19 722 -1.25 1 04.0 0 244, 5C0 2 47. 75 -1.33

203 TABLE V-31 V-31. Comparison of Eqn. V-S and Vapor Pressure Values for R-502 Reported by Loffler (86) t P P Percent F psia pieq Deviation ~F psia ~psia -112,00 2. 146 2.084 2.89 -103.00 3.000 2.902 3. 25 -94, 400 4.1 CO 3*968 3.22 -8,5. 00 5.52 6 5. 332 3, 50 -7t.CO 72 C 2 7,054 3.63 -o7e00 9.550 9,197 3*70 -5 8.00 io2 90 il.829 3.75 -49.00 15l 580 15. 2 7 3.55 -40.0o (39 9.5 9C 1 9E018.69 3 48 * -31.00 24,4CO 23*440 3*93 -22. 00 2 9. EC 28. d28 3. 84 -1 3.00 36.4 5 35 126 3 63 -4.00 43.040 42 429 3.44 5. 00 52.6 10 50. 837 3.37 14. t00 2*.460 60.452 3,21 23o00 73.7 70 7i.#381 3.24 32.00 E6.410 83. 729 3.10 41. 00 1 CO O 597,610 2 88 50 o00 1I 1.2 C 113.137 2,64 59 00 i353.7CC 130.427 2. 45: O0() 153*.1C 149. 02 2,28 77.00 ] 7' CC 170.7 87 2.18 36 oCO! 09-.0uo 14,114.96 95 00 2 23.70 219. 722 1 78 3.0. O0 25:' C 2(47,756 1.64 11 3 o O.0 02 ~ 5 CO 2 7 0. 7 1. 764 122,00 3h:. 6( 3;C 3 ].75. 1.28 i3]..00 352.t() }otC 0 3 C 348,03 1 4

204 TABLE V-31 (contd.) 140. 0 391. 7CC 387.o06 1 e05 149 00 434.4CC 4 0.,564 0. d8 1 5800 480o 0CC 477o302 0.75 167. CO 531 100 5282 72 0.53 176.00 585 8CC 584.166 0.28 180 90 617.30C 6'17.092 0,03

205 TABLE V-32 V-32. Comparison of Eqn. V-8 and Vapor Pressure Values for R-502 Reported by Downing (42) t p P Percent F ps ia psiaq Deviation psia -20.00 29.8CC 30. 146 -1.16 -.00 37, 6 00 7,.4444 0*42 - 1. o 0 36 9:CO 37,444 -1.47 0O 0 463 00 46o 023 -0.05 Xo 00 56.0 CC 56 023 -0.04 20f.:00O 67. 500 67*585 -0o13 30o00 5Co 1 CO 80.857 -0. 94 40. 0 95~ 2 CC 95 $S 89 -0.83 s40Xf00 957C 9C5. 989 -0.30 500 i 1 Il1(00 13,137 -1.38 6 00 i 3 S C i 4o 462 -1.27 70G 0O 150,7 CO io0 o131 -2, 28 80 OU0 17 O 17. 38 -1 2 90,0-J 201o i00 2C 5205 -2.04. o0 30. W 0 224,987 -1, 81 1.t0u 0 (., 2.60, 5CC 267. 8& 7 -2 83'!0 O' J 2 6% r q r 267.8 72 -1.0 8 332. 70 C -3,, 37 vo 42 9(3 4'[ 4aUo54 - (0J

206 TABLE V-33 V-33. Comparison of Eqn. V-8 and Vapor Pressure Values for R-502 Reported by Du Pont (47) t P P Percent F psia eq Deviation psia -100 00.3230 3.228 0.07 -.f80G co 6 2830. 241 0. b2 -60 00 iI.280 11,198 0.72 -40.00 18,970 18e.3869 0053 -20.00 30*22C 30. 14b 0.25 00 0 45. 946 4 6. 023 -0 018 20.00 67o14C 67.585 -0,46 40.00 94*.9C0 95 98*3 -lo15 50.00 1 30030U! 32*462 -1.06 80o00 1746&00 78 i7 318 -2o 13 100400 2 29 10)0 234o9 7 -2.57. 20, 00 295.CC 304. 092 - 3.08 1.4tJ 0'0 373.8 0C;0 387e606 -3,69 1 i,0o 0 6 7,. CC 48,o 244 -4. 4,8

207 TABLE V-34 V-34. Comparison of Eqn. V-19 and Saturated Liquid Densitv Data for R-22 Reported by Benning and McIlarness (14) t d deq Percent F lbs/cu.ft. lbs/cu.ft. Deviation -92,20 9 3.07L4 93.050 0.03 ~ -2 0'3.o1 r3S, E 1 8 6. 850 -0.9'5, 24.57 81.091 81.075 0.02 79. 14 74. 29) 74.237 0. 3 122. 41 67.672 67.648 0.94 152.01 61.929 61.973 -0. 7 1.75.59 55. 986 55.966 0 0t.0 189, 16 51.02I( 23 51.062 -0.03

208 TABLE V-35 V-35. Cornmparison of Eqn. V-19 and Saturated Liquid Density Values for R —22 Reported by Du Pont (46) t d d Percent eq F lbs/cu. ft. lbs/cu.ft. Deviation -155.00 98..669 98.671 -0. O -130.00 96.480 96. 482 -0.00 -110.00 9 1.684 9 4.686 -0. 33 -90.00) 92.843 92.845 -0.00 -70.-00 90.952 90.954 -0.30 -50.00 89..00o4 89.006 -0.00 - 30.00 86. 9 1 86.993 -0.00 -10.00 84901 84.904 -0.00 10.00 82.724 82.726 - 0.D 30. 00 80.1441 80. 444 -0, 00 50.00 78.033 78.035 -0.30 70.00 75. 469 75.471 -0.00 90.00 72.708 72.711 -0.330 110.00 69.639 69.692 -0.00 130.00 3 3 1 2 66.316 -0.0 1 10.00. 402 62. 406 -0.01 7 0.00 57.%8t1 57.587 -0.31 190.00 50.,77 50. 86 -0.02 2<)W 4.:.1 32.760 34,t.497 -5, 30

209 TABLE V-36 V-36. Comparison of Eqn. V-19 and Saturated Liquid Density Values for R-22 Reported by Zander (140) t d deq Percent F lbs/cu.ft. lbs/cu.ft. Deviation 32.00 79.987 80.209 -0. 2 44.83 78.4'45 78.671 -0.29 54.66 77.234 77.453 -0.28 61.30 76.391 76.608 -0. 23 62.85 76. 198 76.408 -0.28 65.79 75.811 76.026 -0.28 67.06 75.649 75.860 -0.28 68.13 75.517 75.719 -0.27 76.59 74. 388 74.586 -0.27 34. 54 73.301 73.437 -0. 25 86.02 73.077 73.278 -0.28 88.47 72. 752 72.930 -0. 24 95.40 71.747 71,924 -0.25 104.47 70. 380 70.557 -0.25 112. 169 69.169 69.342 -0.25 113. 20 69.019 69.179 -0.23 121.03 67.758 67.883 -0.18 123.75 67. 265 67.418 -0.23 131.50 65. 916 66. 044 -0, 19 137.21 64.899 64.981 -0. 13 1142. 41 63. 837 63.970 -0.21 152.51 61.771 61.863 -0.15 157.17 60.729 60.815 -0.14 161.55 59.749 59.775 -0,D4 171.12 57.189 57.275 -0.15 173.8R G56.415 56.479( -0. 11 176.90 55.10 55,561 -0.09 187, 63 51.652 51.717 -0.13

210 TABLE V-36 (contd.) 18S.83 51.165 51.206 -0.08 191.55'49.935 49.958 0.05 196.61 47.207 47.144 0.13

211 TABLE V-37 V-37. Comparison of Eqn. V-19 and Saturated Liquid Density Values for R-115 Reported by the University of Michigan (136) t d d eqPercent F lbs/cu.ft. lbs/cu.ft. Deviation 172.83 49.199 49. 337 -0. 30 153.50 61.655 61.950 -0.48 119.09 72.200 72.369 -0.23 101.97 75.634 75.818 -0. 24 68.32 82.333 81.883 0.55 13.62' 90. 130 89.962 0. 19 10.71 90.455 90.353 0. 11 -36.04 96.423 96.279 0.15 -39. 15 916.860 96.654 0.21 - 14 3. 21 108. 247 108.268 -0.02

212 TABLE V-38 V-38. Comparison of Eqn. V-19 and Saturated Liquid Density Values for K —1]5 Reported by Mears et al. (98) t d d Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation -104.33 103.937 104.100 -0. 13 -3.71 92. 156 92.248 -0.10 16.43 89.528 89.582 -3. ~ 44.90 B5.433 85.53 8 -0. 12 62.53 82.729 82.821 -0.11 76.98 80.170 80.431 -0.33 85. 94 78.559 78.858 -0. 3 9.4. 96 77. 005 77. 187 — 0.24 103.28 75.375 75.555 -0. 24 112.98 73.315 73.515 -0.27 130. 35 69.189 69.358 -3. 211 144. 52 65. 543 65.207 0.51 1 tlq, 27 6 4.026 63.567 0. 72 153.71 62. 059 61. 865 0.31

213 TABLE V-39 V-39. Comparison of Eqn. V-19 and Saturated Liquid Density Values for R-502 Reported in This Work t d d Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation -161.80 1011.220 104.219 0.00 -67.32 )1l.4 1 ) 9t4.5>39 -0. 19 32.00 32.560 82. 642 -0. 10 50.55 7 9.6 80 80.033 -0.44 ~0.25 73.500 78.595 -0.12 63.79' 78.020 -78.055 -0.05 641.83 77.9140 77.895 0.06 102.01. 71.580 71.573 0.01 116.25 68.760 68.718 0.06 157.86 57.290 57.101 0.33 16! 78 57 2 0 1. 71 5 1.00 176,22 46.270 44.926 2.90

214 TABLE V-40 V-40. Comparison of Eqn. V-19 and Saturated Liquid Density Values for R-502 Reported by Badylkes (5,6,7) t d deq Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation -112.00 100.530 99.284 1.24 -103.00 99.090 98.362 0.74 -94.00 98.160 97.428 0.75 -85.00 97.240 96.483 0.78 -76.00 96.190 95. 525 0.69 -67.00 95. 160 94.554 0.64 -58.00 94.160 93.569 0.63 -49.00 93. 170 92.568 0.65 -40.00 92.080 91.552 0.57 -31.00 91.130 90.518 0.67 -22.00 90.080 89.464 0.68 -13.00 89.050 88.391 0.714 -4.00 88.050 87.294 0.86.5.00 86.950 86.174 0.89 14.00 85.870 85.027 0.98 23.00 811.820 83.851 1.14 32.00 83.680 82.642 1.24 41.00 82.470 81.397 1.30 50.00 31.180 80.113 1.31 59.00 80.030 78.733 1.56 63.00 78.620 77.403 1.55 77. 00i 77.350 75.9615 1.81 86.0 -0 715. 850 74. 457 1.84 95.00 74.320 72.872 1.95 104.00 72.510 71.192 1.82

215 TABLE V-41 V-41. Comparison of Eqn. V-19 and Satu-ated Liquid Density Values for R-502 Reported by Loffler (86) t d d Percent eq F lbs/cu.ft. lbs/cu.ft. Deviation - 1 12.00 99.7 20 99.2811 0. 44 -103.00 91.780 98.3 32 0. 42 (-9t. 00 (97. 850 97. 428 0.43 — 85,00 96.790 96.,483 0.32 -76.00 95.890 95.525 0.38 -67. 00 94.870 94.554 0.33 -58.00 93.880 93.569 0.33 -49.00,92.760 92.568 0.21 -40.00 91.800 91.552 0.27 -31.00 90.740 90.518 0.25 -22.00 89.570 89. 464 0.12 -13.00 88. 550 88.391 0.18 -4.00 87.430 87.294 0.16 5.()0 86.230 86.174 0.06 14.00 85.050 85.027 0.03 2 3. 00 83.910 83.851 0.07 32.3 00 82.680 82.642 0.05 41.00 81. 390 81.397 -0.01 5L0.0 0 10. 140 80. 113 0.03 59.00 7.83 0 7 [i. 7 78 3 0 5 6). 0( 0 7 77. 7 4 50 77. 403 0.06 77.00 75. 950 75. 961 -0.02 6.00 74.500 700 74457 0.06 95.00 72. 930 72.872 0.08 10'.r0 71.260 71. 192 0, 10 113.00 6G),529 69.399 0. 17 1 2:. G200C (6, 3. G 3 67. "6, " O. 25 131.00Q 6',.'4() 65.34 8 0. 4

216 TABLE V-41 (contd.) 14 0. 00 63. 3t80 62.991 0.61 1 49.00 60. 0 60.288 0.92 15 8. O 5 7. 60 57., 45 1. 41 16 7.00 54.100 52.782 2.44! 76.00'438.210) 45. 253, 6.13

217 TABLE V-42 V-42. Comparison of Ecn. V-19 and Saturated Liquid Density Values for R-502 Reported by Du Pont (47) t d d eq Percent F lbs/cu. ft. lbs/cu. ft. Deviation 1- 10. 00 9. 40 9 8. 052 0. t5 -30.00 96.550 95.952 0.62 -60.00 9. 5 920 ( 3. 78 9 0. 77 -4L0.00 92.'400 91.552 0.92 -20. 00 90. 1:30 89.2283 1.06 0.0 8783L40 86.800 1.18 20.00 85.390 84.246 1.34 -40.00 82. 800 81. 538 1.52 60.00 0. 0r0 78.633 1.76 80.00 077.070 75. 469 2.08 100.0 7.3 O 00 71.951 2.50 1 2 0.00' 10.O 0 7. 903 3. 1 0 140. 0 65.59-0 62.991 3.96 160.00 59.490 56.21 4 5.51

218 TABLE V-43 V-43. Comparison of Rectilinear Diameter Eqn. V-20 with Data For 1 -22 t d deq Percent eq F lbs/cu. ft. lbs/cu.ft. Deviation 429.67 43. 50 4 3. 47 0.21 1439.67'13. 089 42.954 0. 29 Li49.67 42. 630 42. 501 0.30 459.67 42. 180 42.047 0.31 469. 7 41. 710 4 1. 594 0. 24 479.67 41.260 41.140 0.29 489.67 40. 790 49.637 0.25 499.,7 40. 310 40.234 0.19 509.67 39.830 39.783 0.13 519. 67 39. 370 39.327 0.11 529.67 38.890 33.873 0. 0 539.67 38.420 3. 420C 0.00 549.67 37.930 37.966 -0. 13 55)9. 67 37. 470 37.513 -0. 12 569.67 37.000 37.060 -0. 16 579.',7 36. 530 36.606 -0.21 5R9.67 36. 090 3. 153 -0. 17 59F. 67 35. 620 35.699 -0.22 60)9. f67 35. 150' 35. 246 -0. 27 6194.67 34. 690 34.793 -0.30 629.6 G7 3';.?39 34.339 -0. 32 639.. 6 7 3 3. 750 33.886 -0. 40 64t4.,67 33. r00 33. 659 -0. 47 61t9). 7 33. 300 33. 432 -0.40 6.4. 67 33. 050 33. 26 -0.47 659.6&7 32. 559.32. 979 -1.32

219 TABLE V-44 V-44. Comparison of Rectilinear Diameter Pq!, V..21 With fData nor R-115 t d dPgenb eq F ibs/cu.ft. lbs/cu.ft. Doy t.4 on 429* 67 47 900 47,93?7 o08 439.67 47 420 47,.420 9.00 449.67 46,940 46 903 9.08 459.67 46, 440 46. 387 Q01l 469067 45. 940 45.870 Q. 15 479, 67 45 410 4i. 354 12lZ 489. 67 44. 890 44, 837 3, 12 499 67 44. 350 44 320 9 07-~ 509. 67 43 800 43, 804. 01 519,67 43.250 43.287 Q.~o09 529.67 42.710 42.770 -0 4 539. 67 42 190 420254 549.67 41.680 41. 737 30 14 559j67 41l200 41.221 w0%05 569.67 40. 730 40, 704 Q.:06 579.67 400200 40.187 ~ 03 5 89; 67 3.9.710 39e 6 7l 0 1 0'39. 67 39o 290 3 9, 154 O 35 609.67 38,700 3,,637 13 614.67 38,42 0 38, 379 J).1 619.67 38, 150 38.1 1,01 624.67 37,800 37.663 IP* 1 7 629.67 37. 300 37.604 vp8.

CHAPTER VI SUMMARY AND CONCLUSIONS This work may be summarized in three parts. The experimental part consists of PVT determinations, vapor pressure measurements, saturated liquid density determination and observation of critical temperature for the azeotrope R-502. The second part consists of algebraic correlations of these properties. Best correlating equations for R-502 were evaluated first. Then the components' data were correlated to the same algebraic expressions which enabled prediction of the properties of the mixture R-502. Finally second virial coefficients of the components R-22 and R-115 as well as the mixture R-502 were used in evaluating two characteristic molecular parameters of the potential energy of interaction by a new analytical method. Combining rules for the parameters were tested. PVT measurements for the azeotrope R-502 covered a temperature range of 100 to 250 F, pressure range of 80 to 2000 psia and densities up to two times the critical density. An improvement in volume calibrations was obtained by using mercury as the hydraulic fluid. The volume of the bellows PVT cell is believed to be known within +0.50% while Bhada (15) reported a value of +1.3%. Due to improvements in insulation of the bath, heater capacities and heater placements, temperature of the bath was controlled to within +0.04 F. Using a more sophisticated dead weight gauge of Ruska, pressure gauges were calibrated to an accuracy of 0.1 %. Overall experimental accuracies are as follows: specific volumes: +0.50%, temperature values +0.04% and pressure values +0.17%. 220

221 Low vapor pressure determinations for R-502 ranged from -100 to -40F covering a range of 0.4 psia to 16 psia. Temperature control was of the order of +0.1F. Experimental vapor pressure values are believed to be precise to +0.04 psi. High vapor pressure values were obtained using the PVT cell covering a temperature range of 100 F to the critical temperature. Precision in pressure and temperature values is the same as that given above for PVT determinations. Saturated liquid density of R-502 was determined over a range of -160 to 176 F. Temperature control at the low temperatures was of the order of +0.lFand at the high temperatures of the order of +0.04 F. The density values are believed to be accurate to +0.1%. Critical temperature was observed using an appropriate saturated liquid density bulb and is believed to be precise to +0.2 F. The Martin-Hou (91) equation of state is improved and used to correlate the PVT data for the mixture. The equation of state is capable of predicting volumetric data up to 1.8 times the critical density. The experimental data are correlated to an average deviation of -0.23%, average absolute deviation of 0.60% and standard deviation of 0.95%. Vapor pressure data and saturated liquid density values are correlated by Martin and Downing (90). Vapor pressure of R-502 was correlated to an average deviation of -0.22% and average absolute deviation of 1.28%. The saturated liquid density of R-502 was correlated by Martin and Downing (90) with an average deviation of +0.075% and average absolute deviation of 0.11%. Using the critical temperature of R-502 to be 639.56 R, Martin and Downing (90)

222 determined the critical pressure of 591L0 psia. They also reported the critical density of 35.0 lbs/cu.ft, which was confirmed in this investigation by the analysis of the data, Using the improved equation of state PVT data available in the literature for the components of the mixture, namely R-22 and R-115 were correlated. Using the generalized approach input conditions to evaluate the constants in the equation of state were determined. These input conditions were combined on a mole fr.ttion basis and used with combined critical constants in order to predict the PVT behavior of R-502. The predicted values compare very well with the experimental data over the entire range except around the critical point and at extremely high densities. Similarly, the vapor pressure equation given by Martin, Kapoor and Shinn (93) is transformed into reduced form and these reduced constants were evaluated for R-22 and R-115 using the literature data. Constants of the vapor pressure equation were combined on the basis of factor M (91) along with the combined critical constants to predict the vapor pressure of R-502. The prediction is good in the intermediate pressure ranges but is in error at low pressures and near the critical temperature. The saturated liquid density data available in the literature for R-22 and R-115 is correlated with the Martin-Hou eqn. (91)o Constants in the equation were reduced and combined on a mole fraction basis, which in turn were used to predict the saturated liquid density data. The prediction is excellent everywhere except within a few degrees of the critical temperature. A literature search was made to find accurately determined critical constants of R-22 and R-115. Several methods of prediction

223 of critical constants of mixtures were reviewed. Li, Chen and Murphy (85b) method of prediction of critical temperature method was found to be the best. This method utilizes an extra piece of information, namely the normal boiling point. Critical volume of the mixture was best predicted by averaging, on a mole fraction basis, the critical volumes of R-22 and R-115. A new method of predicting the critical pressure of the mixture is proposed. The method is empirical, but simple. The second virial coefficients for the mixture R-502 and components R-22 and R-115 at three temperatures (TR = 0.8, 1.0, 2.3) were a by-product of the PVT correlations. From these two characteristic molecular parameters, U and d of the potential energy of interaction m m were determined by a new analytical method. Algebraic handling is very easy and the order of magnitude of the parameters is very close to that determined by other realistic methods which are usually tedious and complicated. An extensive literature review on this subject is presented and it reveals that this approach is the first of its kind. The component parameters were combined using well known rules to predict the second virial coefficients of the mixture. The prediction was good considering the accuracy in the second virial values. In conclusion, PVT data is obtained to a better precision than that obtained before by Bhada (15) using the same PVT cell. An extremely improved equation of state has been developed to predict the PVT behavior of substances. A new rule for the prediction of true critical pressure of azeatropic mixtures of halogenated hydrocarbons is develooed

224 A new analytical method to evaluate the intermolecular potential (Martin) energy parameters is presented.

CHAPTER VII RECOMMENDATIONS FOR FUTURE WORK Several improvements can be made in the present investigation. In experimental methods the simplest recommendation is to improve the temperature control techniques for low pressure determinations. A major recommendation is to improve the volume calibration of the bellows PVT cell. Detailed information on Bridgman bellows PVT cell (23) is given in Chapter II which suggests that by employing an extremely well machined screw to measure the change in the bellows position, an improvement in the volume calibration may be obtained. In order to have a duplicate check on volume calibration, a sophisticated mercury pump as used by Keyes (73) and Beattie (8) may be incorporated in the system. Finally if the volume calibrations are determined accurately, simultaneous observation of isometric and isothermal PVT data would be possible. The equation of state can be further extended to higher densities keeping in mind that addition of one extra exponential term in Eqn. (V-1) may cover succeedingly smaller ranges of density. Reduced vapor pressure equation may be modified to incorporate the factor M for completely generalized correlation. Further, the methods advocated here for the prediction of critical properties may be tested for other halogenated hydrocarbon mixtures. Extremely promising is the new analytical method (should be called henceforth as the Martin method) of evaluating intermolecular potential energy parameters. This method should be tested with other 225

226 accurate second virial coefficient data and compared with commonly used methods such as Lennard-Jones (12-6) potential (85).

APPENDICES 227

APPENDIX A DETAILS OF TEMPERATURE AND'PRESSURE MEASUREMENTS FOR PVT BEHAVIOR AI. TEMPERATURE CONTROL SYSTEM: Temperature of a bath was controlled by an on-off control. The bath was a jacketed steel vessel with an inside diameter of 20" and a height of 18". The 3" thick jacket was filled with glass wool in order to insulate the bath fluid. Mineral oil was used as the bath fluid. The bath was equipped with two heaters coming out of its bottom and placed diagonally across each other. Their heating capacity was 1000 watts each. A half horsepower stirrer could be mounted off-center on the bath to give vigorous stirring of bath fluid. In addition to these heaters, a knife heater of 250 watts capacity was used, whose output was controlled by a Variac. The temperature sensor was a dot y magnet thermoregulator. This thermoregulator (Fig. A.-l) has an adjustable wire contact with mercury. The dot magnet "D" connected to contact wire "C" can be rotated as desired by an outside ring magnet "E". Contact wire "C" touches the mercury in capillary "F". Capillary "F" ends in a hugh bulb "G" filled with mercury. Depending on the temperature desired, the amount of mercury in "F" and "G" can be overflowed or added. Cavity "H" serves as another auxilliary reservoir for mercury. The space above the mercury is filled with inert gas. The two leads coming out of the regulator are connected to a relay circuit. The range of temperature control is -30 to + 350 F. Temperature of the bath was controlled to +0.04 F by using continuous heat input of knife heater and on-off controlled heat input through regulator-relay-heater circuit. 228

229 E 11 C F Fi. Doty Magnet e Thermoreulator Fig. A1. Doty Magnet Adjustable Thermoregulator

230 In conjunction with the doty magnet thermoregulator, a relay (Cat. No. 4-5300) supplied by American Instrument Company, was used. Installation of the relay is schematically presented in Fig. A-2. Relay circuit is given in Fig. A-3 specifications of the relay were: Power requirement: 118/208/230 Volts +10%, 50/60 cycles a.c., 17 Voltamperes. Control Circuit: a) Open circuit potential 12 volts a.c. b) Current on shorting control terminals = 10 ma. c) Characteristics: Control contacts resistance must be less than 25 ohms. d) Maximum control circuit lead length limited by cable capacitance of 2 MFD max, or resistance of 25 ohms max. Any one or more heaters can be connected to the relay. Knife heater output was adjusted by variac so that roughly 3 to 4 on-off contacts per minute were obtained. At the highest temperature, control was accurate within +0.04 F and for other temperatures usually less than +0.03F. AII. TEMPERATURE MEASUREMENT SYSTEM Platinum Resistance Thermometer-Potentiometer-galvanometer assembly was obtained from Leeds and Northrupt Company and was used to measure temperature within 0.001 C. Platinum resistance thermometer (Cat. No. 8163-c) is a four terminaltype thermometer in which "potential" leads are joined with "current" leads at branch points. There are four coils each having a branch point at its ends and resistance of the coil is the resistance included

231 50/60Cyc. 115,208, or 230 V 115,208,230,or 440 V tI — SnSame or A.C. or D.C. Separate Source Super Scnsitve Relay o o EOrI(.. \O C..C=i) Thermostat FgA.2Spsnii RI'L Heater iExtra ~~-I I- +4,f~4: Power Bath I Relay Fig. A. 2 Supersensitive Relay Installation

232 17 V. Ao 50/60cyc. Hadtr Power - GND 230 208 1I17V COM Fuse 114 A SLO-BLO Contro l |Selector (-,, JN.CPower 3000Q,, 10% Relay 10V Fig. A. 3 Schematic of Relay Circuit

233 between the branch points. All coils are encased in a high conducting glass tube, with four leads going to a potentiometer. The potentiometer, Ser. No. 1327006, was a 8067 type G-1 Mueller bridge (A-2). It measures resistance between 0 and 81.111 ohms in steps of 0.0001 ohm., which covers the entire temperature range of 8163-c platinum resistance thermometer. Without ambient temperature correction, resistance can be measured within an error of a few ten thousands of an ohm or +0.02%. In conjunction with this potentiometer, a galvanometer, Cat. No. 2430, Type E, was used to obtain null points. This galvanometer has an enclosed lamp and 10 cm. wide scale. There are two light spots on the scale, a primary split by an index and a secondary split to show direction of deflection. Deflections are linear within one percent. The galvanometer operates with a power supply of 115 volts, 50/60 cps. Galvanometer, Ser. No. 1209153, has a sensitivity of 43 iv/MM, period of 3.2 sec. and 16 ohms resistance. Other equipment was an 8068 L&N type commutator, Ser. No. 1511595, and four dry cells. Complete circuit diagram of the temperature measuring system is given in Fig. A-4. 8163-c type platinum resistance thermometer covers the temperature range of -190 to +500 c. Resistance of this thermometer can be easily expressed in terms of international temperature scale by the Callender formula. For temperature above 0 C: R -R t o 0 t t t = R + (A-1) 0

234 S A B Galv. d ~r K Rat io i, Double Throb Commutator Meas TZero MA e Meauing Sytem Resistance Fiq). A. 4 Circuit Diagramn for'iemperalture Measuring System

235 where t = temperature in C R = resistance at temperature t R = resistance at 0 C R100 = resistance at 100 C 100 R o0- Ro a= 10 = characteristic constant of the thermometer 100 R 6 = another characteristic constant of the thermometer. Constant a is determined from R100 and Ro while 6 is determined usually from the calibration at the boiling point of sulphur. For temperatures below 0 C, Eqn. A-1 is modified as: Rt- R 0 t t t t OO 1) + 6 (10 - 1) (ot -) (A-2) 0 where B, one more characteristic constant of the thermometer is determined by calibration at the boiling point of oxygen. For convenience in use, Eqn. A-2 can be written as: R -R 3 t o t t t t tR = a [t-6(- 1) - (- 1) (1 — 1) ] (A-3) Eqn. A-3 can be used to prepare calibration tables of Rt vs. t every one degree apart. Linear interpolation of resistance to evaluate temperature from values which are one degree apart, involves an error of less than 0.001 C. Two platinum resistance thermometers were used in the experimental work, whose characteristic constants are certified by the National Bureau of Standards and are given in Table A-l.

236 TABLE'A-1 CHARACTERISTIC CONSTANTS -IN EQN. A-3 FOR PLATINUM RESISTANCE THERMOMETERS Constant Thermometer Serial Number R 25.543 25.505 abs.ohms xa 0.003926395 0.003926472 B 0.11020 0.11024(below 0 C) 0.000 0.000 (above 0 C) 6 1.49159 1.49160 The thermometer with Ser. No. 1504255 was checked for its ice point and steam point (using a hypsometer) and resistance values were found to duplicate those given by NBS within the accuracy of G-l type Mueller bridge. The second thermometer was not checked since the data of certification was very recent. With on-off control described in the previous section, temperature of the bath fluctuates in a sinusoidal fashion (Fig. A-5). This was clearly noticeable on the galvanometer scale where at worst, the hair index traversed a path between the middle 8 cm region. Two centimeters on the galvanometer scale roughly amounted to about 0.01 C. At any time, resistance R was recorded in data books, whether commutator av position was in normal (N) or reverse (R) setting. Assuming temperature of the PVT cell to be the average value Ta, uncertainty in Tav amounts to +0.02 C or +0.04 F.

237 SCD CD C) R (T.T., _. _max max i/R(T V) (Ti)R (T _(9, ~~~rain min Fig. A. 5. Temperature Fluctuations of the Bath Equal Gaps at Equal Pressure Sensing - - Sensing Coil Coi I 1 L2 Magnetical ly Permeable Core System Pressure Reference Pressure Magnetically Permeable Diaphragm Fig. A. G. Pace - Diaphragm Pressure Transducer

238 AIII. MEASUREMENT OF PRESSURE The pressure measuring system consisted of a nitrogen tank serving as a pressure source to Bourdon gauges. Three Boutdon gauges were connected to a pressure transducer which in turn was connected to the PVT cell. A nitrogen tank supplied the highest pressure of measurement of about 2000 psia. Three Bourdon gauges of ranges and series numbers as follows were used: Pressure Range in psi Serial Number 0-100 H 21471 0-500 H 21470 0-2000 H 26058 The pressure gauges were always calibrated before and after experimental runs. Hysteresis losses were insignificant to show any changes on duplicating pressure readings. They were calibrated "in situ" by a Ruska dead weight gauge, Cat. No. 2400 HL, Ser. No. 13919. A Ruska dead weight tester has a precision of 0.1 psi at 2000 psi. PACE - Pressure Transducer: PACE - Pressure Transducer system consisted of a model KP 15 transducer and model CD 25 transducer indicator. Pressure measurements are based on the magnetic reluctance principle. This system offers the following advantages: 1) Dynamic response characteristic of this system is excellent either in liquid or in a gas system due to low volumetric displacement, low internal volume, and high natural frequency.

239 2) Corrosive liquids and gases can be used on both sides without isolation of pickoff mechanism. 3) Overload tolerance (200 psi) is relatively high, making it operator proof. 4) Severe shocks and vibrations can be with stood easily by the whole system. 5) Due to simple, self contained solid state circuitry, D.C. output level is high with unregulated 115 VAC or 28 VDC. PACE - Pressure transducer is shown in Fig. A-6. A magnetically permeable, stainless steel diaphragm is clamped between two blocks and deflects if there is an imbalance of pressure. Pressures to the diaphragm are applied through the ports shown. In each block an E core and coil assembly is embedded such that a small amount of gas is left between the diaphragm and the E core. Arrangement is symmetrical so that in an undeflected position of the diaphragm, condition of equal inductance is obtained. Diaphragm deflection results in an increase in gap in the magnetic flux path of one core and equal decrease in the other. Variation in gap results in changing magnetic reluctance, thereby determining the inductance value. Thus deflection of the diaphragm results in increasing inductance of one coil while decreasing that of the other coil. A bridge circuit for converting coil inductance ratio into D.C. output voltage is given in Fig. A-7. Four arms of the bridge are given by inductance coils L1, L2, and resistances R1 and R2. The bridge can operate on half cycles due to insertion of diodes in the resistive voltage divider. A potential is established at point B, during half

240 cycle when diodes do not conduct, there is no output. Therefore, the output is half-cycle pulses. If voltages at point A and B are equal, output is zero, while if potential at A is larger than that at B, the output has one polarity. Similarly if voltage at A is less than that at B, output polarity reverses. The ratio AL/(L1+L2) is usually 5% at full scale in typical transducers, corresponding to output voltage of 50 mv per volt of excitation. The effect of filter on bridge output is shown in Fig. A-8. Model KP 15 pressure transducer, Ser. No. 21052, with a diaphragm range of +25 psi was used. Hysteresis was about +0.3% for pressure excursion. The transducer had a specified range of temperature operation of -423 to +250 F. Between -65 to +250, zero shift coefficient was within 0.01% and sensitivity coefficient within 0.02% of full scale per degree F. Therefore, sensitivity of the transducer, at worst, was better than 0.01 psi. However, null point changed with temperature amounting to a drift of about 0.5 psi at the highest temperature of 250 F. The PACE - pressure transducer assembly was used as a null indicator. Pressures were read accurately on calibrated Heise gauges. Error contribution can be divided as: 1) Precision of Heise gauges. 2) Accuracy of the dead weight tester. 3) Precision in calibration of the Heise gauges. 4) Precision in transducer sensitivity. Precision of the Heise gauges was claimed by the mamniacturer

241 r —I I B L R2 L _R Fig. A. 7 Bridge Circuit to Convert Coil Inductance Ratio into DC Output Voltage Unfi l1e red Fi itered CFig. A. 8 Bridge Output with and Without Filter

242 as +0.1%. Manufacturer of the Ruska dead weight tester claimed an accuracy of +0.01% of the reading. Precision in calibration was +0.05% of the reading. Precision in transducer sensitivity was +0.01%. The pressure values are believed to be accurate to +0.17%.

APPENDIX B DETAILS OF VOLUME CALIBRATION The volume of bellows cell is calibrated as a function of height. In order to obtain this function, PVT measurements were made on carbon dioxide whose PVT behavior is well known (57, 101). These measurements ranged over 80 to 250 F and up to 2000 psia. The experimental procedure is the same as that described for obtaining PVT measurements (Chapter III). In this section we shall illustrate analysis of the data. Volume of the bellows is a function of 1) compressibility of the hydraulic fluid due to pressure, 2) contraction or expansion of the hydraulic fluid due to temperature and 3) contraction or expansion of the cylinder due to temperature. All these effects could be incorporated to give the expression for volume as follows: Vh"T P = (Vh)T P + AVh (P-Po + A)T P(- To)} Yh (B-l) o APh T h where Vh = volume of the bellows at any height, temperature and pressure (AV/AP)T = variation of volume with pressure (AV/AT)p = variation of volume with temperature P = pressure, psia PO = reference pressure, psia T = temperature, R T = reference temperature, R 243

244 ho = reference height Yh = a factor accounting for the variation of temperature and pressure coefficients with height In our case the hydraulic fluid is mercury for which temperature effects are large compared to pressure effects. During the preliminary observations our hydraulic pump leaked mercury during compressing. With help of the supplying company we changed gaskets around the piston and inserted improved glands where at least during one run we could not obtain mercury leaks. All the minute amounts of leaked mercury were collected carefully and added to the reservoir tube. This put a severe limitation on our data collection. Experimental procedure was to make both volume calibration and PVT observations on R-502 at the temperature of the isotherm successively and within a period before which the piston gaskets would give up under stress. Thus the data is analyzed at the given temperature only. All the experimental data is listed in Table E-2. The data analysis showed that volume of the bellows could be expressed as a function of height only at a given temperature. Therefore we formulated the following equation: Vh - m h + C (B-2) where Vh = volume of the bellows cell m = slope factor (dV/dh) in 3/cm C = constant.

245 As an example let us take the isotherm at T = 708.94 R. At this temperature, volume of the bellows is given by the following equation: V = 0.529063 h + 20.8449 (B-3) Eqn. (B-3) is compared with the volumetric data of carbon dioxide in Table B-1. TABLE B-1 Comparison of Eqn. (B-3) with the Volumetric Data of Carbon Dioxide Obs. h V V (Eqn.B-3) Percent No. cm in3........ Deviation C47 98.855 73.26 73.15 +0.15 C48 72.860 59.42 59.39 +0.05 C49 49.00 46.74 46.77 -0.06 C50 26.92 35.09 35.09 0.00 C51 13.70 28.08 28.09 -0.04 C52 2.785 22.31 22.32 -0.05 Average absolute deviation = 0.06% Average deviation = +0.01% All the data was analyzed in this fashion and the constants in Eqn. (B-2) with their comparisons to experimental data are sumnmarized in Table B-2.

246 TABLE B-2 Constants in the Eqn. (B-2) and Its Comparison with the Experimental Data of Carbon Dioxide T M C Av.Ab. Av. Max. R in3/cm in % Dev. %Dev. %Dev. 541.1 0.521614 22.2134 0.08 -0.04 +0.20 639.6 0.53645 21.7472 0.12 +0.04 +0.17 664.1 0.529047 21.5752 0.09 -0.01 +0.11 666.1 0.533289 21.2997 0.07 -0.01 -0.12 708.9 0.529063 20.8449 0.06 +0.01 +0.15 711.4 0.529506 20.9197 0.06 0.00 +0.10 perimentalPrecision The mercury level measurement readings should be accurate to +0.001 cm which amounts to a volume of about 0.0053 cu.in. At the smallest bellows volume (about 22 cu.in.) this error amounts to +0.03% and decreases to +0.01% at the largest volume. The PVT behavior of carbon dioxide is known to +0.05% and other experimental errors in temperature measurements, pressure measurements and mass recovery are estimated to be +0.15%. Therefore at best the volumes obtained through calibration are accurate to +0.20%. These volumes are correlated by the equation with the deviations of +0.20%. Weight of the charging cylinder changes with the barometric pressure due to buoyancy. Maximum variation in the barometric pressure during our runs was of the order of +6 mm. This barometric pressure variation gives rise to an error of +6 mg. This amounts to an error of +0.02% for lowest sample weight to +0.001% for the highest sample weight. Sample recoveries were within +0.03%. Calibrated weights were used which were believed to have an accuracy of +0.01%. The accuracy of the whole weighing procedure was estimated to be +0.05% for the smallest sample. The specific volumes reported are estimated to be accurate to +0.5% at the lowest bellows volumes and +0.25% at the highest bellows volume.

APPENDIX C DETAILS OF VAPOR PRESSURE MEASSUREMENTS These measurements covered the pressure range of 0.7 to 590 psia corresponding to the temperature range of -100 to 180 F. Using static method, Vora (138) made low vapor pressure measurements. High vapor pressures were obtained from the PVT measurements. LOW VAPOR PRESSURE MEASUREMENTS, Experimental System: A schematic presentation of the experimental system is given in Fig. III-3. The charging cylinder is a high pressure vessel of 500 cc capacity. A needle valve, V1, controls the discharge from the cylinder. It is shown in an inverted position for the reasons given for charging PVT cells. Stainless steel tube 1/4" O.D. from value V1 is connected to glass tubing by a steel to glass ball joint. A drying U tube was filled with P205. The line from the drying tube then divides, one going to the isoteniscope and the second to the mercury barometric leg. All lines are made of Pyrex glass 12 mm O.D. unless otherwise specified. From the barometric leg, a connection is taken which was used to fill the saturated liquid density bulbs. The mercury barometric leg serves as a pressure safety valve in the event that the system pressure exceeds one atmosphere through an accident. Valve V3 separates the isoteniscope completely from the drying tube and barometric leg. The isoteniscope is made of a 25 mm O.D. glass tube about 5" long. The 247

248 isoteniscope is placed in a constant temperature bath. A dewar flask, about 6" I.D. and 10" high with two diagonally opposite 1/2" wide slits was used as a bath. It was equipped with an air driven stirrer, platinum resistance thermometer, a knife heater and a tube supplying liquid nitrogen cooled air. A platinum resistance thermometer was connected to the usual bridge galvanometer assembly. The isoteniscope is connected to the mercury U tube manometer, the legs of which can be isolated through valve V4. Valve V8 is the vent valve. One leg of the U tube manometer is connected to the vacuum system, which consists of a McLeod gauge, mercury diffusion pump and a mechanical vacuum pump. The McLeod gauge was capable of reading a vacuum of one micron of mercury. The levels of mercury in the legs of the U tube manometer were measured by a cathetometer capable of reading to an accuracy of 0.001 cm. Mercury in the manometer must be as clean as possible. Procedure of Operation: Referring to Fig. III-3, with valves V1, V7 and V8 closed, others being completely open, the mechanical vacuum pump was started. The system is made leak proof, and within a few minutes, a vacuum of about 10 microns is obtained. Then a mercury diffusion pump is started which lowers the vacuum to less than 5 microns. Once the system is evacuated, with valves V4, V7 and V6 closed, valve V1 was cracked slightly. Pressure of about 2-3 psia was allowed to build up in the system and then the isoteniscope was cooled, first by dry ice and then by liquid nitrogen. The test sample, R-502, condenses in the isoteniscope. After making sure that the isoteniscope is about two-thirds full, valve V1 was closed

249 and sufficient time was allowed for any amount left in the lines to condense into the isoteniscope. Now valve V3 was closed and the system is ready for the observation of the data. If by accident valve V1 leaks, any pressure build up will be indicated by the mercury barometric leg. Or if V2 is closed, with lines between V2 and V3 being under vacuum, the mercury barometric leg will show accordingly if valve V3 leaks when pressure in the isoteniscope is of the order of 15 psia. During any experimental run the height of mercury in the barometric leg did not drop. For measurements between -80 to -30 C, normal propanol was used as a bath fluid. Below -80 C, petroleum ether was the bath fluid. The temperature of the bath was controlled manually by setting the bubble rate of cooled air and heat input at different levels, resulting in a constant temperature of the bath. The temperature of the bath was continuously monitored by the resistance thermometer. After about 5 minutes of constant temperature condition, levels of mercury in the U tube manometer were recorded. One leg of the manometer is subjected to the vapor pressure of R-502 contained in the isoteniscope, and the other leg was exposed to a vacuum of less than 5 microns. Therefore the difference in the levels of mercury in the manometer legs directly gives the vapor pressure of R-502 at the bath temperature. No boil-off can be done since it would result in the fractionation of the mixture. In one run, several values of vapor pressure were obtained. This procedure was duplicated at least two times to make sure that all vapor pressure values are consistent. After every run R-502 was vented through valve V8.

250 Due to some leaks on the vacuum pump side, Vora ( 138) used atmospheric pressure on one leg of the manometer to balance vapor pressure of R-502 in some readings. Experimental Precision: Temperature control during the runs were no better than +0.1 F. For low vapor pressure measurements AP/AT _ 0.3 psi/F. This gives a possible error in the vapor pressure of +0.03 psi due to temperature inaccuracies. Inaccuracy in the reading of mercury levels was estimated to be +0.1 mm, giving the differences in the levels accurate to +0.2 mm, corresponding to a pressure of +0.005 psi. Therefore, the total error in the vapor pressure values is estimated to be +0.035 psi. Sample Calculations: Data Point No. 18 Rav = 19.8559 ohms hl = 71.503 cm. h2 = 43.873 cm. B.P. = 737.40 mm. for Rav = 19.8559 T = 217.76 K. Ps = B.P. -(h1 - h2)= 461.1 mm = 8.917 psia. hi + h2 2hl + = 57.688 cm. (hl + h2) = 57.748 cm. 2 av: Possible error = 2(57.748 - 57.688) - +0.12 mm = + 0.003 psi. Error due to temperature fluctuations = +0.05 x 0.3 = + 0.03 psi. T = 217.76 K. Vap. pr. = 8.917 + 0.033 psi.

251 HigahVaor Pressur-re Measurem;entsThe experimental system is the one used to obtain PVT data. On varying volume through the two phase region pressure was noted, which gave vapor pressure of R-502 at the temperature of the bath. Temperature control of the bath was within +0.04 F amounting to a maximum error (Ap/AT = 7 psi/F at the critical) of +0.3 psi. Deviation of the vapor pressure points from the average value was of the order of +0.6 psi. High vapor pressure values are estimated to be precise to +0.17%.

APPENDIX D DETAILS OF SATURATED LIQUID DENSITY MEASUREMENTS Hossain (61) measured saturated liquid density of R-502 from -110 to +180 F. using a sealed glass tube containing a calibrated density float. Details of the measurements are given here. Several density floats with different values of density were prepared. Each float was made of a Pyrex glass tube of about 6 mm I.D. and about one inch long, enlarged at one end in a bulb. After putting in some lead shots, the tube was sealed. Density of this float was determined by weighing it in the air and then in the distilled water. One liquid density bulb was constructed for each density measurement. A high pressure Pyrex glass tubing, 15 mm O.D., 4 mm wall thickness was sealed at one end and a density float was placed in it. Then the tube was necked down to leave a bulb of about 4" long as shown in Fig. D-l. Bulb Calibrated Float j Before After Filling Filling Fig. D-1. Saturated Liquid Density Bulb 252

253 The tube was necked down to about 3 mm I.D. and about 1" long. The tube was necked down again about 1" beyond the first neckdown leaving a bulb. Leaving a length of 2-3" from this bulb, the tube was cut off. The tube was annealed very carefully with a low temperature flame to remove any strain developed during its preparations. The number of the float is carved on the bulb between the necked down tubes. Loading of the bulb was done using the apparatus for the vapor pressure measurements shown in Fig. III-3. After half filling the tube, it was sealed off at the lower necked down portion using a gasoxygen torch. During the sealing process, the density bulb was held at liquid nitrogen temperature, where vapor pressure of R-502 is very small. Therefore, when the bulb was being sealed and the glass is soft, the wall presses inside due to atmospheric pressure. The sealed tip of the bulk was annealed with a low temperature flame. The loaded bulb is shown in Fig. D-1. Each loaded bulb was stored in a 1" I.D. and about 7" long iron pipe, screwed at both ends by caps and supplied with cushion cotton. Each storage pipe was marked with the float number used in the density bulb. The density bulbs were allowed to stand overnight to make sure that no leaks were present. The experimental set up to measure saturated liquid density is shown in Fig. III-4. Here the temperature at which liquid density equals the float density was recorded. A unsilvered dewar flash about 10" I.D., 12" high was used as a bath. It was equipped with an air driven stirrer, knife heater and a supply of liquid nitrogen cooled air. The density bulb was suspended by a rubber tube. The whole assembly was put in a safety box and the safety box had a safety glass to watch the density

254 float. The other 5 sides were made of steel and were painted black. A source of light was provided inside the box. Normal propanol was used as a bath fluid for temperatures up to -80 C, below which petroleum ether was used and for high temperature measurements, ethylene glycol was used as a bath fluid. For a given density bulb, approximate temperature on a mercury thermometer at which float starts sinking or rising is found. Temperature of the bath is then controlled for at least 15 minutes to make sure that the test sample in the density bulb is at the bath temperature and that the pressure in the bulb does not break it. After taking this precaution, a shielded platinum resistance thermometer was inserted in the bath. Temperatures of the bath corresponding to rising and sinking of the float in the density bulb were recorded. The temperature control was such that these temperatures did not differ by more than 0.1 F. An average of these two temperatures were taken as the temperature at which density of the liquid equals density of the calibrated float. Density of the float was corrected for expansion of the glass tube due to temperature. Experimental Precision: The temperatures for rise and fall of the density float did not differ by more than 0.1 F. Therefore temperature values are believed to be precise to +0.05 F. Calculations indicated that such a temperature error would amount to the accuracy in the liquid density of about +0.02%. The densities of the floats were calibrated by weighing them in air and then in water. The weights of the foats in the air were considered accurate to within 0.0001g out of approximately 1 to 3.5 grams. The

255 weights of the floats immersed in water were reproducible within 0.0002 grams. The possible errors of the volumes of the gloats were less than 0.01% or 0.0001 cc out of the total volume of about 1.0 cc. Estimated precision in the float density values is +0.03%. The float densities were corrected for temperature changes. The density float is subjected to vapor pressure of the azeotropic mixture. To evaluate the effect of pressure on volume changes the float may be considered as a thick walled cylinder of 6mm I.D. and 2mm. thickness. Then the change in the outer radius r2 is given by the following equation: 2 2 2 r2P2 1+ r1 Ar 2 ---— ( 2 + ) ( ) r2/r - 1 r1 where Ar2 = change in the outer radius r2 rl = inner radius of the float r2 = outer radius of the float 2 = outside pressure E = modulus of elasticity for glass = 173x106 psi P = Poisson's ratio: for glass = 0.244 For pressures of the order of 200 psi percent volume change amounts to about +0.01%. Error due to pressure effects is estimated to be less than +0.007% for densities greater than 60 lbs/cu.ft. These corrections were not applied to the density values since compared to these pressure corrections, the temperature corrections are of the order 0.1%. Estimated accuracy in the experimental liquid density values is +0.01%. Sample Calculation: Float No. 22 Weight of the string in air = 0.0089 g Weight of the float + string + # 12 float in air = 2.70335 g = W Weight of the float + string + #12 float in water = 0.9946g = Wb Temperature of the water = 25.05C Length of the string in water = 2 3/4" Density of water at 25.05 C = 0.997031 g/cc = d Radius of the string = 0.0015"

256 Volume of the float = (W -W )/d = 1.70875/0.997031 = 1.713838 = A 2 2 Volume of the submerged string = 7r Z=i(0.0015) (2.75) = 0.000319 cc Volume of #12 float = 0.949115 cc Volume of the string + #12 float = 0.949434 - B Real volume of the density float = A-B = 0.764404 cc Wt of the wire = 0.008 Wt of #12 float = 2.1900 g Wt of the wire + #12 float = 2.198 g = C. Wt of the density float = W - C = 0.50535.LDensity of the float=Wt of the float. Density of the float = = 0.661103 g/cc. Float density at 25.05 C = 0.661103 g Rav for sinking = 33.7597 ohms Rav for rising = 33.7590 ohms Average resistance = 33.7694 ohms Corresponding temperature = 179.081 F = 81.712 C Coefficient of cubical expansion of Pyrex glass = 0.00000975/c Volume of the float at 81.712 C = 0.764404 [1+0.00000875(81.712 - 25.05)] = 0.764404 [1+0.000555]. Density of the float at the temperature of measurement 0.661103 1.000555 = 0.660737 g/cc.. Final result = @ 179.081 F, Psi = 0.660737 g/cc.

'APPENDIX E LABORATORY DATA 257

TABLE E-l LABORATORY DATA FOR PVT BEHAVIOR OF R-502 OBS. Mass, GMS (N) Volume, V Temperature (T) Pressure, Psi No. Charged Recovered h, cms V Cuft/ lb. Rt, Ohms R Gauge Bar. Corr. Absolute Fl 32.716 32.715 97.73 0.58242 28.2870 541.14 67.12 14.41 +0.42 81.95 F2 69.72 0.46624 28.2866 541.13 84.65 14.41 +0.56 99.62 F3 54.04 0.40438 28.2869 541414 105.0 14.39 -2.45 116.94 F4 30.80 0.30714 28.2869 541.14 129.8 14.39 -2.90 141.29 F5 16.76 0.24841 28.2872 541.14 155.2 14.40 -3.37 166.23 F6 9.16 0.21655 28.2865 541.13 168.0 14.40 -3.60 178.80 F7 27.010 26.995 70.25 0.57766 33.7513 639.50 85.15 14.30 +0.58 100.93 F8 47.88 0.46102 33.7513 639.50 111.80 14.30 -2.57 123.53 F9 25.685 0.34530 33.7516 639.50 149.5 14.30 -3.27 160.53 F10 13.10 0.27968 33.7515 639.50 183.0 14.30 -3.87 193.43 F11 2.645 0.22516 33.7534 639.53 222.7 14.30 -4.57 232.43 F12 54.210 54.201 97.565 0.35877 33.7594 639.64 143.0 14.34 -3.15 154.19 F13 70.160 0.28757 33.7583 639.62 178.0 14.34 -3.80 188.54 F14 25.72 0.17213 33.7575 639.61 279.7 14.34 -5.55 288.49 F15 13.10 0.13934 33.7577 639.61 330.3 14.34 -6.40 338.24

TABLE E-1 (contd.) Obs. Mass, GMS (M) Volume, V Temperature (T) Pressure, Psi. No. Charged Recovered h, cms V Cuft/lb. Rt, Ohms R Gauge Bar. Corr. Absolute F16 2.375 0.11148 33.7588 639.63 386.5 14.34 -7.35 393.49 F17 355.92 355.81 97.44 0.05460 33.7566 639.59 547.0 14.26 -5.9 555.36 F18 83.50 0.04909 33.7569 639.60 561.0 14.26 -6.0 569.26 F19 74.035 0.04534 33.7573 639.60 568.0 14.26 -6.0 576.26 F20 66.105 0.04220 33.7572 639.60 573.5 14.26 -6.0 581.76 F21 54.875 0.03776 33.7580 639.62 578.0 14.26 -6.0 586.26 F22 18.03 0.02318 33.7555 639.57 582.0 14.26 -6.0 590.28 F23 13.455 0.02137 33.7572 639.60 595.0 14.26 -6.0 603.26 F24 9.695 0.01988 33.7552 639.57 626.0 14.26 -6.0 634.26 F25 5.695 0.01830 33.7569 639.60 722.0 14.26 -6.65 729.61 F26 487.20 487.04 89.405 0.03756 33.7561 639.58 578.5 14.27 -6.0 586.77 F27 38.40 0.02282 33.7536 639.54 586.0 14.27 -6.0 594.27 F28 29.925 0.02037 33.7548 639.56 616.0 14.27 -6.0 624.27 F29 20.635 0.01768 33.7534 639.53 800.0 14.27 -7.8 806.47 F30 18.21 0.01698 33.7548 639.56 924.0 14.27 -8.0 930.27

TABLE E-1 (contd.) Obs. Mass, GMS (M) Volume, V Temperature (T) Pressure, Psi. No. Charged Recovered h, ems V Guft/ib. Rt, Ohms R Gauge Bar. Corr. Absolute F31 16.305 0.01643 33.7542 639.55 1062.0 14.27 -8.0 1068.27 F32 14.675 0.01596 33.7548 639.56 1219.0 14.27 -9.0 1224.27 F33 13.11 0.01551 33.7536 639.54 1414.0 14.27 -10.0 1418.29 F34 11.975 0.01518 33.7556 639.57 1599.0 14.29 -11.0 1602.29 F35 10.765 0.01483 33.7558 639.58 1837.0 14.29 -13.5 1837.79 F36 10.165 0.01466 33.7560 639.58 1976.0 14.29 -15.0 1975.29 F37 512.78 512.78 97.965 0.03761 35.1023 664.06 701.0 14.24 -7.5 707.74 F38 65.885 0.02891 35.1012 664.04 745.0 14.24 -7.5 751.74 F39 51.66 0.02506 35.1014 664.05 776.0 14.24 -7.7 782.54 F40 41.405 0.02228 35.1010 664.04 828.0 14.24 -8.2 834.04 F41 34.40 0.02038 35.1006 664.03 904.0 14.24 -8.2 909.74 F42 28.33 0.01873 35.1003 664.03 1046.0 14.24 -8.6 1051.64 F43 22.10 0.01705 35.1012 664.04 1364.0 14.32 -11.5 1366.82 F44 19.145 0.01624 35.1020 664.06 1650.0 14.32 -14.10 1650.22

TABLE E-1 (contd.) Obs. Mass, GMS (M) Volume, V Temperature (T) Pressure, Psi. No. Charged Recovered h, cms V Guft/ib. Rt, Ohms R Gauge Bar. Corr. Absolute F45 16.875 0.01563 35.1015 664.05. 1965.0 14.32 -17.0 1962.32 F46 177.32 177.30 97.985 0.10894 35.2170 666.15 427.5 14.45 -8.55 433.40 F47 69.455 0.08640 35.2160 666.14 498.2 14.46 -9.50 503.16 F48 41.050 0.06397 35.2162 666.14 585.0 14.46 -6.0 593.46 F49 15.13 0.04350 35.2166 666.15 682.0 14.46 -7.2 689.26 F50 2.83 0.03378 35.2162 666.14 730.0 14.46 -7.5 736.96 F51 117.32 177.30 97.67 0.10740 37.5584 708.99 483.5 14.51 -9.3 488.71 F52 72.855 0.08796 37.5570 708.96 555.0 14.51 -6.0 563.51 F53 51.28 0.07105 37.5573 708.97 641.0 14.51 -6.5 64901 F54 31.665 0.05568 37.5571 708.97 745.0 14.51 -7.5 752.01 F55 12.765 0.04088 37.5610 709.04 876.5 14.51 -8.5 882.51 F56 2.93 0.03317 37.5565 708.95 971.0 14.51 -8.5 977.00 F57 497.3 497.3 99.035 0.03876 37.7497 712.50 919.0 14.10 -8.5 924.60 F58 75.24 0.03210 37.7517 712.54 1011.0 14.10 -8.5 1016.60

TABLE E-l (contd.) Obs. Mass, GMS (N) Volume, V Temperature (T) Pressure, Psi. No. Charged Recovered h, ems V Cuft/ib. Rt, Ohms R Gauge Bar. Gorr. Absolute F59 53.625 0.02605 37.7529 712.56 1147.0 14.10 -9.5 1151.60 F60 42.16 0.02285 37.7536 712.57 1286.0 14.10 -10.8 1289.30 F61 34.935 0.02083 37.7540 712.58 1444.0 14.10 -12.2 1445.90 F62 30.135 0.01948 37.7536 712.57 1613.0 14.10 -13.8 1613.30 F63 27.25 0.01868 37.7543 712.59 1760.0 14.10 -15.1 1759.00 F64 24.36 0.01787 37.7556 712.61 1959.0 14.10 -16.9 1956.20

TABLE E-2 Laboratory Data for Volume, Calibrations with Carbon Dioxide Obs. Mass GMS (M) Height (h) Temperature (T) Pressure Psi. Absol- Z=PV Vol. (Y) No. Charged Recovered CMS Rt, Ohms R Gauge Bar. Corr. ute RT Cl 12.1632 12.1573 96.95 28.2818 541.05 67.40 14.31 +0.42 82.13 0.971819 72.81 C2 71.10 28.2836 541.08 84.85 14.31 +0.54 99.70 0.965732 59.22 C3 53,94 28.2842 541.09 104.8 14.31 -2.45 116.66 0.959725 50.30 C4 33.27 28.2841 541.09 135.3 14.31 -3.0 146.61 0.949069 39.58 C5 20.42 28.2838 541.08 163.5 14.31 -3.52 174.29 0.937463 32.88 C6 10.065 28.2837 541.08 195.5 14.31 -4.10 205.71 0.924197 27.47 C7 2.11 28.2839 541.09 229.0 14.31 -4.67 238.64 0.910324 23.32 C8 96.95 28.2841 541.09 67.40 14.31 +0.42 82.13 0.971819 72.82 C9 21.2381 21.2341 97.755 28.2843 541.10 127.3 14.31 -2.86 138.75 0.951865 73.24 Clo 71.985 28.2840 541.09 156.7 14.31 -3.41 165.60 0.940252 59.89 Cil 54.015 28.2841 541.09 186.3 14.31 -3.96 196.66 0.928009 50.38 C12 33.210 28.2833 541.07 236.0 14.31 -4.81 245.50 0.907434 39.46 C13 20.420 28.2838 541.08 280.3 14.31 -5.56 289.05 0.889088 32.84

TABLE E-2 (contd.) Obs. Mass GMS (N) Height (h) Temperature (T) Pressure Psi. Absol- Z=PV Vol._4V) No. Charged Recovered CMS Rt, Ohms R Gauge Bar. Corr. ute C14 10.065 28.2835 541.08 329.8 14.31 -6.40 337.71 0.868588 27.46 015 2.045 28.2835 541.08 381.0 14.31 -7.25 388.06 0.847377 23.31 016 97.755 28.2843 541.10 127.3 14.31 -2.86 138.75 0.951865 73.24 C17 34.0142 33.9802 97.70 33.7589 639.63 248.5 14.33 -5.02 257.81 0.948715 74.29 C18 66.35 33.7587 639.63 321.3 14.33 -6.25 329.38 0.934029 57.25 019 41.40 33.7589 639.63 413.0 14.33 -7.77 419.56 0.915524 44.05 020 o 25.945 33.7588 639.63 499.0 14.33 -5.40 507.93 0.897391 35.67 021 13.45 33.7596 639.64 602.0 14.33 -6.00 610.33 0.876066 28.98 022 2.335 33.7599 639.65 635.0 14.33 -6.80 742.53 0.847085 23.03 C23 97.70 33.7594 639.64 248.5 14.33 -5.02 257.81 0.948715 74.29 C24 79.993 79.991 97.655 33.7601 639.65 558.5 14.28 -6.00 566.78 0.885324 74.25 C25 66.605 33.7601 639.65 700.0 14.28 -6.40 707.88 0.854690 57.39 026 41.760 33.7615 639.68 874.0 14.28 -8.00 880.28 0.816896 44.11 027 26.00 33.7600 639.65 1033.5 14.28 -8.00 1039.780.781645 35.73

TABLE E-2 (contd.) Obs. Mass GMS (M) Height (h) Temperature (T) Pressure Psi. Absol- Z=PV Vol. ~V) No. Charged Recovered CMS Rt, Ohms R Gauge Bar. Corr. ute = in C28 13.445 33.7611 639.67 1207.0 14.28 -9.0 1212.78 0.739150 28.98 C29 2.32 33.7604 639.66 1415.0 14.28 -10.0 1419.28 0.687911 23.04 C30 97.655 33.7616 639.70 561.0 14.28 -6.0 569.28 0.885324 73.93 C31 80.032 80.276 96.315 35.0994 664.01 600.0 14.4i -6.0 608.41 0.893310 72.61 C32 73.590 35.0990 664.00 708.0 14.41 -7.5 714.91 0.973840 60.45 C33 57.00 35.0988 664.00 812.0 14.41 -8.1 818.31 0.854930 51.67 C34 40.760 35.0984 664.00 946.0 14.41 -8.5 951.91 0.830506 43.15 C35 27.550 35.0992 664.01 1092.0 14.41 -9.0 1097.41 0.803069 36.19 C36 13.315 35.0994 664.01 1310.0 14.41 -11.0 1313.40 0.760943 28.65 C37 3.185 35.0998 664.02 1528.0 14.41 -13.0 1529.40 0.718820 23.24 C38 1.235 35.0985 664.00 1578.0 14.41 -13.4 1579.00 0.709140 22.21 C39 96.315 35.0998 664.02 600.0 14.41 -6.0 608.41 0.893310 72.61 C40 23.0279 23.0279 97.455 35.2143 666.10 178.3 14.50 -4.3 188.50 0.968075 73.18 C41 75.00 35.2158 666.13 214.0 14.50 -5.1 223.40 0.462013 61.36

TABLE E-2 (contd.) Obs. Mass GMS (M) Height (h) Temperature CT) Pressure Psi. Absol- Z=PV Vo1.(y) No. Charged Recovered GMS Rt, Ohms R Gauge Bar. Corr. ute RT C42 51.80 35.2151 666.12 269.0 14.50 -6.1 2.77.40 0.952564 48.93 C43 31.60 35.2159 666.13 344.0 14.50 -7.3 351.20 0.939687 38.13 ~44 15.39 35.2148 666.11 440.3 14.50 -8.75 446.05 0.923138 29.49 C45 2.91 35.2158 666.13 554.0 14.50 -6.00 562.50 0.902819 22.87 C46 97.455 35.2160 666.13 178.3 14.50 -4.30 188.50 0.968075 73.18 C47 23.0279 23.0279 98.855 37.5542 708.91 191.5 14.50 -4.6 201.40 0.972955 73.26 C48 72.860 37.5558 708.94 237.8 14.50 -5.55 246.75 0.966754 59.42 O C49 49.00 37.5546 708.92 303.0 14.50 -6.65 310.85 0.957990 46.74 C50 26.92 37.5556 708.94 402.0 14.50 -8.20 408.30 0.944665 35.09 C51 13.70 37.5558 708.94 498.2 14.50 -9.50 503.20 0.931690 28.08 ~52 2.785 37.5562 708.95 614.0 14.50 -6.10 622.40 0.915401 22.31 C53 98.855 37.5555 708.94 191.5 14.50 -4.60 201.40 0.972955 73.26 ~54 73.5150 73.4840 98.86 37.6911 711.43 601.0 14.20 -6.0 609.2 0.918411 73.23 ~55 74.925 37.6907 711.42 717.0 14.20 -7.5 723.7 0.903063 60.61

TABLE E-2 (contd.) Obs. Mass GMS (M) Height (h) Temperature (T) Pressure Psi. Absol- Z=PV Vol.V) No. Charged Recovered CMS Rt, Ohms R Gauge Bar. Corr. ute =in C56 57.84 37.6920 711.44 830.0 14.20 -8.2 836.01 0.888009 51.60 C57 43.015 37.6906 711.42 962.0 14.20 -8.5 967.71 0.870355 43.69 C58 29.090 37.6926 711.45 1129.0 14.20 -8.5 1134.720.848051 36.30 C59 16.00 37.6929 711.45 1350.0 14.20 -11.4 1352.830.818987 29.41 C60 2.680 37.6925 711.45 1686.0 14.20 -14.4 1685.840.774611 22.32 C61 98.86 37.6931 711.46 601.0 14.20 -6.0 609.2 0.917736 73.23

TABLE E-3 Laboratory Data for Low Vapor Pressure Measurements with R-502 Height of Mercury in Resistance the Legs of Manometer Barometric of the VaporPressur Obs. h1 h2 Pressure Therm. - Ohms Temp. R mmHg psia No. cm cmmmHg 1 58.205 60.273 14.9870 308.55 20.68 0.3999 2 94.050 26.045 736.80 16.228 329.79 56.75 1.0974 3 92.612 27.784 736.80 16.880 340.99 88.520 1.7117 4 92.470 27.681 736.80 16.960 342.53 88.910 1.7192 5 86.462 24.892 734.20 17.4304 350.02 118.60 2.2963 6 88.151 26.414 736.70 17.4340 350.07 119.33 2.3074 7 89.129 27.404 737.70 17.4384 350.16 120.45 2.3291 17.431 350.48 126.45 2.4451 8 90.526 29.491 736.80 9 90.861 29.684 736.80 17.451 350.84 124.03 2.3984 10 87.539 29.055 737.80 17.7907 356.22 152.96 2.9578 11 85.121 29.444 736.80 18.1046 361.64 180.03 3.4812 12 83.402 28.230 733.90 18.1430 362.30 182.18 3.5228 13 82.631 33.936 737.80 18.6337 370.78 250.85 4.8507 14 79.738 31.746 733.90 18.7194 371.18 253.98 4.9112 79,738 31,744 ~733.90

Table E-3 (contd.) Height of Mercury in Parometric Resistance Vapor Pressure Obs. the Legs of Manometer Pressure of the Temp. R mmHg Psia No. h h mmHg Therm.-Ohms No. 1 h2 cm cm 15 75.620 35.666 733.20 19.22 333.66 6.4520 16 76.485 38.425 736.90 19.3235 382.72 356.30 6.8898 17 73.709 42.966 737.80 19.6845 388.10 430.37 8.3221 18 71.503 43.873 737.40 19.8559 391.96 461.10 8.9163 19 68.508 43.429 733.70 19.9644 393.85 482.91 9.3380 20 63.242 51.800 737.40 20.4740 402.71 622.98 11.860 21 60.520 50.780 733.70 10.5753 404.48 636.30 12.304 22 59.108 52.444 733.80 20.5950 404.82 667.16 12.901 23 57.540 57.540 727.70 20.8900 409.96 737.70 14.265 24 52.000 64.710 737.80 21.2735 416.65 864.90 16.725

TABLE E-4 Laboratory Data for High Vapor Pressure Measurements with R-502 Mass of The Observed Barometric Calibration Thermometer Average Average Sample Pressure Pressure Correction Resistance Temperature Pressure psig mmHg Ohms T(R) P (psia) 144.231 210.7 739.5 -0.62 29.2370 210.7 739.5 -0.62 29.2388 558.13 224.38 210.7 739.5 -0.62 29.2387 478.126 212.8 739.2 -0.62 29.2391 212.8 739.2 -0.62 29.2368 558.15 226.53 h 212.8 739.2 -0.62 29.2395 79.7195 211.6 743.1 -0.62 29.2414 558.25 225.35 211.6 743.1 -0.62 29.2422 151.203 218.3 746.2 -0.68 29.3521 218.3 746.2 -0.68 29.3516 560.19 232.05 218.3 746.2 -0.68 29.3528 144.231 219.5 736.4 -0.68 29.3530 219.5 736.4 -0.68 29.3519 560.21 233.06 219.5 736.4 -0.68 29.3523 84.0854 227.8 741.2 -0.83 29.4745 562.38 240.78 227.9 739.7 -0.83 29.4744

TABLE E-4 (contd.) Mass of The Observed Barometric Calibration Thermometer Average Average Sample Pressure Pressure Correction Resistance Temperature Pressure psig mmHg Ohms T(R) P (psia 478.126 253.4 738.0 -1.10 29.9292 253.5 738.0 -1.10 29.9288 570.52 266.63 253.4 738.0 -1.10 29.9285 478.126 290.0 738.0 -1.46 30.4928 290.0 738.0 -1.46 30.4923 580.65 302.77 290.0 738.0 -1.46 30.4929 79.7195 322.4 741.2 -1.65 30.9980 589.71 335.08 322.4 741.2 -1.65 30.9992 144.231 324.0 737.0 -1.65 30.9981 324.0 737.5 -1.65 30.9993 589.72 336.62 324.0 737.3 -1.65 30.9990 478.126 327.0 737.7 -1.68 31.0135 327.0 737.7 -1.68 31.0138 590.00 339.63 327.0 737.7 -1.68 31.0128 151.203 402.0 738.8 -1.50 31.9517 402.0 738.8 -1.50 31.9515 606.93 414.9 402.0 738.8 -1.50 31.9515 478.126 411.7 736.5 -1.80 32.0609 411.9 736.5 -1.80 32.0606 411.7 736.5 -1.80 32.0603 608.89 424.20 411.6 736.5 -1.80 32.0607

TABLE E-4 (contd.) Mass of The Observed Barometric Calibration Thermometer Average Average Sample Pressure Pressure Correction Resistance Temperature Pressure psig mmHg Ohms T(R) P (Psia) 79.7195 420.5 744.7 -1.80 32.1273 420.5 744.7 -1.80 32.1269 610.05 433.1 420.5 744.7 -1.80 32.1266 84.0854 417.3 746.8 -1.80 32.1289 417.7 746.8 -1.80 32.1295 610.09 430.3 418.0 746.8 -1.80 32.1287 151.203 424.4 737.5 -1.80 32.2370 424.4 737.5 -1.80 32.2365 612.08 436.86 424.4 737.5 -1.80 32.2374 144.231 423.0 742.1 -1.80 32.2421 423.0 742.1 -1.80 32.2416 612.17 435.55 423.0 742.1 -1.80 32.2418 478.126 484.5 736.7 -2.12 32.8390 485.0 736.7 -2.12 32.8373 622.94 497.11 485.0 736.7 -2.12 32.8374 144.231 488.0 737.5 -2.32 32.9168 488.0 737.5 -2.32 32.9160 624.33 499.94 488.0 737.5 -2.32 32.9163 478.126 514.5 736.6 -2.35 33.1825 629.22 527.45 515.5 736.6 -2.35 33.1841

TABLE E-4 (contd.) Mass of The Observed Barometric Calibration Thermometer Average Average Sample Pressure Pressure Correction Resistance Temperature Pressure psig mmHg psi Ohms T(R) P (psia) 151.203 577.5 736.4 -3.0 33.7417 577.5 736.4 -3.0 33.7416 639.32 588.8 577.5 736.4 -3.0 33.7408 478.126 578.0 738.6 -3.0 33.7465 639.41 589.34 578.0 738.6 -3.0 33.7470 639.42 589.34

TABLE E-5 Laboratory Data for Saturated Liquid Density Measurements with R-502 Float Weight of Weight of Float Weight of Float Length of Temp. Density No. Wire g +wire+ (Float #12*) +wire +(Float #12*) Wire in of of Float in Air g in Water g Water in.) Water C g/cc 22 0.0080 2.70335 0.9946 2.75 25.05 0.661103 14 0.010524 2.8461 1.0292 5.5 20.5 0.741526 20 0.00655 3.1684 1.0618 2.3 18.55 0.837323 16 0.10017 2.79595 1.2001 5.0 20.2 0.918109 5 0.0075 0.8552 0.0869 2.5 20.2 1.101730 18 0.0075 1.1539 0.1560 2.5 20.8 1.146829 6 0.0075 1.3118 0.2681 2.5 20.45 1.248425 8 0.0075 1.0418 0.2155 2.5 20.8 1.249702 2 0.0075 1.4373 0.3021 2.5 20.6 1.25740 1 0.0075 1.2224 0.2721 2.5 20.7 1.27634 4 0.0075 1.2538 0.3127 2.5 20.4 1.32222 3 0.0075 1.4943 0.5120 2.5 20.6 1.511179 7 0.0075 1.6163 0.6529 2.5 20.3 1.66731

TABLE E-5 (contd.) Float Float Saturated Liquid Density Corrected Sinking Rising Average Temp. for the Expansion Ohms Ohms Ohms R** g/cc ibs/cuft 33.5797 33.7590 33.7593 638.75 0.660737 41.25 33.6022 33.6010 33.6016 635.89 0.741095 46.27 33.1918 33.1893 33.1905 628.45 0.836854 52.24 32.5874 32.5845 32.5860 617.53 0.917660 57.29 30.2764 30.2716 30.2740 575.92 1.101446 68.76 29.4812 29.4772 29.4792 561.68 1.146630 71.58 27.3976 27.3913 27.3945 524.50 1.248425 77.94 27.3375 27.3341 27.3358 523.46 1.249702 78.02 27.1396 27.1341 27.1368 519.92 1.257400 78.50 26.5944 26.5867 26.5905 510.22 1.27634 79.68 25.5440 25.5366 25.5403 491.67 1.33247- 82.56 19.8812 19.8750 19.8781 392.35 1.152295 94.41 14.3868 14.3770 14.3819 297.87 1.66939 104.22 +About 0.1 Ohm _1C *Float #12 is used when needei **R = F+459.67

TABLE E-6 Laboratory Data for Critical Temperature Measurements with R-502 Obs. No. Observation N R Mean Temperature T R 1 Liquid meniscus just appeared 33.7465 33.7440 33.7453 639.3861 2 Liquid meniscus just disappeared 33.7487 33.7461 33.7474 639.4241 3 Liquid meniscus just appeared 33.7468 33.7440 33.7454 639.3879 Average T = 639.40 R C. Cic = 639.72 - Measured by Hossain Critical temperature of R-502 = 639.56 R

APPENDIX F THE EQUATION OF STATE History of the development of the following equation of state goes back to the work of Martin and Hou (91). Improvement to the original equation was made by Martin and Hou (92). The most recent work is published by Martin (89). Bhada (15) used the same equation to correlate his data on PVT behavior of carbon tetrafluoride. The following analysis is in continuation of the previous development work. For this development we used the PVT data on R-22 since it is available accurately over an extensive range. The following equation was found to have the best characteristics: -kt -kT -kT RT A2 + B2T+C2 e A3 + B3T+C3 e A4 + B4T+C e V-b 2 3 2 4 4 4 (V-b) (V-b) (V-b) A5 + B5T A6B6T + aiv a v+ 66av(F-i) a V aaV a V a V e (l+C1e ) e (l+c2e ) Equation (F-i) contains the following 19 constants. A2 C3 B5 al B A A C 2 4 6 1 C2 B4 B6 a2 A3 C4 k C2 B3 A5 b Total = 19 277

278 At first it may seem like a formidable task to evaluate these nineteen constants. But by choosing a few generalized conditions, we need only a few boundary conditions. Complete mechanics of the data fitting is described below. Basis of Equation (F-1) is the fourth degree virial equation. f f f RT + + 4 (F-2) -kT where f. = Ai + Bi T+Cie (Assumed) 1 1 i The first step in evaluating constants is to fit Equation (F-2) at the critical isotherm where Equation (F-3) can be written as follows: RT f2(Tc) f3(Tc) f4(Tc) = — + + + (F-3) Vv 2 3 V2 V There are three unknowns in Equation (F-3) namely, f2(T ), f3(T) and f4(Tc) which can be evaluated by using the following well-known derivative conditions at the critical point. T T= 3T OatVV (F-4) 44) = T = 0 at V = V (F-4) c dV c dV c The result is as follows: f2(T ) = -3R T2/8p (F-5) 2c c c f(T) = R T /16P (F-6)

279 f4(T) = -R4T 4/256P 3 (F-7) Then Equation (F-2) can be written as: 3 3 4 4 RT 3R2T 2 R T R T., V 8PcV2 16P 2V3 256P 3V4 c c Equation (F-8) predicts the generalized second virial coefficient at the critical temperature of -0.375 and the critical.compressibility factor of 0.250. For R-22 the generalized second virial coefficient at the critical temperature is around -0.345 and the critical compressibility factor is 0.2667. Therefore, Equation (F-8) is not expected to do well on the critical isotherm. As elaborated by Martin, we need a translational term on the volume axis which shall be termed "b". Equation (F-8) can now be written: 3R2T 2 R3T 3 R4T 4, RT c c c V-b 2 3 3 ( 8P (V-b) 16P (V-b)3 256P 3(V-b)4 c c c By linearly translating the volume, we do not upset the derivative conditions of Equation (F-4) which is a consequence of differential calculus. In this case we obtain the following relations for the generalized second virial coefficient at the critical temperature and the critical compressibility factor. BP bP c + (F-10) RT 8 RT c c

280 and P V bP cc = 1 + c (F-ll) RT 4 RT C c At this point we can work with the actual critical isotherm data. In order to obtain points in the critical isotherm, we used PVT data of R-22 reported by Michels (99) and Zander (140). This data is plotted as isometrics in Fig. V-l. Analysis of this information gave us points up to 2 times the critical density (Pc). There were no points between the region of critical density and 1.3 times the critical density. To fill this region an interpolation technique was used. A semilog plot of (PR-1) vs. (PR-l), is linear in the region of P to 1.3 Pc (Fig. F-l). Through the experimental data around 1.3pc, a straight line AB (Fig. F-i) was drawn. The same straight line was then translated five times toward pc to obtain synthetic values of PR vs. PR. To extend the data beyond 2.4 pc we used the critical isotherm of CO2 (89). Carbon dioxide has a value of Zc = 0.274 which is very close to the critical compressibility factor of R-22. A semilog plot was made of PR vs. PR for carbon dioxide and R-22 (Fig. F-2). Using interpolation techniques on Zander's (140) isometric data, the last point on the critical isotherm of R-22 was at about 2 Pc. The critical isotherm of carbon dioxide goes to 2.52 c. The overlap of R-22 data and carbon dioxide data up to 2 Pc is excellent as shown in Fig. F-2. Hence by following the critical isotherm of carbon dioxide, synthetic points for R-22 were evaluated up to 2.6 pc. All these critical isotherm values are tabulated in Table F-1.

--- ~~~~~~~~~~~~~~~~~~~~A: O — 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-. _ o c, (1 - d)

282 1 0 1.4 1.6 1.8 2.0 2.2 2.4 10 - _ 3.0 2~6 2.8 > l| / 2.4a/ o CO2 Michels (89) 0 F-22 Michels (99)and Zarnder (140) _____-O —-c~-'"-" - -+7 - tu —- c" —10 2.0 1.8 C- I -_ 10 0.0 0.2 0.4 0.6 0.8 1.0 ig. F. 2. of fm and ioxi at tPre Critic

283 Using the critical isotherm of R-22, we found out that the best fit is obtained if we choose bP /RT = 0.029 in Equation (F-10), giving c c the generalized second virial coefficient at the critical temperature of R-22 to be -0.346. The corresponding critical compressibility factor is 0.279. Equation (F-9), with the selected value of b, fits the critical isotherm data very well up to the critical density but beyond that it deviates from the experimental data. At this stage to evaluate additional terms to Equation (F-9), a semilog plot of residual reduced pressure APR vs. reduced volume VR is made, as elaborated by Martin (89) and Bhada (15). The residual term APR is defined by the following equation: APR = PR - PR exp cal RT 3R2T 2 R3T 3 o 2 RexpPc \V-b- 8P (V-b) 16P (V-b) R4T 4 R3T c 3 (F-12) 256PP (V-b) c Such a plot of APR vs. VR for R-22 is presented in Fig. F-3. Through most of the points in Fig. F-3, a straight line can be drawn up to 2.4 p, thereby indicating that only one term of the form f5(T )/eaV (l+ce ) would suffice. In this term the multiplying term (l+ce ) is a damping factor to take into account that the plot in Fig. F-3 is nonlinear and extremely steep near the critical density. Our investigation showed that if only one term is used, it does not give us enough freedom to obtain good temperature variations of PVT data in the compressed vapor

284 100 l.... 100 r —---— 1 ---- Eqn. F, 13 \ St, aitllt Line Fl Straight \ Li r, Fit \K S iipe = 17.7 | (.3 0.4 0.. 0.6 0.7 0.8 0.9 1.0 Fi.. F. 3. Plot of APr (qn. F. 1.2) vs 01- for Chlorodiluoromethane (E-22) at the Criticai ltemperature

285 region. Further investigation showed that one exponential term must span a distance of about 0.4 pc. Making our objective as to fit the PVT data up to 1.8 pc as best as we can, we selected two exponential terms as shown in Equation (F-1). The method of evaluating the two exponential terms in Equation (F-1) is slightly different from the one used before (15). With respect to Fig. F-3, line AD has a slope of about 17.779. For the fifth term, f5(T )/e aV1 l+clea1 ) to account only up to 1.4 pc,al is selected less than the slope of line AD(17.779). Then the two unknowns f5(Tc) and cl can be determined from the experimental data points. The calculations are as follows: Let al = 16.0 In APR = lnf(T )-alVR-ln (l+ceal1 R) (F-13) The data is given in the following table. TABLE F-2 Values of PR and VR to Evaluate cl and lnf5(T ) No. VR PR alVR lnAPR (lnAPR)calc 1 0.9601 0.0005 15.3616 -7.6009 -7.514 2 0.7805 0.0321 12.4880 -3.4389 -3.439 3 0.7594 0.0534 12.1504 -2.9299 -2.9529 4 0.7150 0.1327 11.440 -2.0197 -2.0197

286 Equation (F-13) can be solved for two values of PR and VR. Here we have a choice of several pairs of values. The best fit was obtained by using the values of VR as.7805 and 0.715. For these data points we obtain the following values of cl and f5(T ): C1 = 0.0000035 (F-14) and lnf5(Tc) - 9.706 (F-15) The fifth term evaluates A PR as shown by the line A'BB'in Fig. F-3. Proceeding similarly we obtain the following values for the sixth term: a2 = 22.00 (F-16) C2 = 0.0000014 (F-17) lnf6(Tc) = 11.2377 (F-18) Equation (F-l) can be written in the reduced form for the critical isotherm as follows: TR 3 1 Zc(VR-b/V 8Z (VR-b/V ) 16 (V -b/(VR-b/V ) c c R c c R c 1 + ________ _______9.706 4 4 + 16V -616V 256Z4 (VR-b/Vc) e R(1+3.5x10 e R 11.2377 + 22VRl+l x-6e22V (F-19) e R(l+l. 4x10 e R

287 Equation (F-19) fits the critical isotherm data as shown in Table F-1. Equation (F-1) can be written in the reduced form as follows: A'+B'T +Cie kTR A'+BTR+Ce-kT R P + 2 2.+.3 R Z (VRb/V) Z (VR-b/Vc) Z (V-b/ ) + + +6 (F-20) z4 (V b/V )4 ealV l+cealR) eaVR(l+c a2VR) where fi(T = A' + B! T + C' e6 R and the following relations can be easily proven. f'(T ) = -3/8 (F-21) f;(T ) = 1/16 (F-22) f'(T ) = -1/256 (F-23) f;I.(T) = -9706 (F-24) f(T ) = e2377 (F-25) Till now, we have determined the following ten terms in the reduced equation of state (F-20) f 3 c ) f(T) f6(Tc), al= c1, a2 c 2 (T 4c' 5-1c 6 12

***e***t*,*'UIMPARISON OF EXPER I MENTAL CRITICAL ISOTr'ER. OjF CHLiCODIFLUROM ETHANE WIT7H THE EQUATION OF STATE *$*** V PEXP PC PL PREXP PiCAL PCD VR RHGR.2 i4 1 24.5 5 -0. 0 -0 i0 7 2 5 0. i725 0.04 20.3464 0, 0491 2 0. 4 319 157.12 -i 00 0. 176 O. l 76 0. 01 15. 8283 0. 0632 2 0.395709 188. 32 -0. 00 0. 26i0 C. 2o0d 0.01 i2.9634 0.0771 2 0.33 276o 2i.62 -u. 00 0.3042' 0. 30,2 O, u2 10.9021 0. C917 2. 270o49 255.22 -O. O0 O. 3535 0. 3535 -0.00 9. i629 0. 1091 2 3.22*-t40 2 d8,44 -0.00 O. 3996 O. 3996 0.00 7.9227 U.1262 2 0.214540 318. C 8 -U. 00 0.4406 0, t4UZ -0.01 7.2d83 0. 1423 2 0.20329 3. 23.0 -0.00 454o 0.454 4547 -0.OL 6.7593 0.1479 2 Ft 0i), 194169 343.50 -0.0. )...758 0.,4771 -0.26 0.3010 0.1572 1 0 0. i7i650 378.ol -. 0 52.5 0 524o -0 33 5. 233 0.1778 2 0. 150000 41 8.5 0 -0.00 0O)797 0. 574 0.05 4.9140 0. 2035 1 cn 0 tM Ft 0.142540 433.52 -0CCG 0.6005 0.6008 -0.04 4.0oo96 0.2142 2 0. 122020 481.5 2 -0.00 0.0c670 0. 6674 -0.06) 3.9974 0.2502 2 F H. i2 0)70 485.38 -0.00 0. s724 0. 672 9 -0.0d 3.946o 0. 2534 2 0 0,105900 525. 74 -0.CO 0. 7283 0. 7288 -0.08 3.4693 0,2682 2 u. 102030 538.00 -0.00 O. 7452 0. 744,9 0.05 3. 3425 0.2992 1 O. 0'9210 545. 39 -0.00 O. 75 2 0. 7509 -0.09 3. 2501 0. 3077 2 0.093570 563.79 -0. OG 0, 7o10 0. 7810 -0.08 3.0654 0.3262 2 0.0843i3 593.00 -0. 00 0.8214 0. d243 -0.35 2.7620 0.3621 1 0.083890 595. 94 -0.00 0.8255 O.d263 -0.09 2.7482 0.3639 2 0. 081554 603.98 -0.00 O. 8 366 U0 83 74 -0.09 2.6717 0. 3743 2 0.0757 7 624,05 -0.00 O. 86.+4 0. 8653 -0.09 2.4822 0. 4C29 0. 074003 625. 50 -0.00 O.8665 0. 6714 -0.57 2.4406 0.4C97 1 0.066950 654.74 -O.Cc 0.i9070 0.9077 -0. 08 2.1933 C,4559 2 0. 064591 658, 00 -0o00 0.91i5 0 9187 -0. 79 2. 1 160 0. 726 1

G.057620 665.00 -0. 00 0. 9489 0. 4'95 -0.06 l.8876 0.5298 1 0. 054 76bu 693.29 -,. 00 O.)o04 0. 9608 -0.05 1.7939 0. 55 74 2 0.0;1672 7 CO. 00 -0. 00 0 96;7 0. 9719 -0.23 1,6 928 0. 907 0,04O6Zb6 712.00 -.0 GO 0.9 83 0. - d73 -0. 10 1. 5167 0. 6593 1 0.044478 715.47 -.0C. 0.9911 0.9912 -0. 01 1,4571 0.6863 2 0.042488 713 00 -0.00 0.9946 0, 946 -0.00 1.39i9 097134 1 O,037339 721.40 -0*.00 039993 O) 9i93 -03J0. 12232. 0, 8175 1 O.0C35992 721 60 -0.0(9 0.9996 C 9997 -0.02 1.1791 0.8481 2 0.030525 721.90 -0.00 1.0HO0 1.3001 -0.01 1.0000 1.0000 2 0.029308 722.20 - -C.0 1.0I04 1.OU01 0.03 C.960i 1.0415 2 0.028528 721.91 -0.C0 i.3303 ioo. l -O1.01 0.9346 1.0700 4 0.02Z 64 72;. 92 -0.00.O1000 1.0 01 -0.01 0 O9259. 1.0800 4 O. 2 b005 721.A4 -0.00 1. 000 1.0001 -0.01 0.9174 1.0 00 4 0.027750 721.96 -O.C0 1.0001i.0001 -0. 01 0.9091 1.1000 4 0.027254 722.04 -0.O0 1.0002 1.0002 0.00 u. 892 101200 4 0.026770 722.20 -C. 0 1.0004 1.0002 0.02 0.6772 l.1400 4 0.026315 722.44 -0.00 1.0007 1.0004 0.03 0.6621. 1600 4 0.025869 722.82 -0.GO 1.0013 1.0307 0.06 0.8,75 1.1800 4 00255433 723.39 -O 30..0021 1.0013 0. 08 0.8 333 1.2000 4 0.025G21 724,19 -0.00 1.0032 1.0022 0.10 0. 197 1.2200 4 0.024617 725.29 -0.0 1.0047 1.0036 0.11 0.6065 1.2400 4 0.024226 726.88 -0.00 1.0069 1.0056 0.13 O 7936 1.2600 4 0.02 3848 728.76 -0. CO 1.0O5 1.0033 0.12 0.7813 1.2800 4. 02 384 727.91 -0.CO i.0uS l. U3O -0.02 0.7805 1.2613 2 0.023461 731.43 -O.0C 1.013Z 1.0119 0.12 0.7692 1.3000 4 0.023181 734.00 -0.00 i.Oi b 1. 0158 G.10 0.7594 1.3168 1 a0.03125 734.53 -0.00 1l0175 1. 0)16 0.09 0.7576 1. 3200 4 0. 022760 736.50 -0.00 1.0230 1.0224 0.06 O. 7463 13400 4 0.0224,45 743.56 -0.00 1.* 3303 1.0295 0.04 0.7353 1.3600 4 0.022120 749.33 -0.00 1.0380 1,0581 -0.01 0.7247 l.3800 4

0.02L824 755.00 -0.00.0458 1. 0477 -0.17 0.7150 l.3987 1. 021804 75b.55 -0.00 1.0460 1.0/'4 -0.04 Oo 7143 1. 4000 4 0.021052 780.37 -0 00 1. 0810 1. C824 -0. 13 0.6897 1.4500 4.0o20350 514.30 -u.00 1.180 1.1312 -0.29 0.o067 i.5000 4 0.C0 Sc3 0 d62. 30 -0.CO i2024 1.207d -0.4> 0 6431 1.5550 1 0.019lJ7 927.64 -0.00 1.2850 1.Z 936 -0.67 0.6250 1.6000 4 0.0 1 8,54 1024. 0 -0.00 1.4165 1. 4321 -0,96 0.6046 1.6541 1 0.017776 iL 56.0 0 -0.00 1.62t29 1. 6540 -0.67 0.5824 1.7170 1.0i 716,.365.00 -C.00 1.8908 i.9454 -2L,.9. 0.5625 1.7779 1. Uol 2l 1612.O -0.0O ~.2Aiu 2. ~0 8 -0. i2 0.5 78 1.8255 O.01621i3 1915.00 -0.00 2.6527 2.6678 -0.57 0.5311 1.6827 1 0.015766 22 82. JC -0.00 3.1611 3.1639 -0.09 0.5165 1.9361 1 3.Oi5299 2766.00 -0.00 3.6343 3.830 0.11 0.5012 1.99>2 3 0.0; 2C3 27,.30 -0.00 3. 703 3. 868d -G.48 0.5003 i.9999 3 0,014536 3855.OC -0.00 5.3400 5.3516 -0.22 0.4762 2.1000 3 0. 01_8 7 5 5349.00 -0.00 7.095 7.,584 2.04 0.4545 2.2000 3 0.013272 7327.00 -0.00 i0.14q5 9.6347 5.07 0.4348 2.3000 3 0. 012719 9o90.00 -0.00 i,.o698 12.' 752 8.94 Uo.41 7 2.4000 3 0,012210 13174. 9q -0.00 18,2503 15.7201 13.86 0.4000 2.5000 3 0.0117i40 i73S7.9 9 -0,00 24. i01 19,2389 20,17 0.3846 2.6001 3 0011Oi3C6 22955.99 -O.CO 31.7991 22.'8009 28.30 0.3704 2.6999 3 0o010902 298860.9 -0.00 41.4001 26 G0942 30.97 0.3571 2.7999 3 0.010526 39126.98 -0.00 54.1996 28.6416 47.16 0.448 2.9000 3 1 = Zander (140) 2 = Michels (99) 3 = Values obtained from Fig. F-1 4 = Values obtained from Fig. F-2

291 We need nine more conditions to evaluate all the constants in Equation (F-20). From the complete description of generalized behavior of gases as analyzed by Martin (89), the nine conditions for R-22 are as follows: 1) Set k = 3.0 (from analysis of PVT data of R-22) 2) Set BP T = -0.740 at T = 0.8T RT c 3) BP RT. B c T = 0.0 at T = T = 2.3Tc 4) dP dT R 1.5V T -, oo dP 5) ( —) 7.40 = M R Pc dPR 6) (-) = 14.10 =.9M R 1.4pc T>M dPR 7) (dT ) = 23.80 = 3.2M R t.8Pc d2P dT 0.0 9) ( —-) = 0.0 dTR 1 c8P Equations for derivatives are as follows:

292 -kT + C ~ -kTR dPR 1 B'-C' ke k R B'-C' ke dR 1 +2 2 3 3 R c( R Z (V -b/V ) Z (VR-b/Vc) c R c c R c B'-C' ke kTR B' B' + 44+ + 6 (F-26) 4 4 alVR(l+e alV) a a Z (VR-b/V ) e 1 R(l+cle 1 R) ee (l+c2e2 R) 2 2'-kT 2e-kT 2-kT d2P C'k2 -kTR C'k e R C'k e R R2 2 2 3 3 4 F27 dTR2 z (V -b/V ) Z (V -b/V ) Z (V -b/V ) c R c c R c c R c Using the conditions (2) and (3) with the value of f2(Tc),A', Bc, and C2 were calculated for R-22. To evaluate the rest of the constants ten simultaneous equations were solved on the computer. Equations (F-20), (F-26), and (F-27) are easy for hand calculations also. Listing of the computer program is given at the end of this section. The experimental PVT data of R-22 is compared with this equation in Tables V-1, V-2, and V-3. The experimental PVT data of R-22 was analyzed to obtain the isochore slopes at the critical temperature. This information is presented in Table F-3 and Fig. F-4.

293 TABLE F-3. ISOCHORE SLOPES FOR R-22 Density Isochore Slope No; lbs/cu.ft. (dp/dT)V.psi/F Reference 1 1.61 0.2139 99 2 2.070 0.2817 99 3 2.527 0.3488 99 4 3.005 0.4255 99 5 3.575 0.5155 99 6 4.135 0.6030 99 7 4.661 0.6944 99 8 4.847 0.7362 99 9 5.150 0.7742 140 10 5.826 0.9091 99 11 6.667 1.093 140 12 7.016 1.130 99 13 8.195 1.37- 99 14 9.443 1.640 99 15 9.801 1.702 140 16 10.080 1.772 99 17 10.687 1.887 99 18 11.861 2.198 140 19 11.920 2.264 99 20 12.262 2.381 99 21 13.198 2.540 99 22 13.422 2.553 140 23 14.937 2.892 99 24 15.482 3.030 140 25 17.355 3.577 140 26 18.262 3.721 99 27 19.353 4.156 140 28 21.600 4.731 140 29 22.483 4.835 99 30 23.536 5.217 140 31 26.782 5.714 140

294 TABLE F-3 (contd.) Density Isochore Slopes No. lbs/cu.ft..(dp/dT)V psi/F Reference 32 27.784 6.429 99 33 29.778 7.037 140 34 33.274 8.205 140 35 34.120 8.571 99 36 38.955 10.91 140 37 41.975 12.08 99 38 43.138 12.50 140 39 45.138 13.79 140 40 50.942 16.67 140 41 54.188 20.00 140 42 56.188 22.22 140 43 58.246 24.00 140 44 59.806 27.00 140 45 61.679 28.88 140 46 63.427 31.75 140 47 65.363 33.33 140 48 66.986 38.52 140 49 68.359 39.68 140 50 69.670 40.78 140 51 70.919 44.64 140 52 72.230 48.08 140 53 73.790 52.63 140 54 75.039 58.14 140 55 76.038 60.24 140 56 77.099 60.98 140 57 77.973 62.5 140 Pc = 32.76 lbs/cu.ft.

295 100 Values Calculated from Experimental Data go," I - - Extrapolated Points Critical Constants for Ch lorodifluoromethane _'. Vc = 0.030525 Cu.ft. /lb Pc = 721.9 psia / Tc = 664.5 R / — (dPldT)Vc 8.05, (dPrldTr)Vc = 7.40 /l 1.8 2.0 2.2 2.4,/ 2.6 2.8 1.0 ------ Pr 1.0 1.2 1.4 1.6 1.8 2.0 Fig. F.4. Plot of [(dPldT)vl(dPldT)vc] vs Pr For R-22 at the Critical Temperature

M!"dri IAN TEP. 14AL Si.ST; f-.JP; J N (,' 41.3. M..IN 01-0'5-73 20:10.'23 PAGE P301 3~~~~~~~3OJ'i~~~~.: FIPL?~r iT ~(A-H,'J-Z,,) 5.030 302 i-,".S.: D; i r -1. ( 1 3,TT F(15),6Ti 3 ):$L;(1 iO),SLP2( 1 5),FTC(1(, 6.0CC,',:, ~),AA('0,10),3t)i0,VVR( ~),)~F(IOPCU EV(200), 7.000 2STC [,S[ P2{ 0), SLPC (10) 8.03CC 0C33 C. A( O),( o (i ) IC(10) C(C,AE 5,CC5,AE6,C CC6, iX,B AAR,LCtAK 9. 00C 0034 NA.,cL[ST /'A;I TA/ TrVC,PC 10. LCC ~3 05;AL'4 LIJT /IT TA2/ AK,,ZCV 1.00 ~i04 ]u'J5 iSt~NL!' /L J TA,/ CC25,E5,ALGF5 1-" ~ ";GOT, "~',;;Et.ISVT /,D-TAq/ CC6, kAcALGF6 13.006G'u.O;;,;;';L LIS'F /:I 4T,5/ Rk5,SL'5 1,.OGC FVL-: LT /D;,T/:./.0o,SL16 15.0CC I, i h.'.~L I'T /DLATA 7/ TT7,RU7,SL!?7. ibJ,00 ~ ~rt 0 ID 1:'~ ELLW' /!)TA/ T A ~T'ldjC8,SLl87 dC 17.0CC~~~~~~~~~L~( 3542,'.;AiC[LI" T /D,,TA / TT9,RC09,SL29 18..000 0303 NAMr.EL I"T /JATAi0/ TT1O,ROiO,SL2iO i9.0CC JO'4 % AMEL I4T / AT~ l/ TT,BT1,TT2,8T2. 20.000 C,,, EAD J Tr2 DTA 21.000.,40Z5 FEAu (:,, DATAr i 22. LCC 20 7 D T ( "' 24.0cC 0 hLI P E A 7D T Al, 5' I 00IC Oi~lo ~[DkC (5,~;Ti;) 2.0cCC 3423 F., o ( 2,:A% ) 27.0C3 0 00 - kItA0 (5 -T A'7,) 26. 03C O0'-J DKE.0 ( A,'4_)A 296. GCC 3-J20 R AD 5 l,%,~0 AO 2j7) 23.000 O0 2i IREA.) i5,AT A7 2b. CC 0022 Z:E~~~~~~~~~A D J`,DkT;8) 2 9.00 k' C;~~~~~~~~~~~~E D2.~ F, TA (5,D-! 3G C O O3:- r4/ A (5,AT'4iO) 31.3' C02 5 A II;,C (,T' ) 32C. CC (1'C -v.' ~ *. 11 3 I i';AL I IN G T hE INPUT VARIABLES 33.303 O.30127 F~ UP. P, Li =.P, 34,96 0 2 27 k L()~~ ~,Z 0S2 i,,;k (7; ~_7 (1)oc Ju? k~Pr (~ -u 3 7. 03%.C IL4"' r~~~~~r'w~~~(7)~ 7U~ 036. 0CC iJ 23 2-, r 4b:;J37. LCC,-J."3 T T hJl- f 2 3, CC,0332 - i'(J —A _>=T-t4.0 HC,333 T,,TT 2 41.3CC (1) i-J q 7TTP (7) =T7 4.2.03J O, 00a3' ~ TTk,(~) =l'T6 43.0CC p' T 4`.003 ~ J37 TT'i )=T- iC,5o0CC 0 0 ]3 5T(l)=T i 4o,.CC0 043 9 bT ( 2 ) =;T 2 47.0CC 0300 SLr' {(5= SL5 0.OO2, 10iS (!- I 3(o):SL, 4 44.;CC ~2 S~LP' (7) =SL 7 50.000 C.:, (=SL4 51. CC I I L PI 9:SL 13 52. CC:13 4;5~~ 5' _c, L P 12', ) r3L Z'i:, L 2, -53. OCC 04o SLP2( O) =SL210 54. 0CC C 4*,'4* P iiJ;T Ti"L DATA 55.0CC S 04 7 WiITC 16,10) 5o. OCC U44,`A iTE (6,,Ll) 57o0CCC 3049 100 FiRMAT ('I,//) 56.0OCC 0350 101 FORMAT ('O',' ** INPUT DATA TC SO3LVE COEFFICIENTS IN 59.0 CC

MICHIGAM T RMi;:AL SYSTE:M F kTRAN G(4133o) 3MAIN 01-05-73 20:13.23 PAGE P002'i-iT- p r_'=JDC~:0 C UAT ION OF STATE *" ) 60.OCC 3051. iTE (T,l 0) TC,VCPC 61oGCC 0052 kiTE 16,!1 ) AK,K,ZCV 62.300 0053,kIlTm (6,!12) CCS,AE5,ALGF5 63.GCC 0054, RiTE (6,113) CC6,AE6,ALGF6 64.GCC 005 VW2IT (6, ti4 TTK.(.),BT()i,TTk(2), BT(2) 65.0CC 0056 iT- (6115 ) PRGR(5),SLPI(5) 66. OCC 035 7 bR ITE (,11 5) RkCR(o),SLP1(o) 67.00C 0 051, v.AITE (6,1i 7) TTR(7)RiOR(7),SLPi(7) 68..OCC 0&59 AF:ITL (6,Zi7) TTR(),RROR(8),SLPL(8) 69.00C C[O0 WPITE (P,120) TTR(9)1RRGR(9),SLPZ(9) 70.0CO 338,5 WR I T E 16,`20) TTR(i0),RRORi(10),SLP2(A10) 71.0CC 0C02' 1:2 FCk,;-'AT (0',10X,'TC =',F10.2,lX,'VC =',F10. 6,I0X'PC =',FiO.3) 72.0CC 0063;il F, PMAT ('0,10X,'AK =',FiO.2, OX.,'R 2F10.6 OX'IC =,F 6IX'ZCV',Fi0.4) 73.000C 3004 122 FORMAT ('0',1OX,'CC5=',FO 0.2,2OX,'AE5=',F10.6,LOX,' ALGF5=',FiO. 74.0CC io) 75.0CC 0065 4~3 F',"AT1AT ('3',iOX,'CCb=',FIO.2,Co10(,AC6=',FIoO.6v0X,'ALGJ-6=',F0.0 76.0C0 z61 o77.J 00 OOb 1i4 FcR!IAT ('' OX,,'TTR=',FlZ2,5X,'8T =',F1O.k4,lOX,'TTR=',F10.2, 78.000 iSX,'ST =',F.0.4) 79.000 0067 115 FCR;4i1 ('0',35X,'kOR=',FlO.6,10X,'SLPl =',F6.2) 680.0CC 0058 117 F3r. MAT ('0', I OX,'TTR=',F10. 2,1OX,'ROR=',FiO. 6,10X,'SLPi ='IFo.2 81.00Cc i ) 82. 0CC 00c9 120 Fje 4MAT ('O',IOX,'TTR',FO0.2,iOX,'RCR:',FiO. 6,iOX,'SLP2 =',F6.2 63.0CC i1) 84.0CC C s,4,, AJDIT I NAL FACTS OF CRITICAL ISOTHERM AND OTHER 85.0C C RELAT!O'~S 85.0CC 3j 73 d6,3C P L T 6, 0070 CX=170 000 60.000 0071 C: PC' C/( r':T C ) 87. OCC C 0072 FTC(:)=-3/8. 88.0cc 0373 FTC(:i1 /16. 9.000 00-7, FTL('t =-). / 25. 90.0C0 0075 FTC(:) =E XP( A LGF5 91,0CC'075F'F ( ) ) OCXP (AL G Fb ) 2.000 j'77 fTC(7) =D0XP(ALGF7 93. o(CC 3o7 ST(31=-0.375+(ZCV-OZ5) 94.UCG 000 bA =LCV-, 250 90. 0CC 003 t = A/ZC 97. CCC 6082 _ / C - C, fL. 96.0CC;053 Z= L.xLZC 2 39. 000 0034, Z C,:Z L3 100.0 C.C C **9* CALCULATION OF A2, 2,C2 101.000 C j v, k.'TRIA ELEE E NTS ARE ~102.0 CC ~3o~5 ~ 30 ZD 2 i,3 i03.00G 5AKT: =AK" TTR (J) 1 4.0 CC 0057 A,A (J,1= l O 0 105.0CG 6035 AAA( J2 )=T T(J) 106. OCO 30; AAA(J, 3) = DEXP (AKTR) 107.OCC a 009 201 btI( J) TR ( J ) ~ TT T (J)-BT(J)8A/TTR (J 08. 0CC;00 CALL CG bLG (0B,AAA,3,1,i.E-15,IEk) 1Ol.OCC 0092 A(2M)=3( l) 11. C0G 0393 (2)=s1=(2 ) 11.0CC 09 C( 2) ( 3 ) 112. 0C C.4 CALCULAT ICN CF A3,B33.... b6 ( T N C ONSTANTS) 113.0CC

MICHIGAN TERMINAL SY"TE;. FPTR AN G(4133o) MAIN 01- 05- 73 20: 10. 23 PAGE P003 Cr~ C C',3Di T I C;I S AR E 1144,i)CC C F 3rCF4Tr, F5TC,F6TC ( 4 CONDITIONS) 115*0CC C i"l~'* EP/ T AT RHOR5,RHOR6 AS T INFl1ITY( 2 CONDITIONS) llb.Oco C LP/ior AT H0kR7,PHORa AT T=TC C 2 C CND I T IOI S) 117.0cc C L O;23/OT2 AT RHOR9,RHOR13 AT T=TC ( 2 C OND I T IONS) 115.000 C m 4 T i. TOTAL C ONDI TI ONtiS 1 1 9. C CC C ArA TIX ELEMENTS ARE; 120.00C C095 XX=OCXP(-AK) 11.0CC 0096 A,22. CC 0397 AA(1,2 =O. 123.000 0098 124.0CC 0ui99 A~A' ~- 0 U 125.0CC 0100 AA(fl;=l,0 1.2.0cc 0101 AA;(.6t)~ e, 0i 17.0OCC 0132 AA(1,7)=0U. 12 8., 0 CC 0103 A-(,c)-0.0 129.000 0104 AA,,) xX 130*. 0CC 0105 A A u,0 1 3I.0CC Oi6 6,6 f 1 r= FT"(,3) 132.JCC 0107 AA( 2 ) 01.0 133.0CC 0105 AA(2,2)=1.0 i34.0CC 0109 1.4C) 035.300 0110 A1 4) 0 0 136. 0CC 0L111 Ah(Z 0 0 141=37.CCC 0112 AA(2,5)=~.0 133.0CC 011.4.1d, 7) u 01240C. CCC 0.1: 1A'.1.0CC 0116 Ak(Z 2,O);0 142. DCC 0 0117 AM=(2,,0.JXX 143.000 oi18 5ob (2r=TC(4) 144.0CC 0119 AA(3 0)=U.0 145.UCC 0120 4A, u.O 146.000 3121 AA(3,3)=-*0 147. 0CC 0~22 AA(3,4.)0.0 1's.000 L0123 AP(3,5) =.O 149. 0GC 0124 AAI(3,6) u. 15 2.0CC 0125 AA(,-l 7)= 0 11.0CC 3126 {,c) 0 3 152.0CO 0127 A ( 3) 0 153.0 0CC 01.25 AA(3,l3) J 154.0CC 01i9 63b(3)=FIC(5) 155.0CC 0130 Ai(4,1)=3,0 1 50.CC 0131 AA(4,2 =0.0 i57.0CC 0132 Ak(4,3)=D0. 156.CCC 013 3 A(4,4)=1.0 159.0CC 013 4 AA(4,5)=i.0 60.0CC 0135 AA(4,b)=0.0 11C; C 0136 A (4,7)C 0 102 * CC 3137 AA(4,6)1.= 1o3.000 0138 AA(4,9)o.0 i 64 0CC 0139 A.(4,J3>=.0 165.0Cc 0140 BBB(4)=FTC(6) 1.c6. 04i C 0141 U0 202'=5,10 lo7*OCC 0142 202 ~VV( I )=I. /RP0kC(I) 166.0CC

MICHIGAN TcrAINAL SYSTL.. 3PRTkAN G(41336) MAIN 01i-05-73 20:10.23 PAGE P004 0!13 DJ 2 7 I=,6 169.00C 0144, cA(. CI 1 )=0.0 7 0. 3CC 0!4 5 l;,A( I,2:0o i. 171.OCC 046 A~A(I1,3)=0.3 217Z.OCC 0147 ( i, 4) =0. O 173.0 00 0143 VF 3i=vVP ( ) -8AA 174. OCC 01149 Vi. %k2=Vk. z;'L,;V RB1 17.O0CC 0L50 V Lk3 =VP R;~ VFS!1 1T75. 0CC 0! 5 V c1 — vP % 3:V RS! 177. CC 3012 A (1,5)= (i /ZC3)/(VI B3) 173.000 0i53 r;A( AI,) =(Ai./L-4 I /ViH.b4 1 79.0CC 0154 EXP5: A -VV ( I) 130.CO 0i55 6XP. A 6, VVRk! ) ii3. 0CG 0'6 IF (LXP..GT.EX) GO TO 203 12. 0CC 0157 AA(1,7) (1./UEXP(EXP5))/ (1.+CCS*OEXP(EXP5)) 183.0CC 0158 A ( i4, 7A ) = ( I./DEXP(EXP5 )/ i.+CC5*0EXP(EXP5)) 5,..,.000 0159 Go TiC 204 185., 0CC 0i63 2_ A-( 1,7)0o.0 13a.uC0 0'6' 204 IF (EXPO.GT.LX) GO TO 205 167.30C o052 AA(I,6)=(i./DOXt(EXP6 )./(i. +CCo*UEXP(EXPt))) 136..OGC 301 3 GL TO 20o is8.00 %)'A. 0% ~ ZC05 AA(i 9,) =G0 19.GCC 0 C5 20 C004TI)J~ 191.00 OLbo 207 ELL( I)= S L1( I )-i./(ZC VFBI) - 812)/(ZC2*VRB2) i 9.3-C 01 7 DO 2 2 1=7,3 193.003' 6) VJ l VVR( I )-8AA I 9. GCC 0L i V I 2 VK13' ~' V RB1 1) 071 VI<32 V V 9 i.C 0177 VKJ3=Ve 4 *V "ii 997. 0CCC Ol 7! Vke 9= v; k g!~:VR F: g 3 ~)1 0i72 ~XP5=AE~'/~( i) 1 93. 0'C 01 73 ~ EApo1'=A!'-. lVV~ ( I ) I!990ICC 0174 Ai?( =-,KTT k ( I ) 200. OC0 0175 XX= AK-,,FXP(AKTR) 20!.0CC 0176 A 1(t,!):O.0 202.0CC 0177 AA( IT,2)= 0 0 203.3CC 0175 AA( I,3)=.0 2 C4, O0 01 7') AA ( I,.) = 00 20. GCC 3 A( I,5)=i./Z(LC34VP 63) 2., 01.',iiA,o~) =,/(ZC,-'V0B4) 2C7. 3CC o I2 IF (0XPS,GT.tX) G0 TO 2C8 203.0CC 01d3 AA(ti,7) (./DEXP(EXPS))/(i.*CC5*DEEXP(EX J5)) 2C9.0CC 0''4 GCO To 209 21C. 0CC 0i5 26 C A(I,7)=00. 2ii.0CC 0L8 20) IF ((XPc. GT.EX) GC TO 210 212.0CC 0137 AA(I, IDi,=(XPE EXP6))(1.++CC 6 ADEXP(EXP6 213.0CC O0B3 GC TO 211 2i4.0CC a 9 213 AA( i,8)=0o0 2i5.0CC 0i9(0 211 A4(I,9) =- XX/(LZC32IV9=63) 21oo.00 C ) r, i ] -.XI/ I Z C,,.V-VR 5 4 ) 27.? O O 0192 212 i;t( I)=SLPi (I )-1./(ZLCVR63 1) -(B( 2 )-XXC(2I/(C2VRb2) 28,. 0 C C 0!93 CO 2~14 1=9,o10 219.0CC 0194 AKT R =-AK*TT F, ( I ) 22 C. C;CC 0195 A X= AK,- AK L)DEXP ( AT R ) 2~i. 0CC 0196 VR81 =VVR( I )-AA 222. OCC 0197 VRb2=VKi1*VR!i 223.000

M!i"HIGAN TERMINAL SYSTEM FjRTPAN Gi41336) MAIN 01-05-73 20:10.23 PAGE P005 01 9 I VPR 3 =Vl. ~j ~'VRB2 2'24.OCC O1 939 V., 4 =VR.I'VR6F 3 ~ 2~2~ C 02; 00D. i3 J=i, 226.0 C 0,39. 2;3 =A('I j 0 Z27. CC 0202,,-, (I,') XX/ (LC3.V5"3) 22d. CCO O03 AI( U =):AXX/( ZC4t-VR. 6) 22';. 00 0254 2' 4 31 ) 9( L r= 1 (i -XX*CL (2)/(L C2*VR6'2 230.0G00 i u2J5 RiT- (o, Z uO) i C.CC 0206 2-U I:,,10'! 232.000 0237 220.r;!i T (6, 121) AA(Ei1,J),J=01i,0),BT6(I) 233.0(C D208 21 FR;-IT ( 10.4) 24. U0C C *",v* ALL CCEFF IC IENTS IN AA & BB ARE DEF I NED 25D.0CC 0239. CLL;S;LG (BBB,AAO,10,1,.*E-40, IES) 23b. 0CC, 02'0 AI3)= 3 -3i I) 237. 0C'2i 14 =M) S (2) 23o.oCC 02.2,(:,-) =; ) 239.00 i0203 Ai. otCL( 4) 240.CC 024 b( 5) 24.0GCC OZ~5 (-):. c{) 242.0CC 0216 8(C'b5 = bI7 243.000 0207 5( 244.c6C C213 C 3I, VA, ) 9 245.0CC 02 I 9 C 4 ) =B% 3( 2 0 ) 246. CC"C'J2 O C (5) =oC o / 47. CC 22' C():0.0 24 c. CC - LL J.JST,-,TS ARE CALCULATED 249.000 - 4;'; P IT C I ST AN TS 25. SACCT 0222,i ( oi20} 251.0CC 0223 k< ITE (6,;.22) 252. CCC 0224,I' TE (6,123) 253.230 3225 v. I T (6,124) 254.0CC 02206.22 F6." ('0','*-; COEFFICIE;.TS IN THE REDUCE3 EQUATION,OF 255.0C'.T ATE'-~'~-**') 25c. CC 0227 123 -:'.LT ('O'' -'x**-** PR=TR/ ( ZC (VR-/V C) ) +(AZ+ 2'TR+C2*'- XP(-K'.TR) 257.0CC i )/ Z C2,/ (( B/VC )'F (V- /VC)+,,+A+STR /{5EXP(AE5S*VR))*(i. +CC5 253I.0003'-EXP{VA 5' VR9) )+') 259.0CC 0_22 024 Fi.;.A-T (',' (A6+E6*TR)/(EXP(AE6*VRR*1i.e CC6*EXP(AE6*'VR) ) *' 8) 260.000 0229 wRITc C,.02) IEa 2i(a. CCC 023C. i T iE (o,102) IES 2b2.0CC 0231 wPiTE 0,31) A(2) 263.0C0 0232 w;<.ITC (6,132) 8(2) 2o4.OCC J233 nRiTL (I,!33) C(2) 265.0OC 20234 3!TC (I6,0134) A(3) 26C,. ClCL 0235 s'.ITC (o,135) b(3) 267.C0C 3236.: ITC (e,i36) C(3) 20.OCC 0237 wiK!T (6,137) A(4) 209.0 CC 0238 wRiTE (0,i38),(4) 27Co0 CC 0239' RITC (6,039) C(,) 271.000 0243 WIUTE (6,140) A(S) 272.0 CC 02'41 w1riTE (6,141) 3(:) 273*3CC 0242 R IITO (6,142) A(6S) 274.UCC 0243 WRITE (6,143) 8(6) 275.0CC 02;4,RITE (5,!44) LC 276.0CC 0245 w.RITTE ({,145),AA 277. 0CC 0246 102 FORMAT'O',20X,' 1IE=',12) 278.0CC

c C 0 C c) C C C.,C C C C. 0C; C,'C) c C C C:O C) C. 0 C', c C C C: O C. c. c c CC O c, ". C- C)C C.. O O ~C) ) O 3') r~., r,,~ r,; i,~ f~ r~o f~, t~ h., t~ IN) tN~ iNJ Nl) N' f~, t"!.%a' t, 1h.J II fNJ r-J r,., I, T, f~.J iN)1 N N, ) r~> rl ~ r,,:~ r.! iN,) N.) )r",J K) I-. N? PO [,. ) N ~ 13 ~ ~ ~ ~ ~'~-''~-'V4 77 V. 7> h' 1-P 3-7IC. —C-C ( t).L J CC) ) -T'T IT IC. C'? C II C-CI VI 0 3C; — C4C —t C;-:c -. U: 4- C,, -, ( T, -l - I- g. A I -' -, V I - - -. -.,.; -,. C:-., [..,:: C. I T, l II i X:'' CL)'; C C C )C C C " C II ~ ~ ~ ~ T II -t T`~H c~I i 0~ I~~ QCC )00(~11 —:,C)00000C n g7. C., -4 >7- >4- 3. C-4- 0, v- 4, w -))cr.> v N'" ~ ~ *-''C;.""',-.. C'r..' r -0 (.: i' "' "A I,'.' "''~ -_. N) L) cr j C:F: 7K', (jC.C7C3C: -i tC CC, C C i; 0 - -TIQ- —' r- C c;-r i4 ~- t~, T rC r C.. I. 4- X'.,- -. C)-N.CC C4 v- 4-l _ C'4) 7,~ r C') IC,~ w C_)". C- C, C- - () C C C) C -" C' C~,~'~;. >< ~< 0:. O; L'~G~ In'-4 * - ~:-'.?, 3~.t~......<L, 7TT. ~ )e y~t. CflG) n -(k Crt. x~ c- w rA -. C.... Il< + 0~0< X l u n V. -- I. II J )-'. II II II II I. II II II II II I..I II.1 II r Ci'C? C)4 < < c) <- -, - r: m r- r-, n Co - m m o - + 4- C) -- 4 - - r- -,- -- 4- - -- - ~ - c-~ 4 — It * O U -. f~ I r' O,O'O,'('tO' O.O"O'(?'~O' * -- — I +'r m- o-', N..NN,..NNT-~lC",.N ~ C —- rT >C > — 4 - — I I-I -'- n --— O —--------- v~ r';e 6 ~~~~~~~~~n Tn r C~~~~~~~ Y ~~~~ Y CI Yy ~~~~~r n - M r Y M I`7 11 r 1`1 TI o- -. > C,— J + + C- C \),;NJ \X r" N N 44 ~ 4 V V ~T - 4) TI/ O C=, -V 1 VI - -. + - -'TI — I - C. 4- m -;'1 6 r1 -r C X! 4tl y r~~~~~~~~~~~~U C. m~ ~~~~~~ 4-TI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. >4~~~~~~~~~~~~c 4-), 0,oc,~ z ~.. -4 ~~~~~~~~~~~~~~~~~~~~r~~~4O C cr Un ~ ~ ~ ~ h, a O~~~~~~~~~~,V~ C' 1..- * C): -n 2N b t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3 eW ~' C U L,, f.t O-j l'-I L.NN, r, N ro,,I - -I- k-., c-I-C, O C, C, C./ )0C_ _ o'-C -J O,, O 4'. b r.O m.(iC ~CO OC-* r. co*..or, v, -4, U, rv t O cn o-, v, 4, CL) -4 * *. k, Ou — J c, v. 4" N, i,- c,, Co -- J r, -,. 1 t*- CC r II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 C; 0 C; C:, C) CD CD C), C, C., C" C, 0 ) C-) C) C 0:C) C; C, C C, C- 0 C, C) C. C?- C0 0 C, C -, C- C- C. C) C; C) C) 0 C) C' C: 0 C) C0 C.; C)') C:* C) C " C) " 1 C) oC e- - ) cC r"(. )C C, C C' C?,C) ( C-) C) c.) C- C, C ) C c, -. C+ C,, C1 C) C' r-. C. C-1 cj C; C) ~O c- C- C) C) "-,'C-) r" -i C) CC', tC) C )CCO )CC) C-) C"I riC) n n C) C( C- C)c7C)C,C)C)C C)C. C; C-, CC) C'> CD nC; C")VI C' CiC.'C) elC)COC) C) TOO

H!CH..GA" TE.'iiNIAL 3YST=-, FJukTAi:.4, 06(4'33 MA6)I 01-05-73 20: lu.23 PAGE P007;'56 CALL CL DT (V?,TR,SLOPE) 334.000 0297 SLP C( i ) =SLCPt 335. OCC 0298 239 RiTE,',, 2,0) TTR(I,)VVvR(I,SLPIS )SLPCIP(I) 336.*OCU &2'-9 240 FL;.:.AiT ('J',20X,'TEi4P:,FiJ. 2,5X,'VOL=',FiO. 6, 5X, SLLP~L=',F10.2 337.0CC i 5 X,S 7L PL = I*,FI ) I 2'.5j 33.OCC 0330 0K'22 I=i,3 33. 0CC 033 3K =-JA.t::"P T 7( K I) 34.0.0CC U0 X2 X XX= P (;KTR) 34 i 0 Cc 0303 te( i)=(( 2)+ (2)'TTR(iI+ C( 2*XXi )T/TTT R I)TTR(I)I 342,.3CC 03-34 ELTC( I )=TC ( I ) +dA/TTR ( I) 343. OCC 303 222 0i'TE- t,223;l TTR( I I) BT( I BTC(I ) 344.0CC 0306 223 F.OP' f. T (''2 OX,''TEMP=',F1lU.2,5XtI&' IF10.4,5Xr BCAL=',FiO.4) 3',50CO C 4," I;,/. T2 AT T=TC 346.0CC 0307 DJ 241 I=9,0 347.0.C 0303 V?=V V,9( I ) 3'. CCC 3330 T R=T T ( I ) 349.GCC,iO CALL J2P)T2 ( VR, TR,SLOPE 2i 3Z0. 0CC 03i i S L P2C( O1}=LLCPC=2 351 000 031~2 24, i: I I,2,2 TR ITRIi),VVI(I),SLP2 ( Ii),SLPZC(I) 352. CCC 03i3;-,2 Fi];.t ('0' T,20X, TEYP=,F1i0,2,5XVOL:' FlO. 6,5X,'SL2 LZ=',F1!2,5 353.oJCC LX,''' ~l~=' iIF-3.2) 354. CCC C "*; V 4 L i [-ITY ThSTING 355.0 LC 03!4.IT (O,!0) 3IS.UCO 331.5,k:-(o2. ) 357. CCC 33' 2 F F T''' * LiNEAiF ITY TESTING *****.. 4 ) 38.,3CC 0317 ~ 24,, i=56 35. 0 C 0 *~Ld P~Sl~u ~ 3t30o0CC ~03i9~V=.""V (I) 3!.i.0CC 0320 T=3 J 362.000 0C2I Tkr= 6 363. CCC,J322 C;LL P-)/,'SR T (VRTR,PR,PRCAL,ODVPCO) 304.C00 03J23 PK =PC,.L 365. UCC 0324 P i = 366.0OCC 0325 Di: V= 3 367.,JCC 032 5 =. " 36o. CCC 0327 Lic (', -'-,51) VR,TR,,PFPCALDEVPCD 36C,. CCC 0 ) T3 = 2 I'i.. 370.0CG 032290 i-:'.,,-,- +S i P' I I)* (r k-Ti ) 371. OCC 0330 CLL'S C V(VR, TP,, PR, PRCAL,DEV, PD) 372.0CC 0331 oPT,,P. I 251) V,,T'k,PRPRCAL,0DVPCD 373.0C0 0332 TF.22.0 374. CC 0335 PR= + LP (I)* (T-TP I ) 375.0CC 0334 CALL Ft ES(VRTTRPR P PRCALOEV PCD) 376. 0CC 0335 3 44 iP.ITE: (,,25L) VR.,Ti, PR,PRCAL(CEV,PCD 3770 CC 0336 25i FCP MAA ('''I F,15 6,4F 15.3,Fi4, 2) 376.0CC 033,7 D'~ 2'03 I =,78 37S.GCC 0338 V k='v V:-., ( I ) 38C. 0CC 0339 T3=:L.J 381.0CC 03430T Tfk=r R 1382.0CC U341 CALL Pt'E.R (V R TK, PR PRCAL, EV, PCD) j383.0CC 3 42 Pk= P C,,L 354.0CO 3343 P-,=P? 385. CC 0344 DE'V= 0. 3 3356. OCC 3345 PfC0=0.3 387.0CC 0346 -, kIT (T,251) VR,TR,PR,PRCALvJEV,PCD 388. CCC

I4ICHIGAN TERmINAL. SYSTE-m FORTRAN G(4i336) MA IN 01-05-73 20: 10.23 PAGE P308 0347 Tk.3I.CC 0340 PR= P~i~+ SL PI (I) ( TRR1 390.0CC 3349 CALL?SCkrk(VTRtPRPRCALDEVPCD) 391.3Cc 0350 WR~ PITE 16.v 251 ) VR, T.R,9 PR, PRC AL, DEV, PCO 332*CCC 0351 TK=142 393*0CC 0352 Pk= Pq$L+ SL P 1 (I ) (TR-TR I 394.000 0353 CAL L PR, E SGS ( VRTR, PR, PRCAL,3 EV, P'uD) 3 95 0 CC 0354 245 WR I T E (6,251) VRTiR,PRPRCALt V,PCJ 30.OC0O 0355 6W.i T E 6,1 30 ) 397.0CC C * -.1 *A 1: CC,UPSRISUN OF EXPER IME' TAL CRITICAL ISOTHE RM OF 398.07CC C ~~'~e * CHLGRC3!FL UCCMETHANE WITH CALCUL ATE POINTS 39.0-CC C P " ~2r:~: ~F; 8 CR CITICAL I S CT H Er R t- IS CONSTRUCT ED FkRM MICHELS DATA 4CD.0CC C l A N ZANOER'S L; AT A, WITH EXT R A P &LAT I JiNT Oj 2.9 RHOR 401.CCC C *C'u4 FULLOWING CRITICAL I SO TH E R M OF C AR B O N OICXIOE 402.000 C INPJT DATA UNITS ARE: 403. 0CC C * v vy VOLUME IN CUBIC FEET P ER POU ND 404.0CC C * p PR E S S UR E IN PSIA 405,000 0116i,:Si WRITE 165551) 4be. OCC 0 357 551 FC? MAT ( I' is','*4* CCMPARISCN OF E XP E R I M E N TAL CRITICAL' 7. 000 I THERM OF C HL OROUJ I F LUR LOMETTHA N E WITH THE EQUATIGN OF STA 403.0CC 2T T? r;41W,/ 409,OCC 33 -;;c~ 1 WRl 0 (6,553) 41.CCC 0 3 535-53 F('-4AT (O', V PEXP PCAL PR 411.0CC IL/Pl PFCAL PCo VR RHOR',/f) 412,OCC 01,,; 0 550 m u 15,304) V,PE XPI 413.0CC oSb- T =21111V-1000.) 41' GCCC 3 -11 62 TF (TcSTLT.0.iI G0 TO 555 4 5.0CC /4~3 ~X-~/ VC 41o. CC ~~64;Pi P /3P/C 4' 7. CCC 330o.6, 418.0CC Pr Pk rPP, =pp 41 3 OCC 03t7 CALL PiicSOR (VRTKPAPRCAL,JEV,PCL) 420. 0 CC 0311 k RHuML, ='_I/V P 42 * -CCC 03j56 9'MITL' (6,552) VPEXP,PCALPR XP,PRCAL,PCuiVRR HRI 42i.JCO 03 70 Cu IC 550 423. iCCC 0371 555 CuNTIN U E 4240CC' 0372 30J4 FORiAT (2F15.*6II1 415. CCC 0373 552 FiU`MU~PAT ('lU'. 9XF12.6,,2FIL'.2',F221.4,Fl2,2F;124,ICXII) 42h. Cc 0374 AQ iTE Iu,100) 427.0CC 0375; =0. 426.0LC C L CiLCPQI F L UU ROM E T1H AN E, F- 22 429.060 C 1 iS T R I C PVT DATA REPORTED BY M ICtHE LS 430.000 C 1,; I NPUT DATA UN ITS ARE: 431.0CC C Vi~* VOLUME IN CU8IC FEET PER POUND 432.0CC ~'r~u;*~ IIT M rIPE R AT UR E IN RANKINE 433.OCC r 7 -' 4kc PI-,1'SU R I t P IA 4:34. DCC 0376 TO (651 35.0CC 0377 51IF.T!I0',' CHL0;kCbAFLU0RCMETH"N E, ISOMETRIC P VT DA 43 6.CC A, EPi'TED BY MICHELS 4-4~4) 4370C C O3Tsj WRI TE (~,S12I ~r38. CCCi 0379 A1L F~~~' FT (' 05'Co *' INPUT DATA UNITS ARE: V IN CFT/Lti, T 439.0CC i IN, P I N PSIA: *V***)j 44 0.0CC 3d IIE (T6,52 ) 44i.,0CC 038 1 51 uR AAT ('0'U,' *4C'*j' OUTPUT IN CROER: VR,TR,Pk1EXP,PRCrAL 4c2.0CC i, 1..OEVPCO *M**U4~ 443. 0CC

MICHIGA' TeRMi NAL SYSTLE4 FORTPAN G(41336) MAIN 01-05-73 20:10. 23 PAGE P009 u3 2 WRITE (o,372} 444.0C0C C383 ii RED (5,30I1) V,T, PEXP 445.CCC ~0398~ TEST=~TAS (V-20 0.) 44o. CLC 0385 IF (TEST.LT.O,I) GO TO 12 447.0CC 3.33 $c N=t-:+ l 48.GOOC 03e7 VW=V/VC 44S 0OCC 0386 TR=T/TC 450.0CC 0389 Pk=? XP/PC 451. O CC 0390 CALL PRESOR (VRTR,PR,PRCAL,DEV,PCD) 452.G CC 0391 xR. iT (5,361) VR,TR,PRPRCAL,PCD 453.0CC 03 92 PCLEV (,: ) =PCD'54.,CC 0393 GG T. 1!i 4 S. CCC 03~4 12 CG.T kJUE 456.0CC 0)95 CALL UEVIAN (PCDEV,N,AVPCC,ABPCL,STPCD) 457. CCC 0396 WRITL (6,1001 458. CC 03197 WRITE (6,302) AVPCC,AEPCDSTPSPCD 459.006 0398 36i FCR;IAT ('#',FiJ5.`3F~15.3,F14.2! I.t oCC 0399 362 FOR;:,AT ('O',20X,'AVPC0=',FlO.2,OXt'ABPCD-',flO. 2,OX,'STPCD= *, 45i.0LC iF40.2) 462.C ~'C 040C WRITE (6,100) 4o3.CCC 0401 11=0.0 464.0J0 -C * CLL"HL FJDI FLULURCMT A N E, F-22 465*o0C C!S/E CP:LTRIC PVT C ATA REPURTED BY LANUER 466. LCC C "*' I-iP uT DATA UNITS ARE: 46 7. 00GC C ~CE,,S I'TY IN GRAMS PER CC. 4668'. 0I C, E' — x T E9,EATUR E IN CENTIGRADE 4c,. CCC C P, P, ESUR IN9 BAR 8.7'P-7 C. C0 0 C C u* CutV.RS I C-N FACTOPS AR E 47', C C C *' %, NE 3AR 14. 503E3 PSIA. A72.0CC C GI` aE RA:!i Pt-R CC. - 62.423327 POUNDS PtR CFT. 473.0CC 0432 WRITE (6,513) 474. OCC w403 513 Fi:T (O',' *'T CHLORLOIFLUROiLTHANEF-22, ISOMETRIC PVT 475.;CC 1 DATA P - EPJTED BY ZANDER ** *4''.,76.000 0404, RIT I6, 514) 477. CC 0405 51I4 Fk,' AT ('O,: INPUl UNITS ARE: RHO IN GMS/CC, T I 478.3CC iN C, P iN EAR 4* 7*9') 479. 0CC 0406 kwITE (6,522) 452. 0, CC 0407 522 FCF;AT i'C.,'~~.~* OUTPUT IN CROER: RHO, T, Pr V,, 431.CC ).PLX', FCALL,0 EV, PCL'L., **",'') 42. GCC C4 C T.TE (o,373) 4-63. CCC O40q 22 i." - (5,302) RHC, TE P,PIRES 484.3 CC 0410 TEST=DAE$(RHO- 3Q0.} 485. CC 0411 I — (T.5.LT.O.i) GO TO 22 480.02CC ~04212.% 48 7.='v100C 0,, 3 P EX - =P, ES';14.5'..3o3 48i.C CC 04i14 V:=Z, /(RH G 6 2 42 327) 439.0CC ~.i 5i ~ T =( T _MP +2 73. ) 5 *.8 490OCC L4,5 P4 =pExP/'C 491. 0CC Ou?1'!7 VP =v/VC 492. CCC 34i8 T.= T7/TC 49 3. 00 041-9 CLL RPk.ESCk (VRTR,PR,PRCAL,0EVPC0) 4,4..~CC 0420 FITO (,363) RHC,TEC-P,PRES SVR,V T,PR,PCAL,?CP'95.0CC 042i PCOE(' )=CPCD 90o. CCC 0422 GO TO 21 497.dCC 0423 363 FORMAT ( I0',F 12.4,2F' 2. 2, iF12. 6, 3F12.3,Fl 1.2) 498.o0CC

MICOHIGAf TERMINAL SYSTEM FORTRAN G(41336) MAIN 01-05-73 20:10.23 PAGE P1OO 042' 22 CONT I;:UE 499,0CC 042: CALL 3LVIAN (PCDEV,NAVPCO,A3PCU,STPCD) 5C. CCC 26 kR[ITE (6,!JO) 501.0CC 3427.RITE (6,362) AVPCD,ABPCC, STPCO 502.0C0 3428 W'RITE (6i,0) 503. CCC 0429:N=,0. 504.OCC' CHLOPOOIFLUOROMETHANEIF-22 505.0CC',*4'*~ ISUTHEkiA AL P/T DATA REPORTED 8Y LANOER 506.OCO C r.** I N'PUT DATA UNITS ARE: 5O7.0CC i iM Il MPR ATUJKE IN CENTIGR-ADE 505.00C ~ PkES$,Uk IN BAR 509. OC CC C =~ CGNVERSION FACTORS ARE: 51O0.0CC C'~~','* CNE 3AA = 14.50383 PSIA. 511.UCC 0433 IklIT6 (, 515) 512.3CC 0431 515 FORMAT i'0,0CH LoRJDIFLURCMETHANEtF-22, ISOTHERMAL DATA REPORTE 513.000 ~3 6Y LANDER ***** ) 514. CCC 0432 WRITE (6,516) 5!5.GCC 0433 516 FL;>AT (l'0',' ***a INPUT UNITS ARE: T IN C, P IN BAR 516.0CC ~~~~~I "v~,.~~'~~~.;' ) 517. CCC C4'.4 IkITE (E,523) 51>3.CCC 0435 52 FC.;4.J ('C',' **** *~*,I*I OUTPUT IN ORDER T, P1 Z1, V, T, PE 5~9.000 iXP, PCAL, 0EV, PCO ******D**'.) 520. CC 3436 Wg FITE (6,374) 521.0CC 0437 31 RtAO (5,303) TEMPIPRES,Z 522.0 C 343 b TrT=S Th=AbS(TEMP-4000o) 523. OCL 0439 IF TE ST.LT, O, 1) GU TO 32 52 4.000 o 0440 5=; + 25.CC CC 04-:' P- XP=PRES'i 4. 50383 526.CCC J,42 T=(TU1P.273.15)*i.8 527.UOCC 0443 V=(L'P*T)/PEXP 526. CCC 0.44 P.k=PLXP/PC 529.0CC O,,,. 5 VR=V/VC 530.0CC 0446 T.=T/TC 531 CCC 0447 CALL PRESOR (VR,TR,PRPRCALDEVPCD) 532.0C0 0443 WRITE (6,364) TEMP, PRESZ,VR,TR,PR,PRCAL,PCO 533.0CC G442 PCDE V(N ) =PCO 534. CCC 0450 Gr TO 31 535,OCC 0451- 32 COUiNT IrUE 53t. CCC 0,52 CALL DEVIAN (PCDEV, NAVPCGCA6PCCSTPC ) 537. CCC 0453 WR IT; (o,100) 53b.OCC 0454', RITE (6,362) AVPCC,AEPCC,STPCD 535G,.CC 0455';vl I T (6,100) 540.0CC 0456 364 FORMAT (', 2F 12.2,2F12.6,3F 123,F 1.2) 541.00G 0O,57 33i FWRM AT (F20.,t2F15.6) 542. OCC 0453 302 -ORMAT (3F15,3) 543.OCC 0459 303 FU.AT (1F20.6,2F15.6) 544.000 04.50 372 FCRMAT ('0',' VR TR PR 545.0CC PkCAL PCD',//) 54o. CCC 04hi 373 FORMAT ('O',' RH3 TEMP PRES V 547.0C 1I PEXP PCAL PC-D',Il/ 54.3.0CC 0462 374 FORMAT I('0',' TEMP PRES Z V 549.0CC 1 T PEXP PCAL PCO',//) 55 3. OC0. 0463 END 551.0CC *CPTIONS IN EFFECT* IO,EBCDIC,SCUFR CE,NOLIST,NODECK,LUA0,N0MAP *OPTIUNS IN EFFECT* NAME = MAIN, LINECNT = 57

F!ICH!G4,N TERMINAL SYSTE;. F)PiRAN G(41336) PRESCRA 01-05-73 20: 1044 PAGE PI01 GO1l i.'.CL)TI,;4E PRESOFR (VRTf,PP,PRCAL,,DEV,?C) 552.0CC u002' I:'P. iIT RL8 (A-t-h,C-Z, S) 553.00C;Ci03 CL' (I'C' hu, CB(Ii)),C( 10,AE5,CC5,AE6, CC6EX,';AAR,ZCAK 554,.CC 0OO)/ -.,Oi'"...SIc." xN:N(1iOJ),YY5),ZLCC(5) 555..0C 0005 LZC ( i)=LC*ZC 550. COC 0036 LCC(3 =ZCC( 2)*ZC 557. CCC 0307 ZCC 4 )=ZLCC(3 C C 558.0CC 0038 AK' R =-A K-T R 559 0CC 0039 XX=JcXP ( ATP ) 5. OCC 00.13 DO 261 i=2,6 56;.OCC 01; 2~61 X.i(i)= A (!) +(I )TR+C( I XX 5o0,OCC 01;2 YY( )=:V-bA'A 563. CC GCi3 YY { 1 ) =YY ( 41 ) *YY( 1 ) 564.000 0034 YY(3)=YY{2i )YY(U ) 565.0CC 03015 YY(4)=YY(3)*YY(I 1 ) 56.CC 003' EXP5=At5*VR 567.00CC 031 7 EXP 6 = A6*VR 568. 0CC O i~g SU;..= G,o 569.00C 03?1 D00 2-2 1=2,4 570C.0C (320 Xi.UM=( XtNN( I ) /YY ( I /ZCC( I) 57i. OCC O323 262 SUg = Su+ X NU M 572.CCC 0322 il (X'XP5,GT.EX) GO TO 263 573.OCO O023 T:.,-' = X:,(NI 5S/CEXP(EXP5 ))/( 1.+CC5*DEXP(EXP5)) 574.0CC 0024 GO Tb 254 575.0CC 0325 2t3 TFEi':= J.GC 57o. CCC C 0026 204 IF (EXtPs.GT.EX) GO TC 265 578.00CC 0027 T.-6= N( 6 )/DEXP (EXP6 ) i. +CC69OEXP(EXP6 ) 5 7. CC 0328 Gv Tu 2 6 563. uCC 3029 2c5 TER;'2=J.0 581O.0CO 0330 266 C3.T i NJE 582.0CC 0031 PFCAL=iR/(ZC*YY 1I ))+SUM+TERM5+TER6o+TERMN7 583.0CC 0032 0cV =Pk-PRCAL 589'.OCC G033 PCu= 0DEV~100 1)/PR 585.0CC 0034 R ETURN 5a6. CCC 0035 END 587.0CC *CPTIONS IN EFFECT* ID,EBC OIC,SGUICEN LIST,NOECKILCAC, NGMAP *CPFiOiV'N EFFECT* NAM!L = PRESGR, LINECNT = 57 *STATiSTiCS SOURCE STATEJcENTS = 35,PAROGRAM SIZE = 1306 *STA TS T' I'S N DIACGNJOSTICS GENERATE0 hO fRR3AS i:. PR.EStH

~ICHIG,',' TE. —INAL SYS-rM F OiTRAN G(41336) 2PDT 01-05-73 20:10., 6 PAGE P001 3' SU(CITI:l;;E DP-,'T VRPTs, SLOPE) 5,..CCGC 0i032 1'PLICTT;A59(. 8O-, i 54-,'CCC O015 CCA:; -:;A(LJ tl),3(i~O),C('.),AE5,CCS,AE6,CCS,EX,i3AAR,ZC,AK 5"C.0CC 0304 l OIIr',S i;u. YY(5),ZCC(5) 54,1.0G0,C0 YS! ) =V.- a 592. dCC OCG' YY(2 )-YY 1)*YY1L) 593.C0C OCJ7 Y (3)=YY 2) *YY ( ) 594. 0CC oa YY(4 )=Y( Y3) ( YY (. 595. CLC'*50. / XP/ V 596.CCC 2,J'.. EX X -AF 5$0 =A', li' 597. 0CC Vz!C Z CC4( 2=Z LC 538.CCC 55i2 ZCC( ) =ZCiC 2C ZC 599.CCC (3 C )= ZCC 3)*ZC 6CC.320 3Oi4 KTR =-A K' TR 601 * 3 CC J ) v5 XX= AKX (A KTR ). 320320 I051 Si= C. 6 C3.6 CC;C!7 DO 271i =2,4 604.0CC 3 iL YXX-= (J )-C(J ):'XX )/(YY(J)*ZC (J) 603j.3 C 3"1g 271 SU~-= %SO4+XXX 6bU. 3CC 3023 if (':-XP..GT.cX) GO TO 272 607.0CCC z33;21 T E~;.:.5= 1: ( {5 15)-C( 5)/OXX)/DEXP SL )/(i.+CC5SDEXP(EXP5)) 6S3oOCC 02;2 GO TC 273 6CGC... CC 60.23 272 T&kM'=O.3 C M C 0024 27; IF (cXoP.GT.EX) GO TO 274 61]..'3 o O-Z 5- TE'; M-= ( 3 t6)- C( 6 )XX) /DEXP (EXPb ) /( 1. +CCb*DEXP(EXPo ) ) O12. _.1 302i GO TZ 275 oi7. C5 L;.;: v7 2 74 TF k:S 5=;.. 6i, JCC. C 02. 275 C *;T i.;' 6-5.0Cv 0,' i SL;,-=Z I./(ZC*YY(- i ) ) +L5M + TE P M5 +TEPM+TE..Me+T7ERM7'CC 0230C rL.:T U 61 7. OCC 0331,K! 61 3.CC *3PTI&,'S 1;i SFFE:Cr* I,, E30D3IC, SiUCE,iNOLIST,NODECKLOAD,NCMAP "*U?TIjjNS iNJ FI-LCT* Ni'i,;E = DPL3T, LINECNT = 5!'ST7.TIST:I ST:UURCEC STATEMaENTS = 31,PROGRAM SIZE = 1094 *STAT I STIil.S NIC DOAG\C0STICS GC;iERPATE3D;L, FlI;S. Il D rlT

HICHIGAN TERMINAL SYSTEM F';kTRAN G(41336) 02PDT2 0i-05-73 20:i0.47 PAGE POOl J3O1 SUbF'CUTI';N E 02PDT2 (VR,TR,SL3PE2 ) 61,.OCC O.J)2 IIPPL IC IT 2EtAL 8 (A-H, tC-Z, S) 62 C. CC u)LA3 C[]?i, L U A(i ),5(O),CilOA),AE5,CCCAE6,CCEX,tBAA,R,tLC,AK c21.OCC 0 003 V I, = I -,;,A 622. OCC 0Zi5 V[L=V Il: I iL 623.0CC L006, i =VI2=VI1 24. 0CC C007 V.4= V I J;XV I 1 625.00C 003 LZC =Z C, Z 626. OO 0>i09 ZCj:= ZC- ZC 627.0iC l3 10 LC4 =ZC3'ZC 62. SCCC ObZ ~ i.AExP 5= AL 5-,;VR 2). C C 0'3!2...XP AcE V; R 63 C. OCc Ci 3 KTk=-A,4 T. b: 31.0 CC 00.'4. XX=A J-A Ar, -:.- E XP AK(TR ) 632,. 0CC 0/ I[ ( EXP 5,GT,EX) C TOT 281 c333 C'CC vOL5 TLkti:T = C ( 5 ) /DtXP EXP5 ) /(1+CC5*DEXP(EXP5) ) 634. CC C 17 GO TO 282 635.0CC 00- d 281 TER,M5=O 0 6Uo. OC0 OO"0 282 IF (EXP;6.T.E-X) GO TO 283 637.0CC 332 TE.<,:I= C(O) /EX[XP XP ) / (i. +CC<#*EXP( EXP,! ) 63.. uCC.2.321i CUL TC 2I-4 63,.OCC u 2, 2 Zb33 T'.,F!T J=Co J 64C.OCC;023 2 84 C' C;T i'.vt C4. JCC G,24 S L!3P- =C { (2)-/( ZLC2V I ) +C (i3 )/ ZC3*VI 3) C( 4 ) / C4V 4) 642.GCC 0,2 5 S'CP~=XX*LLUP'E2 642,.C00 C-2 6 R ETUIN 64.. CCC 00 Ci9.27 E ND 645O0CC *L;'. IN' Iri EFF-CT* IC, ECDICC,SCURCE,NOLIST,O;DECK,L0AD,NOGAP;.;'[:.-S'.; EFFLCT NA:-I,: = D3PCT2, LINECNT = 57 IST >, FO1i C, * SJUPCL.CE STATE:ENTS = 27,PRUGRAM S IZE = 922 ST.Ti T.T'CS NC t! AGN'STICS GENERATED;'C LR0.RO3S IN O2PCT2

M.ICHIGAN TERMINAL SYSTE; FORTRA, G(4133o) DEVIAN 01-05-73 20: 10.48 PAGE PO0l ~~ 32C.. SU.kSSUT- uTINC DEVIAN (PCDEV,N,AVPCC,iA8PCC,STPCDi 6 46. CC C;~s2 iMPLICIT REAL*d (A-H,G-Z, S J 6 O7. 0C 03'.'3 D0..................... i.;~E'SI0r, PCUEV(200) 64S.0CC. SJ 4.$4. SUl", = U O. 649.OCG 0S5 SC,"2 =J. 0 65C. OCCG G 0(0 C SU(M3=O= 0 651.0CC COT7 DU I c' I=1,N 652.0CC 30.3. S UN/=S:'l J1+PCDEVC 1) o53.OCC OGC.'#-......=....L. XX:PCL V( L ) 65'. OCC 03 00 TERM=P A S(XX) o55.0CG G3i'!..............S SU:=.t 2 SJUM2+TERM E5e. OCC C)32 XXX= A,.X.-,'X X 6o57. 3CC 30D 3 SULi':- Su.3+XXX 66. OCO;ti_~~~~ wT~~~i a...................E (i'TI i 659. 0 CC CO 1!5 A.V F'C ~=aV UF'' I//N 66 C.CC 091 AP C -;, U 2 / N 661.0 C 3017 TE kM=SUN3/ (N-1 662* OCO 00i 3 STPCL= USRT ( TEKM) 66b3. OCC 0019 R ETURN 664.00 0O2 0 cNU 665.QCC:?LTi7'!3 ii EFFEL-T Ic,, CICOURACENCLST,NCD CK,LCA0e,NOMAP -C PT!,, IN 5~-FECT* NAME = DEVIAN, LINECNT 57 -STT.'STiCs SCuRCE STATE-'IENTS = 20, PRGGRAM SIZE 716;STATISTI.CS= NJ G.STIC GENERATED NO,R. $ 0'.' cEVIAN N-D STATE:<E;'T FLAGGED IN THN Ab'OVE CCM4PILATICNS.'.

u~*** I INPT OAT% T2 SOLVE COEFFICIENTS IN THE REOUCED EQUATION OF STATE TC = &4.~0 VC = C.03C325 PC = 721.9G6 AK - -.Oo R' = c.:24098 ZCV= 0..2790 CCS= 0.00 AE5= 6.CCCO00Q ALGF15 9.706GOO CC6= 0.00 AE6= 22.000000 ALGF6= i1.237700 TT'= 0.Bs 13T -0.74CC TTk= 2.30 BT c0.0 Ruk= 0 6666!0 SLP1 3.91 FkCR= 1.400000 SLPI = 4.0 TTi<= 1IDO Ruk= 1.CCCOOO SLPI 7.40 TTk= 1.00 RCR= 1.800i0o SLP1 i3.80 TTR= 1.00 RCR= 1 C0000 SLP2 = 0.0 TTN= 100 = 1.800000 SLP2 0.0 0

.20200 3010.0 0.0 0. CCD 0I0,0 0.0 0.0 0.497;0-010.0 O j. i ).0009 0 00 ciI 00 0.0 C0. I 00 C1 C. C 0.u 0.0 0.497 D-Cl-.390SC-G2.0 0.0U 0.20000~'010JO 0. 000.0003i;:0 C.O 00 0.0 0.lclr);2 i5. 0 %.10,3 C.u, 1 022 1 0, 0.0.10000 02.Coo0.00073-,5 U,!r3Ci=S 31~~~~~~~~~~ij 3,~~~~~r' 3`Ci Oi 3.0 0.0:3 0.0? 3 0.0 02;~..50 020. 51320 0~~ ir 20.';C 7 j;~-l 50.~ 0j ~L;3-2I -. 0.9,.-Q- 76-.6 009-0 760.i0 002 t OC' 0.., 0/~~j 0j, 0:~ 0% 0. 03C0 L 40C6 C, L)C 3 2 0. I-4 70-07 -;-)).j~7 76-. c0XOO-7o2.20) 22 O; 0.0 0.0 0.?Y702 11ZlO ~30. 36CsJ-050.60570-13-. 2i020 0.63SO C2-.03j 20 2.C 0.0 0. 0..C-60b C 30. 0~10 J0.3.V 0-03. 5D -, 370820 02;1-.73350 C3 -.i.~50C 03 ~C ci 0 0 02. 20 33.0.0 0 L0-30. 27070 01 O 0.0 0. 3 0.0.00 0.3 0.0C.2G1;D 0 2.2 Z0-00 -D 02 ('

CD EF F IT C ICI Z- TS Ii Tt. E REDLC ED EQ7LATICN CF STATE *s**44* 4c.4,: -og -Or 44 i'C I V ~ - 6 v f- ) + A + 32 ~TF+ C- CE XP K*-il T R Z C 2 V R- i /V C ( (V k- Lj VC + (A 5TP EA P * M +CC 5 iAS* + 6 T) ri /(CX?{A i v,)`( lo + CC A EX P C AE *V R,)) * IE= 0 Z' j -, 4C7902C CO;(2)= O.i5367iL C3 C 2 2 - -2Zi 47C Cl A(3)= 3 1;1 7623-Ci B(3)= O..703360-C2 C 3 7; 7 9 7 31 0 ( 4)= - i;c4 C-3- C2 C(4) = -.63 M 1503-C). A 5 = -.3573343 C4 B( )= C; I 3C- 35 A( )t 0 C) IC3S740) C7 2G61= -.9,Zi6C33 05 LC = D.2 27225 BAA =.,8.523

V4##8 ii C A L C, ULA T IN 0 I NPUT CCM\DIT IONS *** T ",Pl 6 6 4. 5 0 F(TC)=. o2500-01 FCAL= U.62500-01 TNP= 66 IT. 50 F(TC)= -.39C6D-02 FCArL -.-3)0-32 T3P o6o4, 50 - F(TC)= 0.1642D 05 FCAL O 16 42D 05 TEr P= 664. 50 F(TC)C 0.75940 05 RKAL= 0.75S40 35 VOL= 1.499993 SLGPE= 3.91 SLPCAL= 3.91 VCL= 0.714~ 36 SLCPE= 14.13 SLPCAL= 14.10 TE!"P= i.00 VCL= i 0CC0000 SLPOP 7.40 SLPCAL= T E M = O1.00 VOL= 0.555556 SLOPE= 233 80 SLPCL~ 23 3. T Et N P = J,.30 8 = -C. 7,t0 U CAL= -0.7400 lip:~3 = 2.30 8 = 0.0 SCAL= -0.0000 T l~u= r. OC S = -0. 3460 3CAL= -0.3460 1.03~=:,OG VCL=.0 c03 0 ZL 2= 0.0 S L2 C L.0 TLMP= 1.00 \ L= 0,555550 SL2= 0.0 SL~CAL= 0Co

***4* L INEARITY TESTIfG -~****.**4 i, 49' 9' 2 C. 000 75. 474 75.4 74 0.0 0.0!1 o- 49?99 -3 21.000C 79. 384 79., 384 -0.000 -0.00 1. 4999 93 22.000 83. 294 b., 2;4 -. O000 -0.00 O.7142 8c 2.o 000 28o. 426 268.426 0.0 0.0 03 7i42 L 21.00 C 0 282. 526 282. 526 -0.000 -0.00 O0 7ji2 _b 22.000 296.626 29606.26 -0.G000 -o.00v oCOO0 io 00 1.. CCG 1,0o 0.0 0.0 10030O0 _.0 1.740 1.74C -0.000 -0.00,.CC0003 1.200 2.40C 2.4S0 -0.00 -0.00 0. 55 55 i.000 2. C73 2.G073 0.0 0.0 0.55555.!00 4,453 4.4-3 0.000 0.O 0, 5 555 5 1200 6.833 68333 -0.000 -000

APPENDIX G ALGEBRAIC CORRELATION OF VAPOR PRESSURE DATA All of the experimental vapor pressure data has been correlated by the Martin, Kapoor and Shinn equation (93) which is given by the following expression: lnP = A + B + ClnT + DT + E(F-T) ln(F-T) (G-l) T FT There are six unknowns in Equation (G-1), namely, A,B,C,D,E and F. In the process of evaluating these parameters, the first step is to assume F = 1.02 T. Here we shall illustrate the data fitting process with c respect to vapor pressure values of R-115. All of the experimental vapor pressure data of R-115 is given in Figure V- 4. Given the critical temperature of R-115 to be 635.56 R, we obtain: F = 1.02 Tc = 648.27 (G-2) Then five points from Fig. V-4 are selected and substituted in Equation (G-l) to obtain five simultaneous equations which can be solved for the remaining unknowns. The five points on the vapor pressure plot (Fig. V-4) selected for R-115 are given in Table G-1. 315

316 TABLE G-1 Five Points on the Vapor Pressure Plot for 1x103 T P (R)1 R psia 3.0 333.33 0.82 2.5 400.00 8.3 2.1 476.19 48.2 1.8 555.56 173.0 1.6 625.00 406.0 Solving five simultaneous equations of the type (Equation G-l) the parameters for R-115 are as follows. Result A = 80.727001 B =-7885.8583 C =-10.497278 D = 0.00873321 E = 95.588673 F = 648.27

MICHIGAN TERMINAL SYSTEM4 FORTRAN G(41336) MAIN 02-03-73 19:29.48 PAGE P001 C ***=** CALCULATIONS OF CCNSTANTS OF VAPOR PRESSURE EQUATION 5.000 UOO1 IMPLICIT REAL*8A-G-H,-Z, $) 6.OCO 0002 DItIEtSION A(5,5),B(5),T(5G)o,P50),PP(50) 7.0CC00 0003 TC=635.56 8.UOO o 0004 PC =456, 0 S.0CC 0005 1=0.0 1O.0CC (. 0306 11 I=I+1 li.OCC Cl 0007 N=I 120CC t 12.0OCG 0008 REA 4D (5,100,END=12) T(I),P(I) 13.UOC - 0009 Xl1=T( )-1000. 14.0 CC 0010 Xl=CABS(Xll ) 15.0CC I 00'.1 IF (Xl.LT.O.1) GO TO 12 16.000 00i2 GOI TO 1 17.0CC LnOq 0013 100 FORMAT (2F153 18.0oC C 0014 101 FO MAT (2F15.3, 11) 19.00C 0015 50 - CPMAT ('1',/ 20. OCG 00i6 51 FORM-AT (' TEMP PEXP PC 21.0GC IAL PCD I' ) 22.000 O 0017 12 CCtJT INUE 23. OCC' 0018 F=64E.27 24.000G C019! 00 13 I=1,5 25.0CC Y 0020 A I,i)=1.O 26,0CC 0021 AI 1 /Ti 27.0C (D 0022 A I,3)=LCG(T(I ) 2.0) c 0023 AI1,4)=T(I) 29.0CC 0024 FT Il=F-T( I)' 30.0CC C 0025 A( i,5)=(FTI*CLOG(FTI) )/(F*T( I)) 31.0JC 0026 13 BlI)=DLOG(PI) ) 32.0CC < 0027 CALLL DGELG( B,A,51t, 1.E-15t IER) 33.CO0 0028 AA= (1 ) 34. CC O 0021 BE.=( 2) 35.0CC Y 0033 CC=F(3) 36.0 CC 0031 0:=tG(4) 37.OCC 0032 LEt=P5) 38.3CC D 00U3 FF=F 39.0CC 1) 0)034 AA= 8U. 72 7001 4C. CC C 0035 B=-7e85,85 83 41.000 0036 CC= -i0.4C7278 42*000 0037 D='-.0087332099 43.0CC 0038 EE=95.588o73 44.000 C **,* P I NT AA, 8, CC, GD, EE, FF 45.0CC 0039 WRI TE (6,50) 46.0CC OC40 WK ITE (6,200) IER 47.0CC 0041 WRITE (6,201) AA 48.3,C 0042 WRITE ( 6,202) EB 49.OCC 0043 WRITE (6,203) CC 50.000 0044 WPITE (6,204) 00 51.0CC 0045 WRITE (6,205) EE 52.0CC 0046 wFITE (o,206) FF 53.0CC 0047 200 FURMATT('O',20X,' IER=',I2) 54.0CC 0048 201 FORMAT ('C',2OX,'AA=',E15.8) 55.000 0049 202 FORPi AT ('0',20X,'&B=',E15.8) 5t. OCC 0050 203 FORMAT ('0',20X,'CC=',E15.8) 57.CCC 0051 204 FORMAT ('O',20X,'OD=',E15*8) 58.0CC 0052 205 FORMAT ('O',20X,.EE=',E15.8) 59.0Co

MICHIGAN TERMiINAL SYSTLM FORTRAN G(41336) MAI N 02-03-73 19: 29.48 PAGE P002 0053 206 FORMAT I0',020X OFF=',EIS.8) 60.0CC C *~*?** COMPARISON OF THE DATA 61O9CC C ***t * INPUT UNITS ARE: 62*OC0 C 9 TEMPERATURE IN DECREES FAHRENHEIT 63.OCC C ****Y; PRESSURE IN PSIA 64OCO C *n'c* IER IS TI-E REFERENCE NUMBER AS: 65.0CC C s***~e~* IER=L REFERS UNIVERSITY OF MICHIGAN 66*CCC C. IER=2 REFERS MEAR ET.AL 67.3CC C * l-~v * IER=3 REFERS ASTON 68.000 C 4** ItRz4 REFERS CU PONT X-57 8 69.0CC 0054 N=N-1 70.000 0055 DU 14 IlN 71. 0CC 0056 FTI=F-T(I) 72.0CC 0057 UL ULG P=AA+ 813/T ( I ) +CC *DL OG(T (I)+ DD*T (I( EE *F TI *LOG (F T I))/(F*T( I)) 73.0CC 005d PP( )=DEXP(OLOGP) 74. CC 0059 IEV=P(I)-PP(I) 75.0CC 0060 PC0=CEV*100./P(I) 76.J00 0061 14 4P ITE (6,3 00) 7(I),P(I ) PP(IIPCD 77. CCC 0062 3CO FGRt T (0' 20XF102,2F15e4,F1o.2) 78.0CC 0063 10 WRITE (6,50) 79.0CC 0064 tITE (6,51) 80.lCC 0065 15 RFAD (5,101) TtEMPtPEXP,1ER 81i.CC 0066 X12=TE4P-2O00. 82.0CC 00o37 X13=TEMP-30CO0 83.OCC 0068 X1 =T EAP-4000, 840OCC 00 OC69 X15=TEMP-5000. 85,300 3070 X2=0ABS(X12) 86.0CC 0071 X3=u4RS(Xl3) 87.000 0072 X4=CAbS(Xl4) 6f3.0CC 0373 X5=DABS(X15) 89.0CC 0074 IF (X4.LTe0.1) GO TO 10 90.000 0075 IF (X3,LT,O.1) GO TO 10 91.0CC 0376 IF (X4.LT,3.1I GO TO 10 92.0CC 0077 IF (X5,.LT.31) GO TO 10 93e000 0078 TT=TrEP+459.67 94. CC 0079 RHS=AA+d3/TT+CC*DL0G( TT)+D0*TT(EE*(FF-TT)/(FF*TT))*(DLOG(FF-TTI) 95.0CC 0080 PCAL=DEXP(RHS) 96.000 0031 (jEV=PEXP-PCAL 97. 0CC 0082 PCU=0OV*100o/PEXP 98.000 0083.SITE (6.400) TEMP, PEXPPCALPCD, IER 99.0Cc 0084 GO TO 15 ICO.0CC 0085 400 FORMtT ('O't20XFIO,*22F15.4,F1O 2,5XtIl) 101.0CC 0086 END 102.000 *CPTIONS IN EFFECT* I0,EBCDIC,S0UrCENCLISTNO0ECKFLCADNCIVAP * JP:C NS IM EFFECT* NAM E = MAIN, LINECNT = 57 *STATISTICS* SOURCE STATEMENTS = 86,PROGRAM SIZE * 3912 *STATISTICS* NG DIAGNOSTICS GENERATED NC ERRORS IN MAIN NC STATEMENTS FLAGGED IN THE ABOVE COMPILATICNS.

APPENDIX H ALGEBRAIC CORRELATION OF SATURATED LIQUID DENSITY DATA All of the experimental saturated liquid density data has been correlated by the Hou equation (62). The equation is as follows: ds= A + B(1-TR)/3 + C(I-TR) 2/3 + D(1-TR)4/3 (H-l) The form of the equation requires that A = d. The other four unknowns B,C,D, and E are evaluated by choosing four saturated liquid density values. The method of evaluating these constants is illustrated for R-115. All the experimental saturated liquid density data for R-115 is given in Fig. IV-2. Four saturated density values for R-115 are selected from Fig. IV-2which are given in Table H-l. TABLE H-1 Four Points on the Saturated Liquid Density Plot for R-115 (Fig. V-6) Selected to Solve Unknowns in Eqn. (H-l) t ds F lbs/cu.ft. -150 108.98 30 87.7 130 69.45 150 63.3 The result of the solution of four simultaneous equations is as follows: 319

320 A = 37.3 B = 65.70716 C = 39.788587 D = -47.381529 E = 43.599542

.1ICHIGAN TERMTHAL SYSIE1 FORTRAN G(41336) RAIN 02-33-73 20:21.22 PAGE Poo0 C ** f CALCULATIONS OF CONSTANTS OF SATURArED LIQUID DENSIO' 5.030 C EQUATION 5.030 0001 I!PLICIr REAL*8(A-H,0-Z,$1 6.0)0 0002 DIMPNSION A(4,4),B(4),T(30),DS(30),DSS(30) 7.030 0003 TC=635.56 8.030 0t 0004 AA=37.3 9.030 0305 1="0. 10.03) o O006 11 I.=i + 1 11.033 0007: =t 12.030 00309 RaSAf (5,100,END=12) T(I),DS(I) 13.030 0309 X11=lT3O.-T(I) 14.030 0 0310 IF (X11.LT-0.1) GO TO 12 15.030 0011 T (I) =: (I) +459.67 16.030 tJ1OQ 0012 s 1o r3 11 17.0)0 0 0013 12 Do 13 1=1,4 18.030 0314 X=1.-r(I)/TC 19.0300 0015 X-Y*~(1./3.) 20.030 DO c* 0016 A(1,1)=XX 21.030 O 0317 A(I, 2) =XX*2. 22.000 I 0018 A(I,3)=XX**3. 2J.030 0 0019 A(f,4)=XX**4. 24.030 * 0020 13 B(I)=OS(I) -AA 25.330 " C021 CALL J";FLG(9,A,4,1,1.E-15,IER) 26. o000 - CD 0022 B3=W(1) 27.033 O003 Cc=B(2) 28.000 0 0024D D= 3(3) 29.0 33 0. 3025 It=' (= i 30.0) 0 0026 31.0)0 1 C ****?RINT AA,8,CC,DD,EE, 32.033 0027 4ML9S (6,50) 33.033 023 - PTT (6,200) IER 34. 30'1 0029 WPTTL (6,201) A 35.030 0030 WRITE (6,202) BB 36.0)0 ) 0031 WRI7R (6,200) CC 37.030 C 0032 W rr (6,204) 00 38.030 0033 WVI r (6,2059) ER 39. 0 )0 00 3 4 50 FCRIAT ('1',!) 40.0)0 H. 0035 200 FOP'AT ('0',20X'IER= T',2) 41.030 0336 201 F): 1 ('O'V 20X,'AA=',E15.8) 42.030 0037 202 F(73': Ar ('0',20X,'83=,e15.8) 43.030 ) 0038 203 F R'AT, ('0',20X,'CC *,E15.8) 44.030 0039 204 FORIAT ('0'.20X,'ID=,E13.8) 45.030 e 0040 205 FnR",AT ('0, 20X,'EE-',E15.8) 46.030 C ****** CO PARISON OF THE DATA 47.030 0341 DO 14 I=1,N 48.030 0042 X=1.-1'(T)/TC 49.030 00) 4 3 X X = X * * (1I. / I. ) 5,I).3.OUO 0044 7 S (I )= A A + B * X X +C C *(X X*2.) + DD( X 3. + EEIX *4.) 51.033 0 045 DEV= DS(I) -SS() 52. 030 0046 PcD= V 10. /)S(I) 53.030 0047 14 ii~irE (6,300) T(T),DS(I),)SS(I,PCD 54.330 0048 103 FORI(AT (2F15.3) 55.000 0049 300 F rO3ia T (I 0,20 X, F12. 2,2F 15.3, F12. 2) 56.000 C ***+r INPUT UNITS ARE: 57.000 C **+*e TEMPSRATURE IN DEGREES FAHRENHEIT 58.000

MICHIGAN tERMINAL SYSTEM FORTRAN G(41336) MAIN 02-03-73 20:21.22 PAGE P002 $**** DENSITY IN POUNDS PER CUBIC FOOT 59.000 C t***t IER IS THE REFERENZE NUMBER AS: 60.030 C ****** IEP=t REFERS UNIVERSITY OF MICHIGAN 61.030 _ ****** I IR=2 REFERS MEARS Er AL 62.030 005 0 10 WRITE (6,50) 63.030 0051 15 READ (5,101) TEMP,DEXP,IER 64.030 0352 X12=2000.-TEMP 65.000 0053 X13=3000. -TEMP 66.030 0054 X14=4000.-TEMP 67.000 0055 IF (X12.LT.0.1) GO TO 10 68.030 0056 IF (X13.LT.0. 1) GO TO 10 69.000 0057 IFP (X14.LT.0.1) GO TO 10 70.000 0058 TT=rTE2+459.67 71.000 0059 X=1.-TI/TC 72.030 0060 Y=1./3. 73.0300 0061 XX=X**Y 74.000 o 0062 DCAL=AA+8B*XX+CC* (XX**2.)+DD*(XX**3.)+EE*(XX**4.) 75.030 0 0063 DEV=DEXP-DCAL 76.000 0064 PCD=DEV* 10./DEXP 77.000 0065 WRITE (6,301) TEMP,DEXP,DCAL,PCD,IER 78.000 0066 GO TO 15 79.000 0067 101 FORMAT (2F15.3,I1) 80.000 0068 301 FORAr ('0', 10X,F12 2, 2F12. 3,F12 2 5 111) 81 000 0069 END 82.000 *OPrI3NS IN EFFE"T* ID, EBCDIC,SOURCE, NOLIST,NODECK,LOAD,NODAP *OPrIONS IN EFFECT* NAME = MAIN, LINEZNT = 57 *STATISTICS* SOURZE STATEMENTS =. 69,PROGRAM SIZE = 3000 *STATISTICS* NO DIAGNOSTICS GENERATED NO ERRORS IN MAIN NO STATEMENTS FLAGGED IN THE ABOVE COMPILATIONS.

APPENDIX J MIXING RULES FOR'CRITICAL CONSTANTS Several mixing rules are given in the literature to predict either pseudocritical or true critical values of a mixture. Some rules are given by Reid and Sherwood (120). The latest summary of the rules to predict true critical values is given by Spencer, Daubert and Danner (130a). In the following analysis a few simple rules along with highly recommended ones are discussed. For the calculations, several component properties were used and they are given in Table J-1 along with the same properties for mixture. TABLE J-1 Properties of Components and the Mixture R-502 Property Units R-22 R-115 R-502 P psia 721.906 456.0 591.0 T R 664.5 635.56 639.56 c V ft3/lb 0.030525 0(02681 0.028571 c z 0.2672 0.2769 0.2747 c T R 418.33 421.99 409.92 w 0.226 0.2645 0.218 Mol.Wt. 86.476 154.48 111.641 x 0.488 0.512 - y 0.630 0.370 R (psia) (ft )/(lb) (R)0.124098 0.069468 0.0961248 323

324 where P = critical pressure c T = critical temperature c V = critical volume c Z = critical compressibility factor c T = normal boiling point B.P.D W = accentric factor x = mass fraction y = mole fraction R = gas constant G = property denoted generally (I) Kay's Rule - Mole Fraction P = 0.63(721.906) + 0.37 (456) = 623.52 psia cm T - 0.63(664.5) + 0.37 (635.56) = 653.8 R cm V = 0.63(0.030525)(86.476) + 0.37 (0.02681(154.48) cm = 3.1954 ft3/lb mole = 0.028622 ft3/lb Z = 0.63(0.2672) + 0.37 (0.2769) = 0.2705 cm (II) Kay's Rule - Mass fraction Pcm = 0.488(721.906) + 0.512(456.0) = 585.76 psia T = 0.488(644.5) + 0.512(635.56) = 649.69 R cm V = 0.488 (0.030525 + 0.512(0.02681) cm = 0.028622 ft31b Z = 0.488(0.2672) + 0.512(0.2769) = 0.2821 cm

325 (III) Geometric mean averages Gmi = (YAGA1/2+ YBGB / (J-1) P = 616.4 psia cm T = 653.0 R cm cm ~~~1/2 1/2 3 112 1/2~~= 3.157 ft /lb mole V = 0.63(2.63968) + 0.37(4.14161) 3157 ft/lb mole cm = 0.0283 ft3/lb Z = 0.272 cm (IV) Lorentz cube root averages 2 YAYB 1/3 1/3 3 2 G ~ ~~~~~~~ +(-2 mix YAGA 4 (GA + G ( GB (J-2) P = 617.0 psia cm T = 655.0 R cm V = 0.0284 ft3/lb cm Z = 0.2705 cm (V) Chueh and Prausnitz (34a): cm =Z Yi Vci = 0.028622 ft3/lb (J-3) cm i ci cm ='i~j Tcij (J-4) where yiVci i =Y5iVci and 1/2 Tcij = (TciTc) (-k) (J-5)

326 where h(v e1/3 1/3 0.5 kij=1 - [ ci'Cj ) ] where ij [(V il/3+V 1/3)/2 ~1 = 0.5204 =2 = 0.4796 kij = 0.00841 Tcij = 644.4 R T = 647.81 R cm (VI) Chueh and Prausnitz (34b): v = 8 v + E 0 Ov (J-6) cm i ci 1 j ij T = 8. T. + ZZ 8 8 T., (J-7) cm 1 ci 1 13 where 2/3 yV Yi ci i 2/3 YiVci T.. = 0 11 V = 0 Vii ~ 1 = 0.56 e2 0.44 T c-T2.c.... = 0.02226 cl+Tc2

327 Tij 0 T = 652.1 R cm V = 0.0296 ft3 /lb cm (VII) Ekiner and Thodos (479): 2 3 T -T' = A y. + (B -A.) Yi B y (J-8) c c ij j i ijiij i where T = yiT [6.048 (T -1) 1/3_11 A. = e ij [6.356 (T.-1) -l4_1] B.. = e T.1/M. ci i T.. = >1 Tij Tcj /M cJ J. T - T = 5.3 R c c T = 5.3 + 653.8 = 659.1 C (VIII) Grieves and Thodos (52a): T TC2 T = + (J-9) cm Y2 Yl + 1 1+ Y-A2 Y 12 21

328 Tb2 where A12 and A21 are functions of T > bl *. T b2 = 1.0087 bl A21 0.8 A =12 12 T = 650.78 R cm (IX) Leland-Mueller (84a): 1/2 2 1/O T [ yi(Z R Tc l/Pci) ] (J-10) cm V cm where V = 1 Y [V1/3 + V 1/3 ] 3 cm 8 iyi cicj Z = Z y.Z cm iZci = 2.43 - 0.74 8 1.9 > e > 0.5 = 2.2 0 < 0.5 =1.0 0 > 1.9 P cm (K) T P (K) cm T (K) = Z YITci P (K) = Z y. cm iPci P RT Z cm/V cm cm cm cm (J-11)

329 Values are: = 1.72 V = 0.028388 ft3/lb cm T = 655.0 R cm Z = 0.2705 cm P = 600.0 psia cm (X) Joffe-Method A (67a): T T T cm c= Y2 = K (J-12) P 1/2 Y 11/2 2 1/2 cm cl c2 T T T cm = ci. c2 (J-13) P Y1 p Y2 P J (J-13) cm cl c2 T = K /J = 645.53 R cm P = T /J = 589.2 psia for T = 645.53 R cm cm cm = 583.9 psia for T = 639.56 R cm P = K /T = 578.6 psia for T = 639.56 R cm cm cm (XI) Joffe-Method B (67a): 1/3 3 1/3 3 T T T Ti13 T cm 2 cl 2 c2 1+ u[ () (14) J. = Y1 + Y2 P 08 cm cl c2 u = 1.0881

330 T = K /J = 649.98 R cm P = T /J = 597.35 psia for T = 649.98 R cm cm cm = 587.9 psia for T = 639.56 R cm (XII) Li (85a): T = z.iT (J-15) cm i ci where = 1iVci i YiVci ~1 = 0.5204, Tl = 664.5 R 2= ~ 0.4796, Tc2 = 635.56 R T = 650.6 R cm (XIII) Kreglewski and Kay (82a): T -T P = P + P [5.808 + 4.93 (wlYl+W2y2)] cm- p (J-16) cm cp cp' T cp.. Pm = 623.52 + 623.52 [5.808 + 4.93(0.2403)] 639653.8 = 528.56 psia (XIV) Li, Chen and Murphy (85b): Tbm Tbl Tb2 T Y1 T + Y2 T (J-17) cm cl c2

331 409.92 06)418,33 421,99 409.92 = ( 63664+5 (0 37) 63'5.56 cm T = 638.23 R cm (XV) This work: 1 Yl Y2 -- L+ -- (J-18) cm Pcl c2 0.63 + 0.37 721.906 456.6 P = 593.79 psia cm

APPENDIX K ANALYTICAL METHOD TO OBTAIN INTERMOLECULAR POTENTIAL..... ENERGY PARAIMETERS.... General form of the intermolecular potential energy is given before in Fig. II-8 and reproduced here in Figure K-1. A A' U(r) I doX dm r C Fig. K-1. General Representation of the Intermolecular Potential Energy Lennard-Jones (85) described the potential energy by the following equation: d 12 d 6 U(r) = 4U [(7) - ( ) ] (K-1) m r r This equation can be substituted in the following equation to obtain the second virial coefficient: 332

333 B = 2wTN (e -1)r 2dr (K-2) Resulting expression is given in Eqn. (II-49) which involves two parameters U and d. The methods of evaluation of these parameters are m m given by Hirschfelder, Curtiss and Bird (58). These methods are very time consuming. Here a method is proposed to evaluate these characteristic parameters Um and d analytically. The parameters are calculated for the 1R m mixture as well as pure components. First the potential energy curve is split into positive and negative portion. Then for the positive portion the curve is modified as following A'B rather than AB in the Fig. K-1. Negative portion of the curve is left as before. The total curve is defined analytically by the following two equations: d 12 d 6 0 0 U = -4U (7-for d < r < oo (K-3) m r r o and -U/kT 12 e = Cr for 0 < r < d (K-4) where C is independent of the temperature. From the condition that at r = do, U = 0 we obtain the constant C. -12 C =d o (K-5)

334 Combining Eqns. (K-3), (K-4) and (K-5) with (K-2) we get: d O oo 12 2 -U/kT 2 B = -27N () -1] r dr +2rrN j(e -1l)r dr (K-6) o d o The magnitude of the term U/kT is not great in the region from do to o, 0 therefore the following assumption may be made in this region: -U/kT 2 e = 1 - U/kT + 1/2 (U/kT) (K-7) Combining equations (K-6) and (K-7) we get: d 0 12 00 =-2nN I [ 2o 1] r d- U 1 U 2 2 B = -2rN J [(d-) — 1] r dr - 27rN | T[+ (kT ]r dr (K-8) o d o Integration in Eqn. (K-8) can be carried out to yield the following result: 3 U m 16 2U B = 8Nd3 1 U 16 (K-9) o 15 9 kT 315 kT Eqn. (K-9) is used in evaluating the parameters do and Um. The calculations are illustrated here for R-22. Calculation of intermolecular potentialparameters In Eqn. (K-9), it is easier to solve U /kT from the fact that at m Boyle temperature, B = 0.

335 16 m 2 2 m 1 * 16 B) - 2(m)_ = 0 (K-10) 315 ~' kTB 15 Root of Eqn. (K-10) is U /kTB = - 0.282 (K-ll) For R-22, T = 2.3 T = 849.1 K. B c U. km =0.282 (849.1) U k -239.3 K (K-12) To evaluate d we must use the following fact: 0 BP @ T = T = 369.17 K =-0.346 (K-13) c ~~RT c RT B = -0.346 C (-0.346)(82.06) (369.17) (14696) (721.906) = -213.38 cc/gmole Substituting this in Eqn. (K-9) do can be obtained 21338 8 (6023x1023(d 310-24 1 2 2239.3) -213.38 = 8 (6.023x10o )(d 10 )- 9'36 —-7 16 239.3) 2 315 369.17 ]

336 d3 = 14.48 0~~ o d = 524 A 0 d 21/6 d 0 d = 21' d = 1.22 d = 5.88A m o o 0 *. For R-22, d = 5.24A, U /k = -239.3 K (K-14) 0 m Let us see how these values predict the second virial coefficient at the other condition where BP @ T = 0.8 T =295.33 K, =.740 c RT or B = 365.1 cc/gmole exp Substituting values from (K-14) into (K-9) we get: B = 8T(6.023xlO23)(5.24)310-24 E[ + 2 -239.3 15 9 295.33 16 -239.3 2 315 295.33 = -361.0 cc/gmole compared to -365.1 cc/gmole Proceeding similarly for R-115 we obtain: O O Um /K -2889 K, do = -288.9 K, d 5.98A, d 6.71A (K-15) In 0 m

337 Intermolecular Potential Parameters for R-502 There are two ways we can calculate the parameters Um and do for R-502. We can assume that it is a pure substance and from generalized second virial coefficient, calculate the parameter or treat it as a mixture. Both approaches are described below. For R-502: T = 355.13 K c TB = 2.3 T =817.22 K B = 0 BP T = 355.31 K, c =-0.3425 c RT and BP Tc =0.8 T = 284.25 K RT = -0.735 (K-16) C c RT Proceeding as before: from TB = 817.22 K, Um/k = -230.33 K (K-17) and from -B = 248.4 cc/gmole, at T = T 0. =5.5 A o (K-18) Values of U /k and do from Eqns. (K-17) and (K-18) predict the second virial at T = 0.8 T as follows: c B c = -420.0 cc/gmole (K-19) B = (0.735)(82.06)(284.25)(14.7) exp 591.0 =-425.0 cc/gmole (K-20)

338 Thus the second virial coefficient at 0.8 T is predicted within 5 cc/ gmole which is usually the precision of second virial values. For a binary mixture the second virial coefficient is: 2 2 Bmix = X1 B1l + 2 XlX2 B12 +2 B22 (K-21) where B = second virial for the mixture mix Bl,B22 = second virial for the components 1 and 2 B = second virial for the interaction between a molecule of component 1 and component 2 Xl,X2 = mole fractions of components 1 and 2 Therefore the second virial coefficients of the components must be evaluated at the temperatures at which the mixture second virial coefficients are known. These temperatures are 817.22, 355.31 and 284.25 K. To accomplish this we used the equation of state of R-22 and R-115 as follows: BPc f2(TR) RT 2 T RT T 2 + TR (K-22) TR where -kTR f2(TR) A2 + B2TR + C2 e 2 R 2 2 R 2

339 for R-22: A2 = -0.417902 B2 = 0.153671 C2 = -2.22487 b = 0.029 T = 369.17 K C Using Eqn. (K-22),values of second virial coefficients for R-22 are as follows: T = 817.22 K B =+4.578 cc/gmole T = 355.31 K B = -234.61 cc/gmole T = 284.25 K B = -399.1 cc/gmole (K-23) For R-115 constants in Eqn. (K-22) are: A2 = -0.405920 B2 = 0.142469 2 C2 = -2.24052 b = 0.035 T = 353.09 K (K-24) c And we obtain the second virial coefficients as follows: T = 817.22 K B = 1.076 cc/gmole T = 355.31 K B = 312.54 cc/gmole T = 284.25 K B = 537.35 cc/gmole (K-25)

340 Using these values in Eqn. (K-21), B12 can be calculated and the results are summarized in Table K-1. TABLE K-1 Summary of Second Virial Coefficients of R-22, R-115 and R-502 Second Virial Coefficient cc/gmole T K R-22. R-115 R-502 1....B12 calc 817.22 -4.578 +1.076 0.0 +3.58 +3.02 355.31 -234.61 -312.54 -248.3 -241.09 -251.53 284.25 -399.10 -537.35 -425.0 -431.35 -402.3 Using the mixing rule for the intermolecular parameters, we can obtain interaction parameters as follows: do= (d + d )/2 = 5.61A ~12 01 02 1/2 U (Uml ) = 234 cc/gmole (K-26) m12 1 2 The parameters given in (K-26) are used in Eqn. (K-9) to predict B12 and the results are given in Table K-1. Examination of Table K-1 reveals that the B12 predicted is within close agreement with values obtained from the mixture and pure component data.

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UNIVERSITY OF MICHIGAN II 90IIIIl1IIl11111lI11Il11I111 2lII 3 9015 02229 1457