THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE CONSTANT VOLUME HEAT CAPACITIES OF GASEOUS TETRAFLUOROMETHANE, CHLORODIFLUOROMETHANE, DICHLOROTETRAFLUOROETHANE, AND CHLOROPENTAFLUOROETHANE Yu-Tang Hwang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1961 February, 1961 IP-496

ACKNOWLEDGMENTS The author wishes to express his gratitude to those who helped him in this research. Professor Joseph J. Martin, his committee chairman, gave substantial help in many respects. Without his advice and encouragement, the completion of this project would not have been possible. The other members of his committee, Professors D. W. McCready, D. V. Ragone, G. J. Van Wylen, and E. H. Yound also gave freely their advice and help. Dr. Noel de Nevers, who preceded the author on this project, supplied a great deal of useful information and many constructive suggestions. Mr. Lynn E. Paul, Associate Research Engineer of Electrical Engineering Department, helped with the design and fabrication of the electrical seals, and many persons in the machine shop of the Department of Chemical and Metallurgical Engineering assisted with other mechanical details. The Esso Research Grant provided part of the funds for this research. The University of Michigan and the Nationalist Government of China supported the author by means of fellowship and scholarship. E. I. du Pont de Nemours and Company and Precision Rubber Products Corp. supplied materials without charge. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS.............. ii LIST OF TABLESo......................*................ V LIST OF FIGURES......................................... vi NNCENCLATURE.............................. ix ABSTRACT............... o................. *. * *.............. xii I, INTRODUCTION............................. *................ 1 I-1 Objectives of This Research,..,........... 1 1-2 Constant-Volume vs Constant-Pressure Calorimetry..... 2 I-3 Constant-Volume Heat Capacity Calculated by the Method of Statistical Mechanics..................... 3 I-4 Constant-Volume Heat Capacity and the State Behavior.. 5 I-5 Constant-Volume Heat Capacity and the Speed of Sound.. 9 II, PRIOR WORK IN CONSTANT-VOLUME CALORIMETRY*. *............ 10 II-1 Calorimetric Measurements of Constant-Volume Heat Capacity.................*......, O............... 10 1-2 Constant-Volume Heat Capacity from Speed of Sound,.., 13 II-3 Other Methods of Measuring Constant-Volume Heat Capacity................................... *........ 14 III EXPERIMENTAL APPARATUS,.................................. 16 III-1 General Discussion.................... 16 III-2 The Calorimeter..*.............................. 17 III-3 The Adiabatic Shield......,.. *................. 24 III-4 The rmocouples,......................... 27 III-5 The Vacuum Container,........4.. ~..........,...... 32 III-6 Electrical Junction Box......................... 34 III-7 The Vacuum and Loading System*.........*....... 35 III-8 The Measuring Systems.....,.....7....*........, 37 IVT, EXPERIMENAL PROCEDURE AND MATERIALS.....,4.............. 44 IV-1 Transferring the Material Into the Loading Bomb*..... 44 IV-2 Loading the Calorimeter,....................... 44 IV-3 Operating the Calorimeter...... **.,............. 47 IV-4 Unloading the Calorimeter.........,,, ~............... 51 IV-5 Material Used for Investigation,...........*****... 52 iii

TABLE OF CONTENTS (CONT'D) Page V. METHOD OF CALCULATION AND ESTIMATED ACCURACY,........... 54 V-1 Calculation of the Gross Heat Capacity............ 54 V-2 Calculation of Constant-Volume Heat Capacity....... 55 V-3 Estimation of the Accuracy......*.*..*.........* 56 VI, CALIBRATION OF HEAT CAPACITY OF THE CALORIMETER........ 61 VI-1 General Discussions,6....,...,.......... 61 VI-2 Calibration by Extrapolation.,,,*n.*.....,........ 62 VI-3 Results of Calibration6......................... 63 VI-4 Comparison with the Former Method*................. 69 VII, EXPERIMENTAL RESULTS............**..**.................. 72 VII-1 Constant-Volume Heat Capacity of Dichlorodifluoromethane........,....,,.t..**.**.***. 72 VII-2 Constant-Volume Heat Capacity of Tetrafluoromethane,...*......................~................ 75 VII-3 Constant-Volume Heat Capacity of Chlorodifluoromethane*,**, ******........** *****..******....*** 81 VII-4 Constant-Volume Heat Capacity of Dichlorotetrafluoroethane.................~,,................ 89 VII-5 Constant-Volume Heat Capacity of Chloropentafluoroethane *.......... ~...*.................. 97 VIII, DISCUSSION OF THE EXPERIMENTAL RESULTS. *............... 105 VIII-1 Characteristics of Cv as a Function of Temperature and Density..................... 105 VIII-2 Statistical and Experimental C.............. 108 VIII-3 Comparison of the Experimental Data with the Equation of State..,..*................. 110 VIII-4 Law of Corresponding State and Cv Data.*....*.. 122 IX CONCLUSIONS........... *. *. *..... *.............. 125 APPENDIX A. DETERMINATION OF THE CALORIMETER VOLUME.......... 128 APPENDIX B. CALIBRATION OF THE RESISTANCE THERMOMETER........ 131 APPENDIX C. SAMPLE CALCULATIONS*..........,................ 133 APPENDIX D. DETAILED GROSS HEAT-CAPACITY DATA*............... 138 APPENDIX E. C-Cv* DERIVED FROM THE MARTIN-HOU EQUATION OF STATE 151 APPENDIX F. CONSTANTS AND CONVERSION FACTORS.,............... 153 BIBLIOGRAPHY.................................... *.. ~ ~........... 157 iv

LIST OF TABLES Table Page 6-1 Gross Heat-Capacity Data of Tetrafluoromethane Used in the Calibration of Heat Capacity of the Calorimeter.,.... *...*.... * J.......,........,,...... 64 6-2 Gross Heat-Capacity Data of Chlorodifluoromethane Used in the Calibration of Heat Capacity of the Calorimetera+,..,...........*.........*.............66 6-3 Calibration of Calorimeter Heat Capacity by the Old Method Using Dichlorodifluoromethane......,,,*....*.. 70 7-1 Constant-Volume Heat Capacity of Dichlorodifluoromethane (CF2C12).,...................... 73 7-2 Constant-Volume Heat Capacity of Tetrafluoromethane. (CF4)X.****6***Z*,..,....^,.,,.#................. 76 7-3 Constant-Volume Heat Capacity of Chlorodifluoromethane (CHC1F2)....... J......,,..... 82 7-4 Constant-Volume Heat Capacity of Dichlorotetrafluoroethane (CCF 2-CC1F2).Ji 90*S*S** 90 7-5 Constant-Volume Heat Capacity of Chloropentafluoroethane (CC1F3-CF3)... *................... 98 8-1 Fundamental Frequencies of Chlorodifluoromethane...4* 111 8-2 Fundamental Frequencies of Chloropentafluoroethane *................... *... * J. *... * a. 1 D-l Gross Heat Capacity with Dichlorodifluoromethane Loading....*... ~.. *. *~...,.. ~,, *.. ~..**.. * 139 D-2 Gross Heat Capacity with Tetrafluoromethane Loading.. 140 D-3 Gross Heat Capacity with Chlorodifluoromethane Loading,... ^.. J I <,*~....,................ 143 D-4 Gross Heat Capacity with Dichlorotetrafluoroethane Loading,.... *,....*.....#..,,.. * 146 D-5 Gross Heat Capacity with Chloropentafluoroethane Loading*,....^,* J *,.................... *... *** 148 v

LIST OF FIGURES Figure Page 1-1 Type of Isotherm on a Cv-C vs, Density Plane Predicted by Several Equations of State,............ 8 3-1 Cross Section of the Calorimeter,.,........*.X* * l. 18 3-2 Calorimeter, Shield. and Vacuum Container in Their Relative Positions.,.............,... 19 3-3 The Platinum Resistance Thermometer and High-Temperature Motor Used Inside the Calorimeter2......**.* 23 3-4 Cross Section of the Hermetic Electrical Seal........ 25 5-5 Vacuum Container and Adiabatic Shield,.....,,.**,. * 28 3-6 Circuit Diagram of Heaters...,.*.......... 29 3-7 Circuit Diagram of Thermocouples............... 31 3-8 Schematic Diagram of the Vacuum and Loading System... 36 3-9 Circuit Diagram of the Measuring System.**.,*..*...... 39 3-10 Control and Measuring Instruments.....*...*...***.... 40 4-1 Loading the Calorimeter*.....,...*...*.............. 46 6-1 Calibration of the Calorimeter Heat Capacity by the Extrapolation Method Using Tetrafluoromethane........ 65 6-2 Calibration of the Calorimeter Heat Capacity by the Extrapolation Method Using Chlorodifluoromethane..... 67 6-3 Heat Capacity of the Calorimeter*.... *............* 68 7-1 Constant-Volume Heat Capacity of Dichlorodifluoro-..methane.''..* *.*.......*...........7.h 74 7-2 Constant-Volume Heat Capacity of Tetrafluoromethane,, 80 7-3 Constant-Volume Heat Capacity of Chlorodifluoromethane.*..,~*..*..*....****.* ~.............. 85 7-4 Constant-Volume Heat Capacity of Chlorodifluoromethane..C.*.....,. *.*,,.*...*.*.*......... 86 7-5 Cv-Cv* of Chlorodifluoromethane....,................. 87 vi

LIST OF FIGURES (CONT'D) Figure Page 7-6 Cv-Cv* of Chlorodifluoromethane....,.,,*,..... 88 7-7 Constant-Volume Heat Capacity of Dichlorotetrafluoroethanee*** *.... *~*,~ ^.. *~ ~...*.....* ** *.*.*. *.. 93 7-8 Constant-Volume Heat Capacity Of Dichlorotetrafluoroethane,..^......................... ***** * 94 7-9 Cv-C"v of Dichlorotetrafluoroethane............ 95 7-10 C -C of Dichlorotetrafluoroethane................ 96 711 Constant-Volume Heat Capacity of Chloropentafluoroethane.<,,...* J,........... J,,* *.,..... *...... 101 7-12 Constant-Volume Heat Capacity of Chloropentafluoroethane...~.......... *,.,^ J...~,.,...........~.....~.. 102 7-15 Cv-C* of Chloropentafluoroethane... *-*.. 105 7-14 CV-C * of Chloropentafluoroethane................ 104 V V 7-14 CVCv of Chloropenta.luoroethane,.. *.*...... 104 8-1 Comparison of Experimental C -C* of ChlorodifluoroV V methane with Those Predicted by the Martin-Hou Equation^*,.*...**...*....**,. *.*.,.*., *...*..**.. 113 8-2 Comparison of Experimental C -Cv of Dichlorotetrafluoroethane with Those Predicted by the Martin-Hou Equation 4e*.*o ** * *S* * * * * 114 8-3 Comparison of Experimental Cv-Cv* of Chlorodifluoromethane with Those Predicted by the Martin-Hou Equation.. * * * * * * * * * * * * *...* *.*.... * *.. * *. ** *.. ll6 8-4 Comparison of Experimental C -C * of Dichlorotetrafluoroethane with Those Predicted by the Martin-Hou Equation * *.......... *................ 7117 8-5 Comparison of Experimental C -C * of Chloropentafluoroethane with Those Predicted by P = A + BT - C/T3 Type of Equation of State.*....................... 120 8-6 Effect of k in the Martin-Hou Equation Upon the Curvature of a Temperature Function,*.*,.*..........** 121 8-7 C -C * As a Function of Reduced Temperature and Reduced Density..b **,.. *......*.. 124 vii

LIST OF FIGURES (CONT'D) Figure Page A-1 Schematic Diagram of Determining the Calorimeter Volume,..ef....... *.4....******,. *,,,...,. 130 D-1 Gross Heat Capacity with Tetrafluoromethane Loading.. 141 D-2 Gross Heat Capacity with Tetrafluoromethane Loading,, 142 D-3 Gross Heat Capacity with Chlorodifluoromethane Loading.4.... o....... O J...................... 144 D-4 Gross Heat Capacity with Chlorodifluoromethane Loading*...................^....^... a *a*........**.. ** 145 D-5 Gross Heat Capacity with Dichlorotetrafluoroethane Loading, o....,,.,,.,,...,,,...,......... 147 D-6 Gross Heat Capacity with Chloropentafluoroethane Loading o..^........ o.... o A...........*........ 149 D-7 Gross Heat Capacity with Chloropentafluoroethane Loading.. * * * * * a *.. * * * * *.. *. * * *. 150 viii

NOMENCIATURE A Work content, Helmholtz free energy A,B,C, Used as arbitrary constants in various equations A1 B31 C A2 B2, C2 Constants used in the Martin-Hou equation A3,BC C3of state A4 B4, C4 A5,B5,C b Constant used in the Martin-Hou equation c Speed of sound or speed of light C Heat capacity of the calorimeter C Constant-pressure heat capacity.p Cv Constant-volume heat capacity C * Constant-volume heat capacity at zero pressure V Cgross Gross heat capacity of calorimeter and contents C Heat capacity of two-phase mixture at constant volume sat C1 Heat capacity of the saturated liquid sat d Differential operator exp Exponential operator E EMF f g > Functions h h Planck constant ix

I Electric current k Constant used in the Martin-Hou equation k Boltzman constant In Natural logarithm m Mass P,p Pressure Q Quantity of energy q Rate of energy input R Resistance R Universal gas constant r Radius S Entropy T Temperature t Temperature V Volume z Compressibility factor Greek Letters Ca 37,5 Arbitrary constants used in various equation ~A Finite increment Q Time p Density 2 Ohms v Vibrational frequency w Wave number x

Subscripts c Critical corr Correction i Summation index mean Mean value over some interval R Reduced sat Saturated 1 At the start of the heating period 2 At the end of the heating period Superscripts -* At the zero pressure g Gas phase 1 Liquid phase xi

THE CONSTANT VOLUME HEAT CAPACITIES OF GASEOUS TETRAFLUORCMETHANE, CHLORODIFLUOROMETHANE, DICHLOROTETRAFLUOROETHANE, AND CHLOROPENTAFLUOROETHANE Yu-Tang Hwang ABSTRACT Constant-volume heat capacity (Cv) data have been determined for four common refrigerants, tetrafluoromethane, chlorodifluoromethane, dichlorotetrafluoroethane and chloropentafluoroethane, as a function of temperature and density in the range of 70-400OF and 100-500 psi. Ideal-gas heat capacities (Cv ) were obtained by extrapolating the Cv data to zero density and the results compared with values obtained by the method of statistical mechanics. The variation of the experimental heat capacities with density were compared with the variations predicted by equations of state, The applicability of the law of corresponding states to the Cv-Cv data was also considered. A thin-wall large-volume adiabatic calorimeter was used. This type of calorimeter, first developed by N. H. de Nevers, was improved in this research in the following ways: (1) Safety provisions were greatly increased; (2) The maximum working temperature was raised from 150 to 200~C; (5) Fluctuations of data were minimized and the over-all accuracy was enhanced by a better designed adiabatic shield and by a newly developed method for calibrating the calorimeter heat capacity. Comparison of the experimental Cv* with those calculated statistically has revealed that, except for tetrafluoromethane for which agreement was unusually good, the currently available assignments xii

of fundamental frequencies for chlorodifluoromethane, dichlorotetrafluoroethane, and chloropentafluoroethane, are generally inadequate. Comparison of the experimental C -Cv* data with those predicted by the Martin-Hou equation of state shows that the equation neither predicts the isotherms with the right curvature at a low density range nor represents the isometrics (Cv-Cv* vs. temperature) with a sufficient curvature. However, the Martin-Hou equation does correctly predict the small C-Cv at high temperatures. The law of corresponding states has been shown to be applicable to CvCv* if the gases are similar in their molecular structures, xiii

I. INTRODUCTION I-1 Objectives of this Research The accurate constant-volume heat capacity (Cv) measurements, at several densities and over a range of temperature, are useful in at least wo ways. (1) Ideal gas heat capacity (Cv*) may be determined by extrapolating isotherms to zero density on the Cv vs. density plane. A set of Cv* thus obtained may be utilized to shed light on the questions of molecular structure or the assignment of the fundamental frequencies. (2) Through exact thermodynamic relations, Cv may be related to the data of state. If the first or second derivatives of the pressure-volume temperature (PVT) data are involved in the corresponding expression, the chances are that Cv data may be more accurate than the same quantities calculated from the state data. This provides an opportunity to check or improve existing equations of state. In 1958, Noel de Nevers(12) constructed a thin-wall large volume adiabatic Cv calorimeter and collected Cv data for propylene and perfluorocyclobutane at several densities and over a range of temperature from room temperature up to 150~C. This was the most recent effort in the field of constant-volume calorimetry. Although his calorimeter exploded at the estimated pressure of 860 psi, it certainly excelled previous calorimeters in many respects. For this reason, the present author decided to construct a similar but improved calorimeter, intended to achieve the following: (1) An increase of the safety provisions to minimize the accidental damage to the instruments and operator. -1

(2) A raise of the maximum workable temperature from 150~C to 2000C (approximately 400~F), (3) A better designed adiabatic shield to minimize fluctuations of data and enhance the over-all accuracy. The main objectives of this research were: (1) To collect Cv data for four common refrigerants as a function of temperature and density in the range of 70-400OF and 100-500 psi so that tables of thermodynamic properties may be calculated, (2) To determine the idea; gas heat capacities by extrapolating the Cv data to zero density, and to compare them with the statistical calculations, (3) To compare these experimental data with the available state data and the existing equations of state. 1-2 ConstantwVolume Versus Constant-Pressure Calorimetry Although the constant-volume heat capacity of gases is one of the most important thermodynamic properties, the basic technique for measuring Cv has not been as fully developed as constant pressure calorimetry. For instance, Osborne, Stimson, and Sligh(36) constructed a flow calorimeter in 1924 which produced Cp data reliable to plus or minus 0.1%. No comparable constant-volume calorimeter has been built, In a flow calorimeter, a steady flow of gas passes through an apparatus where a known amount of heat is added to the gas, All measurements are made only when the entire system is at steady state, The net result is that only the gas changes the temperature, and the heat capacity of the apparatus is not involved in the calculation of CD of the gas, In

-35 the Cv measurement, however, the gas must be confined in the closed vessel of fixed volume which also changes its temperature with the gas when a known amount of heat is added. Thus the heat capacity of the calorimeter enters into the calculation and affects the accuracy of the results. Reducing the heat capacity of the calorimeter is clearly a good approach to the problem; the concept resulted in the pioneering work of de Nevers and Martin(1^) for the construction of a thin-wall large-volume Cv calorimeter. I-3 Constant-Volume Heat Capacity Calculated by the Method of Statistical Mechanics If sufficient data are available on the spectrum and structure of the complex molecule, Cv* calculated by the method of statistical mechanics is often more accurate than the experimental Cv* Also, values can be determined over a temperature range far greater than the experimental range. Unfortunately, assigning fundamental frequencies and other necessary molecular constants still requires either largely empirical work or guessing. The experimental Cv data are often extrapolated to zero density to obtain Cv* as a guide to the selection of the fundamental frequencies. Once a reliable set of fundamental frequencies is worked out, Cv may be calculated over a wide temperature range. The calculations are based on the assumption that the heat capacity may be divided into translational, rotational, and vibrational components. The translation and external rotation are independent of the nature and size of the molecule, and contribute R/2 per degree of

-4freedom per mole or a total of 3R for non-linear molecules. The total vibrational contributions are obtained as a sum of the contributions of all individual degrees of vibrational freedom, each corresponding to a particular value of the fundamental frequency vi, as follows: n,2 x. nC xi e(Cv ) = R = xi (1-1) where X- hVi - cLi 1.4586&i where X. =, n is the number of vibrational degrees 1 kT kT T of freedom (n = 3m-6 for non-linear molecules where m = number of atoms), T is in degrees Kelvin, and m is in cm1 Equation (1-1) assumes harmonic vibrations. A correction may be added for anharmonic effects which are estimated by various empirical equations. For instance, McCullough, et al ) presented the semi-empirical equation for the total anharmonic contribution as follows: C h Z{ H( )/- H [1 + RT ~} (1-2) (anh)-R R U RT 0 hco H*-He o where U = kT and the values (C*/R) and RT -~ are those for an anharmonic oscillator of frequency v, The adjustable parameters v and Z are an arbitrary frequency and a term involving an arbitrary anharmonicity coefficient, respectively. If the experimental data and a reliable set of fundamental frequencies are available, two adjustable parameters v and Z may be evaluated by assuming that the anharmonic contribution is the difference between the experimental C * and the calculated C* based on V v harmonic vibration, Mathematically, only two sets of conditions (C* (anh) and corresponding temperature) will be required for evaluation of two arbitrary constants. The better results, however, may be obtained by evaluating two parameters from experimental values of C* at three or v - tE~~eo

more than three temperatures, using an appropriate mathematical procedure. I-4 Constant-Volume Heat Capacity and the State Behavior The constant-volume heat capacity is related to the state data through the following exact thermodynamic relation, valid for the single phase of a pure substance: f^ = p2( d )f= (1.5) dV)T p dpT T (1-3) where V is the specific volume, T is the absolute temperature, P is the pressure, and p is the density. In the integral form, Equation (1-2) may be modified as follows: or -^ - -y^co Cv C = T (dP dV (-) V or P C - - v.T dp (1-5) Equations (1-4), (1-4), or (1-5) are frequently used as a check on state data and equation of state, since the second derivative of P with respect to T, or the curvature of the isometrics in P versus T plane, is not known with high accuracy. Each differentiation magnifies the fluctuation of data and the second derivative may present a considerable error, even though the PVT data are accurate within 1%. In other words, the check on the second derivative is a very severe test on the equation of state. The general behavior of PVT relations has been discussed by various authors. Martin and Hou(27) pointed out the general characteristics

of the isometric and P versus T plot as follows: 2 = as P - O (1-6) Q _= 0V atV=V (1-7) (2p) = 0 for high T (1-8) V 2p (d ) < 0 at V > V= (1-9) (dj) >0 atV<Vc (1-10) (29) Later, Martin, Kapoor, and de Nevers9) pointed out another condition, as follows: idu ) = 0 atV= e (1-11) n where n lies between 1.5 and 2.0. If the conditions represented by Equations (1-6) through (1-11) are substituted into Equations (1-4) or (1-5) in an appropriate order, it can be seen that for an isotherm of not too high temperature Cv - Cv* as a function of density starts from zero at zero density, increases gradually to a maximum at the critical density, then decreases to a certain point, and flattens at about 1.5 to 2.0 times the critical density. It is interesting to compare the result of the above analysis with the isotherms predicted by various equations of state. The following are the analytical expressions of C, - C * by various equations of ITb aiu eutoso

-7(12) state as derived by de Nevers. (15) Berthelot equation: 2 p.2a "c -j = a d I= = f(T)p (1-12) v v C T 2 0 Beattie-Bridgeman equation:(5 * 6CR [ Bop2 BP Cv-c C = 6 +- BP ] (1-13) Benedict-Webb-Rubin equation: (6) c T3 [ p + - {2 exp(-p2) - 2 + 7p2exp(-7P2)}] (1-14) Martin-Hou equation: (27,29) C C k 2 /-kT\r C2P _ C3p' 2 C, - Cv T exp -pb pb+ 4- p-b (1-15) where all letters other than T and p are arbitrary constants, all of which (12) are positive. de Nevers( has fully discussed the shape of isotherms on the C - Cv* versus p plot, and has shown that the Berthelot equation predicts the straight line through the origin; the Beattie-Bridgeman equation predicts the upward curvature at low density and the downward curvature at the high density; the Martin-Hou equation and the BenedictWebb-Rubin equation predict the downward curvature at low densities and upward curvature at the very high densities. The latter three equations all predict (d2P/dT2) is zero at the critical density, and therefore, the isotherm reaches a maximum at the critical density. Figure 1-1 is a summary of de Nevers' conclusions and is reproduced from his thesis.

-8Type of isotherm predicted by Type of isotherm predicted by Benedict-Webb-Rubin and Martin- the Berthelot Equation Hou Equations ~/ / /y^ I~ < Type of isotherm predicted I / by Beattie-Bridgeman Equation PC P --- Figure 1-1. Types of Isotherm on a Cv-Cv* vs. Density Plane Predicted by Several Equations of State. (This figure is reproduced from de Nevers' thesis, p. 11. ))

"91-5 Constant-Volume Heat Capacity and the Speed of Sound The constant-volume heat capacity is also related to the speed of sound by the following exact thermodynamic relation, valid only for the single phase of one component: ^ dP T 1/2d T (1-16) where c is the speed of sound. By Equation (1-16), C, may be evaluated if the speed of sound and the state data are known. However, since the first derivative of P with respect to T or V is generally less accurate than PVT data itself, it is to be expected that Cv thus calculated may have a considerable error.

IIo PRIOR WORK IN CONSTANT-VOLUME CALORIMETRY II-1 Calorimetric Measurements of Constant-Volume Heat Capacity Joly's(22) work on carbon dioxide in 1894 was probably the earliest attempt in this field. His apparatus was a differential steam calorimeters, and data were collected over a temperature range from room temperature to 100%Ca at low pressure, Although his data were superseded by later work, he correctly concluded that Cv increased with increasing temperature and increasing density for the range he studied. In 19035 Dieterici(l4) measured the heat capacity of carbon dioxide and isopentane using a Bunsen ice calorimeter. He worked on the two-phase systems but convered his two-phase saturated heat capacity, Cgsat. into the heat capacity of the saturated liquid Csat and Cv of gas by means of the PVT data of Young 6) In 1905, Reinganum(39) compared Dieterici's data with those calculated from the PVT data of Amagat(2) and Young/(46) and came to the postulate that Cv as a function of density at a constant temperature would exhibit a maximum near the critical density. On the basis of more extensive PVT data later available, his postulate has been confirmed by subsequent investigators. Most modern equations of state also show this behavior (see Figure l-1), To test Reinganum's postulate, Bennewitz and Splittgerber(7) constructed a calorimeter in 1928 to measure the Cv of carbon dioxide near the critical point. Their calorimeter consisted of a steel vessel placed in the evacuated space and surrounded by a water bath of constant temperature, The resistance thermometry and electrical heating method p)10

were used in their calorimeter. Their data were mostly taken in the two-phase region below the critical temperature, but they computed the Cv of the liquid and Cv of the gas by means of the PVT data. They concluded that (dCv/dV)T was zero at the critical point, and that just below the critical temperature both the Cv of the liquid and that of the (25) gas had a negative values. Keenans23) reasoning on the impossibility of negative values of Cp in the stable system can also be applied to Cv, and it is logical to conclude that Bennewitz and Splittgerber's work must have been in error. In 1928, Eucken and Hauck(l6) measured Cat and C for argon, carbon dioxide, ethane, and air in the liquid and supercritical region, using an adiabatic calorimeter, simply "to increase our deficient knowledge of heat capacities in this region." The heat capacity of their calorimeter was five to eight times that of its contents, Interested in the "hysterisis" effects near the critical state, Pall, Broughton, and Maass(37) measured the Cv of ethylene in 1938, using the adiabatic calorimeter. They measured the Cv as a function of temperature for only the critical density, and found that the Cv might differ by as much as 5% at a particular temperature of measurement, depending on the past history of the gas: whether it had been heated up to the experimental temperature from below the critical state or had been cooled to the same temperature from well above the critical temperature before the experiments The heat capacity of their calorimeter was 5 to 8 times the heat capacity of its contents* In 1950 Hoge (20) measured the Cat and Cv of oxygen in apparatus originally designed for vapor-pressure measurements, He wished to assess

-12the possibility of determining the two-phase boundary by measuring the liquid and gas heat capacities, perhaps a more accurate method than the PVT measurements He came only to the tentative conclusion that Csat and Cv measurements should be as reliable as PVT measurements for determining the two-phase boundary, and that the former would be much easier. The heat capacity of his calorimeter was about twenty times that of its contents Up to 1951, Sage and various co-workers(lO) had made a series of measurements of Csat to determine saturated-liquid heat capacity C They adjusted the sample of two-phase mixture so that the correcsat tion for the gas-phase heat capacity and that for the heat of vaporization were always small. Their calorimeter was the first one of its kind which utilized mechanical stirring for obtaining temperature uniformity. All others merely relied upon conduction of heat through their heavy metal walls and natural convection by their contents,. In one of the calorimeters used by Sage et al,, the stirrer was driven by the external motor whose shaft entered the calorimeter through a rotary seal; in the other one, the entire calorimeter was rocked to cause the liquid to move within. The heat capacity of their calorimeter was about one-half that of its contents, In 1952 Michels and Striland(35) constructed a differential calorimeter which consisted of two identical containers, of which only one was filled with the gas. An identical amount of electrical energy was added to both containers, and the Cy calculated from the resulting difference in their temperature rise. They collected the Cv of carbon dioxide over a considerable range of temperature and density, and

-13presented the comprehensive picture of the relation among these variables. Comparison of their experimental results with those computed from the PVT data indicated that the agreement was good for temperatures and densities well removed from the critical point, but that near the critical point, experimental Cv was much larger than what could be predicted from the state data. In 1958 de Nevers (2) constructed an adiabatic calorimeter, using the thin-wall large-volume stainless-steel sphere. The heat capacity of his calorimeter was about 1/3 to 1.5 times that of the contents depending on the loading density. The special feature of his calorimeter was an inclusion of a tiny motor-stirrer into the calorimeter to avoid the complexity of the externally driven stirrer. He collected Cv data for propylene and perfluorocyclobutane over a considerable range of density from saturation temperature to 1500C. Comparison of his experimental results with those predicted from the available PVT data indicated that in the Cv vs. p plane the experimental isotherms presented an upward curvature at the low densities and then changed to the downward curvature at the higher densities, while the Martin-Hou equation and Benedict-WebbRubin equation all predicted the downward curvature starting from the zero density. II-2 Constant-Volume Heat Capacity from Speed of Sound The speed-of-sound measurement has been utilized by various authors to determine Cv, mainly for helping the selection of fundamental frequency or the determination of some molecular constants, for instance a potential barrier It has not been common to use this method for measuring the Cv itself as a single purpose.

In view of the excessively high values of Cv at the critical point as measured by the calorimeter, Curtiss, Boyd, and Palmer(l) tried to verify these results by the measurement of the speed of sound. They assumed that (dP/dV)T was zero at the critical point, and simplified Equation (1-16) as follows: c = V (P 1/2 (2-1) Curtiss et al, measured the speed of sound at the critical point for carbon dioxide and ethylene, and, together with the available data on the critical volume, critical temperature, and the slope of the vapor pressure curve at the critical point, calculated Cv according to Equation (2-1), Their computed values were less than one-half of those calorimetric values for both compounds. Schneider and Chynoweth(41) explained the above discrepancy by pointing out the inadequacy of assumption used in the derivation of Equation (2-1), Although (dP/dV)T is indeed zero at the critical temperature for the static measurements, it is not zero for the small adiabatic pressure changes caused by the sound wave. So they maintained that the assumption (dP/dV)Tc = O was not justified and consequently that Equation (2-1) was not reliable, although Equation (1-16) was valid. 11-3 Other Methods of Measuring Constant-Volume Heat Capacity For a gas at subatmospheric pressure, two methods have been proposed for Cv measurement. One of them, proposed by Trautz and Grosskinsky,(44) is as follows: An identical amount of heat is added to the gases of both known and unknown heat capacity. By comparing

-15O their pressure increases, the Cv of the gas of unknown heat capacity is computed. But the numerous assumptions involved in this method lessen its reliability. Another method. proposed by Schaefer,(40) is based on measurement of the rate of heat loss from a wire electrically heated. However, no data obtained through this method. Eve been published.

IIIo EXPERIMENTAL APPARATUS III-1 General Discussion It is apparent that a slight error, say 1%, in the gross heat capacity will be magnified to an intolerable extent in the final results if the heat capacity of the metal container is several times greater than that of the contents, This is the basic difficulty inherent in the constant-volume calorimetryo There are two ways to overcome this difficulty: (1) By reducing the weight of a container to an extent that the apparatus is operated at marginal safety, we may optimize the ratio of heat capacity of contents to that of a containers (2) By improving the design of the apparatus, we may enhance the accuracy of gross heat-capacity data and, consequently, suppress the fluctuation in the final results, Along the first line, de Nevers(12) pioneered in the development of the thin-wall large-volume calorimeter, which proved practical when the density of gas was considerably high, But effort in this direction has an inevitable limitation due to the possible deformation when the wall of a -container gets too thin, On the other hand, de Nevers' work left much room for improvement along the second line, Work in this direction appeared to offer the only way to achieve the projected goal, to determine the ideal gas constant-volume heat capacity, Cv*1 by the extrapolation of Cv data at reasonably low densities, It was known from experience that the fluctuation was mainly caused by the poor temperature control between the calorimeter and the 16

-17shield. In other words, the radiational heat transfer was not negligible in this type of calorimeter, The convectional heat transfer was not so important in an evacuated surrounding of about 0O03 mnm-Hg, The conductional heat transfer was significant but could be estimated with a reasonable accuracy based on the drift measurements before and after the heating period. Thus it was apparent that the shape of the radiation shield, smoothness of its surface, and the number of thermocouples attached to it for the temperature control all had significant effects on the fluctuation of data. Since the calorimeter was to be operated with the marginal safety factor at the most severe condition, the appropriate safety device was also provided. III-2 The Calorimeter The calorimeter proper was actually a thin-wall spherical gas container which accommodated a tiny dec motor-stirrer and a resistance thermometer-heater. Figure 3-1 shows the cross section of the calorimeter, The fabricated calorimeter is shown in Figure 352 at its operating position relative to the other parts of the experimental apparatus. Except for a few improvements or necessary modifications, the idea of the first successful model as developed by de Nevers(12) has been generally followed by the present author* For completeness of presentation, de Nevers' descriptions will be briefly recapitulated, emphasizing details of improvement and modification.

-188.015" I.D. NEEDLE VALVE -.sss22 G=^A=====s (HOKE # 321) 22 GA.(.O31 ) 30 GAUGE CHROMEL > PLATINUM THERMOMETER -HEATER ~~~~~GUY WIRE j-V J "2" DIA. FAN I/8" COPPER WIRE BRASS WASHER EYLM 40705 MOTOR STAINLESS STEEL HEMISPHERE BY ARO EQUIP. CORP., MOUNTING STRUT # 13577 MOUNTING STRU 5 KOVAR-GLASS HERMETIC SEALS Figure 3-1. Cross Section of the Calorimeter.

-19Figure 53 2 Calormeter, Shield, and Vacuum Container in Their Relative Positions. (1) Calorimeter, showing the the rmocouple well on the top, valve, and also the suspension Fiberglas stringsX (2) Adiabatic shield, showing three baffle pieces which also serve as the suspension frame for the calorimeter. (3) Vacuun container showing a silicone rubber ~"O"ring in the groove. and Fiberglas insulation outside the container,

-20The spherical shape was chosen because it demanded the lowest mass of container material for a given volume and allowable stress. The calorimeter shell was fabricated with two 8.015-in. ID., 0.031-in.-thick stainless-steel hemispheres, Aro Equipment Corporation No. 13577, which were cold-drawn from sheets of type 304 extra-low-carbon stainless steel, After fixing all necessary fittings and essential parts into the upper and lower hemispheres, respectively, the two hemispheres were jointed by Heliarc fusion welding (actually in the argon atmosphere). After welding, the exterior of the sphere was copper plated for the purpose of reducing heat transfer by radiation, The welding and copper-plating were done by Aro Equipment Corporation, The stress analysis showed that the tensile stress was 64,500 psi at a pressure of 1,000 psi. However, considering that de Nevers' calorimeter exploded at about 860 psi, it was decided to operate the calorimeter up to 500 psi and by no means to exceed 550 psi. For loading and unloading the calorimeter, a small stainlesssteel needle valve, Hoke No.321, was silver-soldered into the top hemisphere. Also, three small brass washers were silver-soldered to the bottom hemisphere along a line roughly one inch below the welding seam, for mounting purposes. It is to be emphasized that in the de Nevers' calorimeter the inclusion of the motor-stirrer was, in fact, a key to the success achieved. It was reported that natural convection alone was not able to yield a sufficiently uniform temperature distribution. Even with a forced convection by means of the motor-stirrer, the temperature difference was still observed; but the difference was o small that the he at leakage to the surrounding could be reasonably controlled, The motor was a

-21No. EYIM 40705 d-c motor by Barber Colman Company and was specially designed to operate in the ambient temperature of 400~F or approximately 200~C, The Delco No. 5074368 motor was used in de Nevers' calorimeter, which was operated up to 1500C, Since the motor was a limiting factor in the temperature range, this meant the substantial increase of 500C in the workable temperature range. The EYLM 40705 motor was 1.38 in. in diameter, 2 in. long and weighed 0.31 lb. It was operated cn 6 to 12 volts d-c (see Figure 3-3). The motor speed varied with the voltage, gas density, gas viscosity, etc. Since neither density nor viscosity was adjustable, the applied voltage alone was adjusted to limit the temperature difference between any two control points within 0*.2C. To reduce the weight, a part of the protective shell was removed, and eight 1/8-in. diameter holes were drilled into the rest of the shell to improve the heat transfer between the motor and the gas. The stirrer was a 2-inchlong propeller made of a 3/32-inch-thick stainless-steel sheet, with a 1/4-inch stainless-steel rod for a hub. The motor was mounted on an 1/16-inch thick brass plate, which was supported by two 1/8-inch-diameter copper wires, which in turn were silver-soldered to the inside of the lower hemisphere, In this calorimeter, the thermometer was also used as a heater during the heating period for its simplicity in design and construction of the calorimeter. The thermometer-heater was essentially 10 ft. of 56-gauge platinum wire wound bifilarly on a mica cross (see Figure 3-3). The cross was made of four pieces of 3-inch long, 7/8-inch-wide mica. All pieces were appropriately slotted and inserted into matching slots to make 5 1/2-inch-long cross, They were secured together with 30-gauge

-22chromel wire for strength and rigidity, Before assembly all mica pieces were appropriately notched for the winding purpose. The notches, 1/16 inch deep and divided into two sections of 2 inches each, were made by clamping the mica sheet between two notched brass templates and filing away the excess mica. To increase the strength of the structure, a mica disc, 1 1/8 inch in diameter, was attached to each end of the cross by 30-gauge chromel wire. Four 24-gauge copper wires were anchored to the base disc, These were joined, in pairs, by silver-soldering to the ends of the platinum wire, to form the four leads of the four-terminal type thermometer~ Figure 3-3 shows many of the details hitherto described. Before winding on the mica cross, the platinum wire was annealed to reduce the stiffness by connecting it across a 110 volt a-c for 30 minutes5 After winding the wire on the mica cross, it was again annealed by the same procedure for 48 hours to remove the strains imposed by the winding, Annealing was repeated three times, followed each time by the measurement of the resistance at the ice point to make sure that the resistance was not significantly changed by the further annealing. After this treatment, the resistance of the thermometerheater as a function of temperature was calibrated according to the method discussed in Appendix B. The thermometer was mounted on the strut made of 1/8-inch copper wire, and was secured firmly by three 30-gauge chromel guy wires. Both the strut and the three guy wires were silver-soldered to the inside of the bottom hemisphere~ The six electrical leads (4 from the thermometer, 2 from the motor) left the calorimeter through five kovar-glass seals Formerly

F4 C) C:-:i::_~~~ C)~,,,,,,,-_,.~~.~'~:3 b~lg:~L~:l-:sbC) cc ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ i 4:S t`"~~~~~~~~~~~~~~~-CC S t;-:::-: ~ ~ ~ ~ C:~~~~~~~~~

six seals were used., but since the motor and thermometer-heater were connected electrically in series, one lead from the motor did not have to leave the calorimeter but was simply connected to one of the four thermometer leads. The omission of one seal resulted in the reduction of the total weight of the calorimeter, and was highly desirable in this type of calorimeter~ The cross section of one of the electrical seals, which were all made by the Electron Tube Laboratory of the University of Michigan, is shown in Figure 3-44 The ruggedized cable end seals, ADVAC No. ES-250, available from the Advanced Vacuum Products Company, were also tried.. Although the specification was excellent, their use was finally rejected for two reasons: (1) They weighed considerably more than the "home-made" kovar-glass seals and roughly increased heat capacity of the calorimeter by 8%. (2) They were not 100% reliable; of six seals tried, one was found to leak seriously. The kovar-glass seals were silver-soldered into the wall of the calorimeter with a long part of the seals inside the calorimeter. This orientation was intended to produce the compressive stress in the glass. The reversed orientation would have produced a tensile stress in the glass which would have been less satisfactory. All electrical connections within the calorimeter were done by silver-soldering. Except the motor leads and one of the longer leads, no insulation was made on any wire. III-3 The Adiabatic Shield The adiabatic shield in de Nevers' calorimeter was cubical in shape, and thus obviously had more geometrical nonuniformity than the spherical form. Therefore a spherical form was employed in this

o - * la 40 GA. KOVAR WIRE l t. t CORNING 7052 GLASS ---— KOVAR TUBE 0.127" O.D. ~"'1 ed ^0.100' I.D. — ^ l ^i-^^- N BRAZED WITH Cu- Au EUTECTIC cm - IN H2 ATMOSPHERE — O.F.H.C. COPPER TUBE 0.250" O.D. 0.1 I00" I.D. CALORIMETER WALL — Iw SILVER SOLDER,,,3 Figure 3-4. Cross Section of the Hermetic Electrical Seal.

-26project. The adiabatic shield consisted of two 12-inchI.D., 1/4-inchthick copper hemispheres. Three 7/8-inch-diameter holes were carved off along the contact edges of two hemispheres to facilitate the evacuation. Three baffle plates, made of copper sheets, 1 1/2-inch wide, 2 1/2-inch long, and 1/16-inch thick, were placed in front of these holes to serve as a radiation shield and also as a frame for suspending the calorimeter. The base of a baffle plate was appropriately bent so that the clearance between the baffle and the adiabatic shield was approximately 3/8-inches. The base of the baffle plate was fixed to the inside of the bottom hemisphere of the adiabatic shield by two 1/8-inch brass screws. Close to the top of each baffle plate, a 1/8-inch diameter hole was drilled for hooking the calorimeter4 The interior of the adiabatic shield was handpolished to a mirror-like smoothness to reduce the heat transfer by radiation. Three legs, made of 1/2-inch-diameter brass rod., were brazed to the lower shield to locate the shield in the concentric position with the vacuum container, Two handles made of 1/8-inch steel wire were attached on the top adiabatic shield for liftings To avoid the dislocation of the top shield from the bottom one, three small pieces of copper block were attached to the bottom hemisphere with 1/8-inch screws; each was located just between two adjacent 7/8-inch holes. Twenty-four small brass washers were brazed to each hemisphere for mounting the heating tapes. All details described above can be seen in Figures 3-2 and 3-5. The adiabatic shield was heated by six 1/2-inch by 6-ft "Briskeat" flexible heating tapes which were attached to its outer surfaces The heating rate of these heating tapes was 288 watts per tape at 115 volts.

-27Three heating tapes were uniformly distributed on each hemisphere of the adiabatic shield. The actual distribution of the heating tape was as follows. The total area of the hemisphere was divided into two parts: a top circular space, 1/3 of the total area, and the rest of the hemisphere. One heating tape was attached to the top circular area in a zig-zag pattern, and two heating tapes were attached to the side ring in a spiral fashion. All tapes were fixed by 20-gauge copper wire which ran between two washers. These washers were arrayed in two rings, one close to the edge and the other along the dividing line as mentioned above, Most of the details can be seen in Figure 3-5. No special attempt was made to cement or glue the heating tapes to the copper shield. Six heating tapes were grouped into three pairs for the regional temperature control, i.e., top, side, and bottom respectively. The power was supplied to each heating tape in parallel through three "Powerstat" variable voltage transformer, one for each pair of tapes. The circuit diagram of the heaters is shown in Figure 3-6. The calorimeter was held in the center of the spherical adiabatic shield by three glass strings, to the ends of which steel hooks of convenient shape were attached. These strings ran from the three brass washers silver-soldered to the bottom hemisphere of the calorimeter to three holes drilled into three baffle plates bolted to the bottom hemisphere of the adiabatic shield. III-4 The Thermocouples As mentioned in Section III-l1, the temperature control was of great importance to the accuracy of data~ From a practical point of view, however, only a few points might be selected for the control purpose.

-28Figure 355 Vacu Container and Adiabatic Shield, (1) Lid of the vacu contaixerj suspended by a chaiin hoist. (2) Adiabatic copper shield~ showing "Briskeat" heating tapes, small brass washers, handles for lifting holes for facilitating evacuation~ and small pieces of edge guide~ (5) Vacuum container showing silicone rubber " ring in the grooYe and FibTerglas insulation outside (4) Part of safety cabinet~ (5) Part of vacu systemn

110 V. A.C. 6 BRISKEAT FLEXIBLE HEATING TAPES,-.- ^-^ (288 watts at 115 volts per tape) // " /i \\ / a\ /, I i IoI / \ \ \I / M ~ \ / i —— ^ / z- 3 "POWERSTAT i/>_,, v-'VACUUM CONTAINER VARIABLE TRANSFORMER ADIABATIC SHIELD Figure 5-6. Circuit Diagram of Heaters.

-30Three points (top, side, and bottom) were selected on the surface of the calorimeter, and corresponding points were also selected on the adiabatic shield except the side. For the side of the shield, two points were selected instead of one since this region did not consist of a single piece of copper. Across the contact edge, two points were located closely but on different hemispheres* The temperature difference between any two points was indicated by means of copper-constantan differential thermocouples. Seven thermocouples were installed at seven control points and all constantan wires were brought to a common junction, at a point within a vacuum container. The seven copper wires left the vacuum system through the electrical junction box. After that, all copper wires were brought to a junction board, from which eight combinations were selected (see Figure 3-7 for these combinations). By measuring EMF between any two copper wires, it was possible to determine the temperature difference between any two of the seven control points. In practice, no definite value of ENF was measured but the desired. combinations were led to an eleven-point, doublepole, rotary switch, Leeds & Northrup type 8240, No. 1210525, from which they were directly connected to the moving coil galvanometer, Leeds & Northrup No. 1193782. To adjust the sensitivity of the galvanometer, three extra resistors of 1,000, 10,000, and 100,000 ohms were arranged in series with the galvanometer. These resistors were seldom used unless the temperatures were excessively off balance. The circuit diagram of the entire thermocouple system is shown in Figure 3-7. The circuit involved no reference junction since only the temperature difference

CALR. CALORIMETER CALR. TOP TO CALR. SIDE CALR. SIDE TO CALR. BOTTOM _ __________CALR. TOP TO CALR. BOTTOM_____ CALR. TOP TO SHIELD TOP lU' vCALR. SIDE TO SHIELD UPPER SIDE w a. CALR. SIDE TO SHIELD LOWER SIDE w | 0 l CALR. BOTTOM TO SHIELD BOTTOM o CALR. UPPER SIDE TO LOWER SIDE la E5_ i i55 JUNCTION BOARD = 0 0 -- - - CONSTANTAN' - C COPPER TOP SIDE BOTTOM TOP UPPER LOWER BOTTOM, % SIDE SIDE j CALORIMETER ADIABATIC SHIELD GALVANOMETERFigure 3-7. Circuit Diagram of Thermocouples.

-52was of interest. The galvanometer was of a null-type and no accurate EMF might be observed. but the rough temperature difference might be estimated based on the published data for a copper-constantan the'rmocouple and galvanometer. It was estimated that one centimeter of deflection on the galvanometer scale corresponded to 1/100~C. To place the thermocouple in thermal contact but not in electrical contact with various surfaces, insulated thermocouple wells were employed at all control points. The wells were made of 20-gauge copper tubing (0.125-ind O.D.. 0.0655 in. I.D., and 1/2 in. long), and were soldered to the places by silver-solder or high melting solder (melting point 7100F), The Teflon tubing (0.052-in. OD. and 0O030-in. I.D.) was coated with vacuum grease and forced into the copper tube. The Teflon tubes were again filled with vacuum grease using a hypodermic syringe, and the thermocouples were then forced into them. III-5 The Vacuum Container The purpose of the outer container was two-fold: (1) to provide an evacuated space for housing the calorimeter and radiation shield with an aim of eliminating the heat transfer by convection; and (2) as a safety device to contain various parts of the calorimeter from flying in every direction in case of rupture of the calorimeter. For these reasons the container demanded not only a good vacuum seal but also quite heavy construction. The vacuum container consisted of two identical parts, each of which was fabricated by welding a "Taylor Forge" 16-inch Schedule 80 welding cap to a "Taylor Forge" 16-inch 500X slip-on flange, The thickness of the container was 0*843 inches and the flange was 2 1/4-inches

355thick. The total weight of the vacuum container was about 680 lb. Figure 3-5 shows the lid of the container being lifted by a chain hoist, After welding, it was found that the flanges were slightly warped and gave about 3/16-inches clearance at the outer edge. Three legs, each made of 3 x 1-1/2 x 2-1/2 in, channel, were welded to the bottom of the vacuum container and bolted on the other end to the concrete slab which formed a basis for the safety cabinet. A silicone rubber "O"-ring was used as a vacuum seal between two flanges. The "0"-ring was provided by Precision Rubber Products Corporation (PRP6543, I-D. 17-000 in. CS *275 in. Compound.1130-80)* The matching "O"-ring groove was machined on the lower flange, with the following dimensions: grove I.D.: 17o000-o005 + o000 inr; groove depth:,225 +.005 in; groove width: approximately.375 in. The bottom of the container was connected to the vacuum system through 7/8-inch copper tube. Two flanges were bolted together by twenty 1-1/4 x 6-in.machined bolts0 An iron ring was welded to the top of the vacuum container for lifting the lid with a l/2-ton chain hoist equipped with a sliding roller. The heating tape leads left the vacuum container through the Stupakoff Multi-terminal Header,- No, 954003, The multi-terminal header was silver-soldered to a 2 inch-long stainless-steel tube, which in turn was welded directly to the wall of the container. The calorimeter leads left the vacuum container through a 6-ft-long Tygon tube to the junction box. The lower half of the container was insulated by approximately 2-inch-thick Fiberglas. A removable canvas-covered mat of Fiberglas was placed on the top of the container after the flanges were bolted together.

As an additional safety measure, a steel cabinet was built to house the entire vacuum container and vacuum systemn The steel cabinet, roughly 8 x 31/2 x 8 ft in size, was bolted to the concrete slab, cast into the rectangular frame made of 6 x 2 inch channels The frame of the cabinet was made of 2 x 2 x 3/8 inch angles on which were attached 1/4 inch hot-rolled steel sheets. The front of the cabinet consisted of two doors of 4 x 8 ft, each fixed to the side of the cabinet by four 7 1/2-inch hinges. The doors were secured to the place by four 3/4-inch bolts and a latch made of 2-inch pipe. No steel sheet had been attached to the rear side of the cabinet, which faced the windows directly, Naturally it was expected to blow into the direction of the window when the rupture of the calorimeter should takeplace4 One 6-ft long, 6 x3-1/2 inch I beam was fixed to the ceiling of the cabinet to slide the roller of the chain hoist; III-6 Electrical Junction Box As reported by de Nevers(12) thermal EMF would be induced in the Stupakoff multi-terminal headers if the headers were soldered directly to the wall of the vacuum container, because of the irregular temperature gradient across the wall. To avoid this difficulty, the header was installed in a separate junction box which was connected to the vacuum container by a 6-ft long piece of Tygon tubing. By this separation the heating elements did not affect the headers and the temperature gradients were usually negligible (see Figure 4-1). The junction box consisted of a 500-cc stainless-steel beaker, to the bottom of which was silver-soldered a piece of stainless-steel

-35tubing and to the top of which was silver-soldered a l/8-inch.thick, 1-inch-wide steel flange. The matching brass plate was bolted to this flange with eight 1/4-inch bolts, An "O"-ring was used between them as a vacuum seal., Two Stupakoff eight-terminal kovar-glass headers No, 95.4003 were soft-soldered into the holes in the brass plate. Of the total 16 terminals, four were for the thermometer, two for the motor, seven for the differential thermocouples, two for spare wires, and one was left unused. All the wires used were 30-gauge copper Formvar - and Fiberglas-insulated III-7 The Vacuum and Loading System A Cenco Hyvac No. 2 mechanical vacuum pump was used to evacuate the vacuum container and also to provide vacuum necessary for loading and unloading the calorimeter. Figure 3-8 is a schematic diagram of this system, Three sizes of tubes were used: 1/8-inch copper tube for the loading and unloading line; 5/8-inch 0D. copper tube for connecting Lippincot-McLeod gauge via flexible Tygon tubing, into which a number of 1/8-inch 0.D, 5/8inch long pieces of glass tubes were inserted to prevent the Tygon tube from flattening during the evacuation; and the main line tubing consisting of 7/8-inch copper tube for fast evacuation. The pump was connected to the heavy-wall rubber tube, approximately 1-ft loog, which, in turn, was connected to the U-shaped cold trap made of 5/8-inch glass tubings The cold trap was eventually removed from the system because the vacuum pump alone was able to provide sufficient vacuum, It was replaced by an L-shaped glass tube which was connected to the main line by the "O0-ring sealed fittings This tube served not

CALORIMEIE LOADING BOMB 500 lb. GAUGE CALOR IMETER (while loading only) /(used for tetrofluomethone (while loding only) looding only) LIPPINCOT- McLEOD GAUGE V2 VACUUM CONTA INJ ER TO CENCO HYVAC-2 VACUUM PUMP Figure 35-8. Schematic Diagram of the Vacuum and. Load~ing System.

-537only as the connection but also as a safety measure for keeping highpressure gas from reaching the pump in case of rupture of the calorimeter. The valves were all Imperial Diaphragm type vacuum valves, except one located near the intersection of the loading line and the main line. This was a Hoke needle valve primarily used as a double check to make sure no sample ever got into the pump. During the loading period, the calorimeter was taken out of the adiabatic shield and placed on the flange of the vacuum container. II1-8 The Measuring System The measuring system consisted of two parts: the temperaturemeasuring system and the power-measuring system; the latter included the power circuitry~ Figure 3^9 is a circuit diagram of this system, and Figure 3"10 is an over-all view of the measuring and control instruments Six electrical leads from the calorimeter reached the 8-pole double-throw master switch via the vacuum junction box described in Section IIII-6 At this master switch, located on the control and measuring panel, six leads were switched either to the temperaturemeasuring circuitry or to the power circuitry in accordance with the experimental procedures. While the master switch was set to the temperature-measuring circuitry, two leads from the motor remained idle and four leads from the platinum resistance thermometer were directly connected to the Leeds & Northrup mercury cup commutator, type #8068, serial No4 1194595, which provided the so-called "potential terminal" type of circuitry to compensate the resistance of the leads as described by Mueller. From this commutator three leads went into the Mueller Bridge} which was essentially

-38the modified Wheatstone Bridge for measuring the resistance of the platinum thermometer The bridge was a Leeds & Northrup type C-i, serial No. 1192498.. The power for the bridge was supplied by four 1 1/2-volt dry cells in series, using a small rheostat as a potential divider, It was not necessary to know the exact voltage, and the rheostat was adjusted to give the appropriate sensitivity. A moving-coil galvanometer, Leeds & Northrup type 2284-d, serial No4 1193782, was used as an indicator for the Mueller Bridge. This is the same galvanometer which was used for the thermocouplesX It was mounted on a wooden bracket bolted to the wall of the building. A copper guy wire was also used to secure it against accidental dislodgement. The galvanometer was read with a Leeds & Northrup light and ground scale, type 2100, serial No. 223883, located about 1 1/2-meters from the galvanometer. As this is a null-type instrument, the exact calibration of the deflection was omitted. The 11-point double-pole rotory switch was used to relay the signal from the Mueller Bridge to the galvanometer. In general, the signal was transmitted directly, although an extra resistance could be added in series with a galvanometer as mentioned in Section III-4*. To prevent too much current from passing through the thermometer and thus slightly increasing the temperature, the zero-ohm key was generally avoided; the 220-ohm key was used mostly. While the master switch was set to the power-measuring circuitry, one pair of thermometer leads, directly connected to one of the motor leads, reamined idle. One of the thermometer leads, one of the motor leads, the milliammeter, balancing resistor, 01-ohm standard resistor, and 30- to 42-volt batteries formed a main power circuit whose current was determined

-39MOTOR THERMOMETER - \,\ CALORIMETER - STANDARD CELL POTENTIOMETER AUTO BALANCING BATTERIES |,~~s~o,~,1B~ATTERIES RESISTOR7 v, I OOOOl. A MILLIAMMETER.... _ -! -- — 8 - POLE 2-THROW l I AX - _, t MASTER CONTROL ~_______________I________SWITCH COMMUTATOR- DUMMY TIMER -rnI- RESISTORl 110 V. AC GALVANOMETER MUELLER BRIDGE — Figure 3-9. Circuit Diagram of the Measuring System.

40Figure 3-10. Control and Measuring Instruments. (1) Lippincot-McLeod gauges (2) Potentiometer. (5) Mueller bridge. (4) Galvanometer light and scale. (5) Battery charger. (6) Clock and timer. (7) Balancing and dummy resistor. (8) Lead storage batteries. (9) 11-point 2-pole selector switch, (10) 8-pole double-throw master control switch. (11) Powerstats variable transformers. (12) Milliamieter and voltmeter,

-41by measuring the potential drop across a standard 0.100000-ohm resistor, Leeds & Northrup type No. 4221-B, serial No. 1216562. Two remaining leads,} one from the thermometer and one from the motor, were connected to a potential dividers A voltmeter was added to the circuit in parallel with the potential divider, The potential divider was essentially a combination of two standard resistors in series, i.e., a standard 10,000-ohm resistor, Leeds and Northrup type No* 4025-B, serial Not 1196149, and a standard 10,000-ohm resistor, Leeds and Northrup type No. 4040-B, serial No, 1201941, All resistors were certified in November, 1956~ by the manufacturer with 0*01% accuracy. With this setup the voltage across the thermometer-heater and motor combination was determined by measuring the potential drop across the standard 10.000-ohm resistor. All three of these standard resistors stood in an oil bath: a stainless-steel pan, 10 by 7 by 5 inches deep, filled with 20-weight motor oil# The potential drop across these standard resistor was determined by means of a Leeds & Northrup No4 8662 portable precision potentiometer, serial No. 1042502. This potentiometer had a self-contained galvanometer, and a standard cell. An external standard cell, Epply No. 425935, however, was used for all measureme nts considering the accuracy of its calibration. The standard cell was calibrated against Weston standard cell mode 4 No, 15559, whose NBS calibration on October 28, 1958 was available. Power for the potentiometer was supplied by the self-contained dry cell. A milliammeter reading o-800 ma and a voltmeter reading 0-25 volts were mounted on the control panel to show the current through and voltage across the thermometer and motor combination (or just a current

442p through a dummy resistor during the non-heating period). These rough instruments took no part in producing the experimental data, but were simply used for minor adjustments such as a balancing resistor, dummy resistor, or rough potentiometer.-reading setup, These instruments also served to warn the operator of malfunctions of the equipment* Power for the calorimeter, for both thermometer-heater and motor-stirrer. was supplied by lead storage batteries. Two 12-volt and three 6-volt automobile batteries were available for various combinations to yield over-all voltage of 30, 36, and 42 volts. The selection of the voltage was made so that a net voltage across a motor was always more than 6 and less than 10 volts. A battery charger was used to recharge the batteries when they were not in uses Before or after the heating period., the batteries were connected to the dummy resistor, of about the same resistance as the thermometer and motor combination, by simply switching the 8-pole double-throw master switch to the temperaturemeasuring position. This was to prevent the rapid change of the battery voltage at the start of a heating period. To minimize the change of power input with changes in thermometer-heater and motor resistance, a balancing resister was connected in series with thermometer-heater and motor. Hoge (21) has given a detailed account of the use of the balancing resistor. Both a dummy and balancing resistors were l00-ohm, sliding-contact "Ohmite" No. 2921-A resistors. The elapsed time of a heating period was measured by a synchronous timer with an electrically actuated clutch (Standard Electric Time Company model S-6). The clutch was actuated by the 8-pole doublethrow master switch which started the heating period simultaneously.

A two-pole double-throw switch was also mounted on the control panel, connecting potentiometer to either Ovl-ohm standard resistor for measurement of current or to 10*OOO-ohmn standard resistor for measuring the voltages

IV. EXPERIMENTAL PROCEDURE AND MATERIALS IV-l Transferring the Material Into the Loading Bomb Prior to any loading of the calorimeter, the material under investigation was first transferred from its shipping container to one of the light-weight loading bombs. Two types of bombs were used: for the condensable gas whose vapor pressure at room temperature was less than 500 psi, war-surplus, stainless-steel oxygen bottles; for noncondensable gas such as tetrafluoromethane, a specially rated heavywall container. The loading bomb of the first type had a capacity of about two liters; its rated pressure was 500 psi, Each bomb was equipped with a needle valve (Hoke #321) and a small aluminum identification tag bearing the name of the contents. The loading bomb of the second type was also cylindrical in shape, had a volume of approximately 1.2 liters, and a rated pressure of 2,000 psi. To transfer the material, the loading bomb and the shipping container were connected to both ends of the loading line, respectively~ Then the loading bomb and the whole line were evacuated to less than 10 >i with the main valve close to the vacuum container shut off (see Figure 3-8). Finally, the loading line was isolated from the vacuum system and the valve of the shipping container was opened. The material was transferred either by heating the shipping container or by condensing the gas into the loading bomb with liquid nitrogen. IV-2 Loading the Calorimeter First the loading bomb was weighed on the precision balance, Seederer-Kohlbusch serial number 2F-2756, which could weigh quantities

-45up to 3,000 grams and could be read to 0O01 gram. Then, as shown in Figure 3-8 the loading bomb and the calorimeter were connected to the loading system. With valve No. 1 and No. 2 shut off, valve No. 3 and the calorimeter valve open, the line and the calorimeter were evacuated down to less than OOlO0-mm Hg. After this, the loading line was isolated from the vacuum line by closing valve No. 3. As soon as a valve of the loading bomb was opened, the vapor flew into the calorimeter and was condensed there except tetrafluoromethane. This procedure was facilitated by heating the loading bomb with a flexible heating tapes To determine the approximate amount of material loaded, the loading bomb was placed on one pan of a crude 2-kg balance, and the needed weights were placed on the other pan. As the loading proceeded, the weights were removed from the pan gradually until the total weight removed was approximately equal to the desired quantity of loading. At this point the calorimeter valve was closed, and the residual vapor in the line was collected back into the loading bomb by condensing it with liquid nitrogen. At the temperature of the liquid nitrogen, the vapor pressure in the loading bomb was reduced to a negligible value, so material left in the line should also be negligible. Figure 4-1 shows many details hitherto described. The valve of the loading bomb was then closed, the bomb was disconnected, warmed to room temperature, and again weighed to 0,01 gram. The difference between the initial and final weights corresponded to the mass loaded to the calorimeter. The crude balance was able to regulate the loading to about + 15 grams. The calorimeter was then disconnected from the loading line. The surface was carefully polished by "Boyer's Instantaneous Metal Polish'

ig'uo )1 1.. Loa&d..ing the CalorixLeter (1) Load.-.ing bortb -resting on the balance panL (2) Vacuum pixrp (5) Junction box. (4) Vacuum manifold. (5) Callorximeter on a wooden base. (6) Lower'half of the vacuum container and adiabatic shield

-47if necessary. The "Instantaneous Metal Polish" was also applied to the adiabatic shield for the best result in reducing the radiation heat transfer. The calorimeter was then suspended in place by the Fiberglas strings. All thermocouples were installed in the corresponding wells, and then the top of the shield was mounted. After the heating tapes were electrically connected. and the "0"-ring was installed, the lid of the vacuum container was lowered to the position and secured by twenty 1 1/4-inch bolts. Finally the Fiberglas mat was placed over the vacuum container, and the system was evacuated. IV-3 Operating the Calorimeter The actual calorimetric measurements were not started until the system had been evacuated to about 0.030-mm Hg. Any series of measurements for one particular density was begun at the lowest temperature above which only a single phase existed. Each normal run consisted of the first temperature-measuring period, a heating period, and the second temperaturemeasuring period. For the successive runs the second temperature-measuring period also served as the first temperature measuring period of the following run~ To begin a run, the shield heaters were controlled by the variable transformers so that the differential thermocouples indicated zero average temperature differences between the control points on the adiabatic shield and those on the calorimeter. In fact, this was the most difficult part in the whole experiment and involved considerable uncertainty if its fluctuation was not limited to a certain value. It was} in practice, adopted as a criterion of acceptance that the galvanometer deflection should always stay within + 10 cm on a ground glass

scale during this period., Fluctuations of about 0.1~C were quite common. Before the temperature reading was taken, at least 20 minutes were allowed for thermal equilibrium after the zero average temperature difference had been attained. Temperatures of the calorimeter were measured at 5-minute intervals by means of the platinum resistance thermometer and the Mueller bridge. Generally four readings were taken to determine the "drift" or the rate of temperature change with respect to time. If the drift thus determined appeared reasonable for the circumstance, the heating period was begun by throwing the 8-pole double-throw master swithc to the heating position. This switched the power from the d.urmmy resistor to the thermometer-heater and motor} and simultaneously engaged the clutch of the synchronous timer. Of course, the Mueller bridge was automatically disconnected from the thermometer at this time to prevent current from flowing through the bridge. The total length ofthe heating period ranged from 18 to about 30 minutes depending on the contents of the calorimeter and the intended temperature rise. The temperature rise was usually from 10 to 14o~C At the start of the heating period., a burst of power was given to the shield to compensate the slow response of the adiabatic shield to the heat input. Of course, during the heating period., the adiabatic shield was continually controlled to maintain zero average temperature differences between the control points on the surface of the calorimeter and those on the adiabatic shield. The temperature control during this period was much more difficult than that during the temperature-measuring period., and the following criterion was observed.: The galvanometer deflection should not exceed the observable scale about + 30 cm,

Power supplied to the thermometer-heater was determined twice or three times in each run depending on the duration of the heating period, In general, one reading was taken every 10 minutes, It was determined at times corresponding to 1/4, 1/2, and 3/4 of the heating period if three readings were necessary; otherwise, they were determined at times corresponding to 1/4 and 3/4 of the heating period. First the potentiometer was standardized by the external standard cell, Then with the two-pole doublethrow knife switch set to the "current" position, the current was determined by measuring the voltage across the 0.10000-ohm standard resistor, which was in series with the thermometer-heater and motor. Next. with the two-pole double-throw knife switch set to the voltage position, the voltage across the thermometer-heater and motor was determined by measuring the voltage across the 10.000-ohm standard resistor, a part of a circuit which was in parallel with the thermometer-heater and motor, Then the current measurement was repeated. Two current measurements differed slightly due to the change in the resistance as temperature increased. Thus, the average of two current measurements was assumed equal to the instantaneous current reading at the time of the voltage readings The product of this average current and voltage was regarded as the instantaneous power of the thermometer-heater and motors At the end of the heating period, the master control switch was thrown back to the temperature-measuring position. This simultaneously switched the power from the thermometer-heater and motor to the dummy resistor, disengaged the clutch of the timer and reconnected the Mueller bridge. After the time and reading of the timer were recorded, the timer was resets To prevent the adiabatic shield temperature from

overshooting that of the calorimeter, the power to the shield was cut down substantially one or two minutes before the end of the heating period. Ten minutes were allowed for the calorimeter to attain the thermal equilibrium while the temperature of the shield was controlled as before to maintain zero average temperature differences between the control points on the surface of the calorimeter and those on the surface of the shield. The temperatures were then recorded at 5-minute intervals as in the first heating period, until the drift had been determined, If another run was planned, the heating period was started immediately; otherwise, the operation ceased at this point* Due to the large mass of the vacuum container, its temperature increase always lagged behind that of the shield or calorimeter. From the experience, we knew that the greater the temperature difference between the shield and the vacuum container, the higher the value of drifts and the more difficult was the temperature control. In practice, the continuous operations never exceeded three runs, and at high temperatures they were limited to two successive runs each time. With an appropriate power supplied to the adiabatic shield to keep the desired temperature, the whole system was left idle for three or four hours for the vacuum container to attain the same or close to the same temperature as the calorimeter, The experience also indicated that the best results could be obtained if the shield was controlled by a small adjustment of the voltage of the variable transformer at a greater frequency rather than by operation of "OnOff" switch and a burst of power in an attempt to obtain a quicker adjustment.

-51l IV-4 Unloading the Calorimeter When sufficient Cv data were collected over the allowable temperature range for a given loading. the contents of the calorimeter were recovered into the loading bomb. The recovery of the material served to check the possible leakage of the calorimeter or the loading line. It also saved the material for the further study. The loading bomb and the calorimeter were connected to the loading line, which alone was evacuated to less than OO10-mm Hg. Then the loading line was closed off from the vacuum system, and the valves of the loading bomb and calorimeter were opened. With the loading bomb immersed in a dewar of liquid nitrogen, and the calorimeter warmed by a flexible heating tapes if necessary, the material was transferred from the calorimeter into the loading bomb. The completion of the transfer process was indicated by the cessation of the violent boiling of the liquid nitrogen and also by the disappearance of the atmospheric condensation or frost on the bottom of the calorimeter. At the completion of the recovery process, the valves of the loading bomb and calorimeter were closed, and the loading bomb was then disconnected. warmed to room temperature, and weighed on a precision balance, The loss of material during these two transfer operations was usually less than 067 grams for the gases condensable at a normal condition. The loss could reach 1,5 grams for the gases not condensable at a normal condition, for instances tetrafluoromethane, The loading bomb was always weighed immediately before the recovery process to make sure there was no leakage in the loading bomb itself by comparing it with the weight determined immediately after the loading.

-52IV-5 Material Used for Investigation The four compounds selected for the investigation were tetrafluoromethane, chiLorodifluoromethane, d-ichlorotetrafluoroethane, and chloropentafluoroethane. The statistical heat capacities have been calculated for four compounds by various authors, but none of them has been fully tested by the calorimetric measurements. For chloropentafluoroethane, a few data have been determined by measuring the speed of sound.(30) The Martin-Hou equations of state have been developed for chlorodifluoromethane,(26) tetrafluoromethane, (8) and dichlorotetrafluoroethane (.25) All four compounds were supplied by the "Freon" Products Laboratory of E, I. d-u Pont de Nemours & Company. These compounds are known commercially as "Freon"* refrigerants~ Tetrafluoromethane is known as "Freon-14" chlorodifluoromethane as "Freon-22," d-ichlorotetrafluoroethane as "Freon-114," and chloropentafluoroethane as "Freon-115o" The purity of the samples was specified by the supplier as follows,. Tetrafluoromethane (sample No., J-5452) has a purity of 99.7 + % by volume. It contains 5ppm H20, less than 0O01 volume % dichlorodifluoromethane, 0*02 volume % chlorotrifluoromethane, 0.16 volume % air, 004 volume % H2 and no CO. Chlorodifluoromethane (sample No. KCD 2210) has a purity of 99.9 + % by gas chromatography. It contains 3 ppm of moisture and 0o04 volume % of air in the vapor phase. Dichlorotetrafluoroethane (sample No. FCD 909) contains 7 mole % of isomeric CF3CFC12 and no detectable impurities. The minimum detectable amount of probable impurities is as follows: * Trad-e name copyrighted- by E, Io d-u Pont d-e Nemours & Company.

Trichlorotrifluoroethane 042 mole % Isodichlorotetrafluoroethane 0^o6 mole % Chloropentafluoroethane 0O,1 mole % Dichlorotrifluoroethane 0.05 mole % Chloropentafluoroethane contains no detectable impurities by infrared absorption analysis, It probably contains less than 0.1% of air and moisture, Dichlorodifluoromethane (sample No, KCD-1506) contains no detectable impurities by infrared spectrum, The moisture content is 4 ppm and air content is 0.0008% by volume in the vapor phase.

V. METHOD OF CALCULATION AND ESTIMATED ACCURACY V-1 Calculation of the Gross Heat Capacity For the perfectly adiabatic calorimeter, the gross heat capacity may be expressed as follows: d oQ qo C - 5Cgross T 0E or Cgross = - (5-1) or in the integral form: T2 92 T2 Cogross grossT = Q - 1 (5-2) T!'1 T1 where Q is a total heat input, q a rate of heat input, T the temperature, and Q the time* For a small interval of temperature increase, AT, the following approximation is valid since q is nearly constant or linear in its change. If we define the mean gross heat capacity (Cgross)mean as ( gross)mean - 5Af 3) it follows that (Cgross)mean qmean A (5 It would not cause too serious an error to regard this mean gross heat capacity as a true gross heat capacity at the mean temperature. The perfect adiabatic calorimeter, however, is merely an imaginary device which never existed in the practical calorimetry, All actual calorimetries rely very much on the appropriate estimation of the heat leakage. If the heat leakage rate is known explicitly in terms of

-55energy per unit time, Equation (5"4) may be modified as follows: (Cgross)mean = (qmean + qcorr ) - (5-5) where qs are added algebraically, If the heat leakage rate is known only in the form of an equivalent temperature change ATeorr, that is, the change in temperature which would have taken place in the time interval AG if no energy had been added electrically, Equation (54) may be modified as follows: qmear/-~O (Cgross)mean (Lf= c r) (5n6) where PT's are subtracted algebraically, Equation (5 6) has been employed for the calculation throughout this project. For further illustration, a sample calculation is included in. Appendix Co V-2 Calculation of Constant-Volume Heat Capacity The gross heat capacity Cgross was a sum of the heat capacity of the contents of the calorimeter, plus'the heat capacity of the calorimeter itself, plus the heat capacity of those parts of electrical leads and suspension strings which receive heat from the calorimeter. Thus the net heat capacity of the contents could not be calculated without knowing the heat capacity of the calorimeter, etc. The calibration of the heat capacity of the calorimeter, etc., is discussed in detail in the following chapter. The value of this calibration was then designated as Ccalr, which was a function of temperature. It is obvious that Cnet = Cgross" Ccalr, (5-7)

-56and Cv m= (5-8) where m is the total mass of loading. Equations (5-7) and (5-8) were used for the calculation throughout this research. The Cv was then plotted against the temperature, and a smoothed isomettic was drawn through these points. For the low densities, however, C was not calculated for each run but the gross heat capacity was first smoothed in the C vs. T plot; then Cv was calculated at every 10~C interval based on the smoothed gross heat-capacity data. There should be no difference whether the smoothing process was carried out for the Cgross or for Cv, as far as the final results were concerned. However, if Cv was smoothed, we could show the actual fluctuation of C~ clearly on the same plot. The fluctuation of CvR was greatly magnified at low densities, and. the smoothing process was extremely difficult due to the jamming of points with the adjacent isometrics, Once several isometrics were determined at a suitable interval, data were cross-plotted in Cy vs. density with temperature as a parameters Each isotherm was then extrapolated to the zero density to give Cv* (ideal gas constant-volume heat capacity). V-3 Estimation of the Accuracy Taking the logarithm of both sides of Equation (5-6), and then its differentials, we have d(cgross)mean dcmean + dA..(-.Tcorr.) ) (Cgross)mea ean d Ae d. AmTcorr*)

-57If the uncertainty of the quantities involved in the right-hand side of Equation (5-9) can be estimated reasonably, the possible error of Cgross may be estimated accordingly. The first term dq/q can be estimated as follows: n ( S E 2 z q~ imeanT- n. - (5-10) and i = IiEi (5-11) where I is current, E is voltage, R is resistance of the voltage measuring circuit, and qi is instantaneous heat input rate. Equation (5-11) may be modified to dqi dIi dEi = — - + -- (5-12) qi Ii Ei where dI/I could reach 00004 and dE/E approximately 0O0006. Hence, dq/q could be as much as 0Ol0010 This value refers to the maximum instrumental error only. In fact, the presence of the motor in series with the thermometer-heater increased the uncertainty of the mean power considerably since its counter EMF was not too steady and fluctuated erratically over a relatively small range. The balancing resistor did serve to minimize the steadily varying mean power but was not able to damp out this type of erratical fluctuation. The average of two or three readings was taken as mean which never varied from any instantaneous power by more than 0.3%. The last term of Equation (5-10) represents the power consumed in the voltage measuring circuit, which never exceeded 5% of the apparent power. So if the

-58same uncertainty were assumed, this term corresponds only to less than 0.01% in the over-all accuracy estimation. Based on the above consideration, the value of qean was probably reliable to about 2 parts per thousand.. The elapsed time, AQ, was measured by an electric timer which could be read to 1/1000 of one minute without any trouble, Since the heating period was usually 20 to 30 minutes, the elapsed time measurement was probably reliable to one part per ten thousand Of course, the accuracy of the frequency of the a-c source had an important bearing to the estimated accuracy6 Nevertheless, over a period of 20 to 30 minutes an average frequency should be extremely close to 60 cps and the over-all error should be negligible. The accuracy of temperature measurement was probably no better than 0o05~C. This refers to the absolute value of the temperature and not to the change of temperature AT, which was the difference between two measured temperatures, Ti and T2, Since the thermometer calibration was internally consistent, any error in the absolute value of temperature reading would be systematic, and an accuracy of temperature difference was definitely better than temperature itself* The estimated accuracy of the temperature difference, independent of its size, was probably around one part per thousand. There was still another uncertainty involved in AT because T2 was not directly measured., but was determined by extrapolating the reading back to the time at the end of the heating period, using the drift rate. Except for a few cases at the high temperature, the drift rate was less than 0O0120~C/min. Assuming the drift rate was known to + lOo0 the possible error in total drift over a

-5910-minute period should be less than 0.012~C. The average AT was 12~C, and. thus the uncertainty caused. by this extrapolation was less than one part of one thousand in AT. Hence, AT was probably reliable to plus or minus two parts per thousand. The heat leakage correction, ATcorr' was usually less than 2% of AT, and never exceeded 2.5% of AT, Therefore, the last term in Equation (5-7) may be approximated by d(AT-ATcorr) dAT dATcorr -------- _ -- - ---— ^(5-13) AT-ATcorrAT AT Assuming the drift rates were accurate to + 10, dATcorr/AT would be about two parts per thousand. For the worst possible case in which all these uncertainties combined to cause the observed Cgross to deviate in the same direction, the maximum possible error in Cgross would be about 0.6%. Actually, the errors were random in their nature, and experimentally observed deviation seldom exceeded 0.4% of C; most of the data fluctuated within + 0*3% gros _ of Cgross The calibration curve, discussed in the next chapter, was essentially the smoothed curve based on the extensive experimental data. Therefore, its reliability should be higher than any single measurement. It would not be too much out of line to assume that the calibration of the calorimeter heat capacity was better than two parts in thousand. Again for an unfavorable condition in which the observed Cgross deviated 03% in one direction and the calibration curve deviated 0*2% in the opposite direction, the error of final Cv would be 2.8% for the lowest density and 0.8% for the highest density attempted. According to the

principle of statistics, the reliability of the isometrics obtained by smoothing the extensive exerimental data should be much better than the above estimationo Considering the observed fluctuations, we are inclined. to claim 1/2% accuracy for the high density and 1% accuracy for the lowest densities4 The volume of the calorimeter was determined by means of nitrogen gas (see Appendix A)o Its probable error was estimated as abou+ one part per thousand. The mass of the contents of the calorimeter was also knonm to at least one part per thousand. The volume varied over t-he course of a series of runs at one density, by up to 0Q32%. The data were based on the volume which the calorimeter. would take at the mean temperature and pressure of that particular series. The thermal and elastic expansion were taken into consideration to evaluate this mean volume- the correction never exceeded O5% of the original volume and the uncertainty involved in this correction should not be more than 002% of the original volumeo Considering the above factors, the maximum probable error in density might be as much as 0,35%o

VI. CALIBRATION OF HEAT CAPACITY OF THE CALORIMETER VI-1 General Discussion.(12} The former method of calibration as employed in de Nevers' (12) work was as follows. The calorimeter was loaded with a small amount of gas whose heat capacity had been known. The gross heat capacity was then measured according to the normal procedures described in Section IV-3. The heat capacity of the contents was evaluated as the known ideal-gas heat capacity plus a correction for non-zero density used in the calibration; the latter value was estimated by means of the established equation of state. Apparently, the calibration by this method depends on the accuracy of published C. data and also the second derivative of the PVT equations Besides these uncertainties, the method presents another difficulty, In this type of calorimeter, there is a limitation in the range of operating densities, While the upper limit is determined by the mechanical strength, the lower limit is mainly determined by the rate of convectional heat transfer, The low density results in the less effective forced convection and consequently, the less uniform temperature distribution during the heating period. This excessively uneven temperature distribution renders the reliability of the gross heat capacity data very doubtful. Thus, reasonably high density is required for accuracy of the gross heat capacity, but this increase of density, in turnn magnifies the uncertainty of correction term. Therefore, the ultimate result is by no means improved.

-622 VI-2 Calibration by Extrapolation A new method was devised to overcome these difficulties. The basic idea was to take the gross heat capacity at reasonable densities, and then to extrapolate isotherms to the zero mass on the gross heat capacity vs. mass plot. This extrapolation method is feasible only when linear or approximately linear extrapolation is possible at the range of low densities* If the isotherms are curved, the reliability of extrapolation is definitely insufficient for the critical requirements. Mathematically, Cro Ccalr. + mv* + m(Cv C*) (6-1) If the correction term (Cv Cv*) is negligible, Equation (6-1) reduces to Cgross = calr + mCv* (6-2) Equation (6-2), then, is a linear equation of mass mo The C cal can be obtained as Cgross at m = 0o Now the problem is to find one actual gas whose Cv differes very slightly from its Cv* in the projected operating range, In the P vs0 T plot, the greater curvature of isometrics is generally observed below the critical temperature, For temperatures far above the critical, the isometrics are almost straight or (d2P/dT2)- 00 Consequently, Cv - Cv* - 0 at this range. Similar conclusions can be reached if we examine several Cv vs. T plots. Regardless of the compounds under consideration, the general tendency of all isometrics is to converge as the temperature increases, This relation can also be predicted from the analysis of the equation of state. For instance, using the Martin-Hou equation, we have T Cv C = eT )2 e o - + + (6_3) ) 2(V-b)2 4(v+)

-635or T -kT C - C = g(V) T e c (6-4) The temperature function decreases roughly exponentially and Cv - C* becomes very small at temperatures far above the critical temperature. Thus we may conclude that the suitable gas for calibration is a gas whose critical temperature is well below the room temperature. Most of the so-called permanent gases probably suffice for this condition. However, the convenience of loading and weighing must also be taken into consideration, VI-3 Results of Calibration Tetrafluoromethane was chosen for the calibration purpose for two reasons; (1) Tetrafluoromethane was one of the common refrigerants under study, so the extensive gross heat capacity data can be used for both purposes. (2) Tetrafluoromethane satisfies the requirement discussed in the preceding section. For the convenience of actual plotting, we may plot CgrssmA vs. m instead of Cgross vs. m where A is an arbitrary constant, If A is equal or close to Cv*, we may have an approximately horizontal isotherm. It is obvious that this procedure is merely mathematical in nature and does not even slightly change physical significance* For tetrafluoromethane, statistical Cv* calculated by Chari(9) was used in place of constant A. The data are summarized in Table 6-1, and the results are presented in Figure 6-1, at 10~C intervals, The intercept of each isotherm is then cross plotted in Figure 6-3. A few isotherms for chlorodifluoromethane are shown in Figure 6-2 to show the consistency

TABLE 6-1 GROSS HEAT CAPACITY DATA OF TETRAFLUOROMETHANE USED IN TEE CALIBRATION OF HEAT CAPACITY OF THE CALORIMETER CCv*( statia) Cgross mC* Cgross mC C grosmC* Cgross mC C -mC C mC Cgross-mC* (sa gross gross v gross go ss v gross v gross v gross Mv rossv OC cal/gm~C cal/-C cal/~C cal/~C cal/C cal/~C cal/~C cal/C ca/ cal/ C c al/~ C c al/~C cal/C cal/ m = 160.70 gm. m = 257.44 gm. m = 334.72 gm. m = 410.69 gm. 30 0.1466 131.60 25.56 108.04 145.82 37.74 108.08 157.10 49.07 108.03 168.30 60.21 108.09 40 0.1498 133.00 24.07 108.93 147.49 38.56 108.93 159.07 50.14 108.93 170.48 61.52 108.96 50 0.1530 134.53 24.59 109.94 149.30 39.39 109.91 161.08 51.21 109.87 172.80 62.84 109.96 60 0.1560 135.92 25.07 110.85 151.09 40.16 110.93 103.07 52.22 110.85 175.00 64.07 110.93 70 0.1591 137.31 25.57 111.74 152.75 40.96 111.79 165.07 53.25 111.82 177.20 65.34 111.86 80 0.1621 138.71 26.05 112.66 154.50 41.73 112.77 167.06 54.26 112.80 179.35 66.57 112.78 90 0.1651 140.10 26.53 113.57 156.10 42.50 113.60 168.90 55.26 113.64 118.52 67.80 113.72 100 0.1680 141.46 27.00 114.46 157.70 43.25 114.45 170.73 56.23 114.50 183.61 69.00 114.61 110 0.1708 142.80 27.45 115.35 159.30 43.97 115.33 172.59 57.17 115.42 183.62 70.15 115.47 120 0.1736 144.06 27.90 116.16 160.90 44.69 116.21 174.35 58.11 116.24 187.60 71.30 116.30 130 0.1763 145.29 28.33 116.96 162.38 45.39 116.99 176.10 59.01 117.09 140 0.1789 146.40 28.75 117.65 163.80 46.06 117.74 177.70 59.88 117.82 150 0.1815 147.52 29.17 118.35 165.20 46.73 118.47 179.40 60.75 118.65 160 0.1840 148.63 29.57 119.06 166.59 47.37 119.22 180.93 61.59 119.34 170 0.1865 149.71 29.97 119.74 167.93 48.01 119.92 182.45 62.43 120.02 180 0.1888 150.80 30.34 120.46 169.25 48.60 120.65 183.97 63.20 120.77 190 0,1912 151.95 30.73 121.22 170.50 49.22 121.28 185.38 64.oo 121.38 200 0.1935 152.98 31.10 121.88 171.70 49.81 121.89 186.80 64.77 122.03

-65123 122 2000C_ ------ 190~C I121 -------- 180 ~C 120 119 150 OC 118 U11 3 _______- ___=-__ = 115 o E 115 100 OC o 1140 90 OC 113 sooc 00 __,-_ — -— 0 —-0 60 OC 500C 110 _____pl Mt- - 40 0C 109 - 0 50 100 150 200 250 300 350 400 450 MASS OF CF4, gi. 10 7 I07 ----------------------------- I 0100 5 0 5 0 5 0 5 MASS OF0^ Fiur 61 Clirtin fth Clrietr et apctybyte xta 4 0 ~ ~ ~~plto ~ehC sngTtalormtae

TABLE 6-2 GROSS HEAT CAPACITY DATA OF CHLORODIFLUORCMETHA1E USED IN THE CALIBRATION OF HEAT CAPACITY OF THE CALORIMETER T C* C.-C* C. - MC...* C MnC* C. ( statis.) Cgross mC Cgrossm C gross mC Cgross mCgos mv gross 0C cal/gmiC cal/~C cal/DC cal//C cal/~C cal/~C cal/ C cal/~C cal/ C cal/~C m = 166.96 gm. m = 254.10 gn. m = 346.08 gm. 90 0.1539 140.22 25.70 114.52 154.68 39.11 115.57 170.70 53.26 117.44 100 0.1564 141.37 26.11 115.26 155.83 39.74 116.09 171.80 54.13 117.67 110 0.1590 142.47 26.55 115.92 157.08 40.40 116.68 172.96 55.03 117.93 C\ 120 0.1614 143.63 26.95 116.68 158.30 41.01 117.29 174.21 55.86 118.35 130 0.1636 144.75 27.31 117.44 159.50 41.57 117.93 175.46 56.62 118.84 140 0.1659 145.88 27.70 118.18 160.84 42.16 118.68 176.75 57.41 119.34 150 0.1681 146.99 28.07 118.92 162.12 42.71 119.41 178.12 58.18 119.94 160 0.1704 148.10 28.45 119.65 163. -2 43.30 120.12 179.62 58.97 120.65 170 0.1726 149.15 28.82 120.33 164.71 43.86 120.85 181.11 59.73 121.38 180 0.1749 150.21 29.20 121.01 166.03 44.44 121.59 182.68 60.53 122.15 190 0.1771 151.30 29.57 121.73 167.27 45.00 122.27 184.19 61.29 122.90 200 0.1791 152.38 29.90 122.38 168.53 45.51 123.02

-67123 ------ 122 — 9121 180 ~C." " 170 ~C 120 119 oU 150 ~C -l A "118 1 — |40 OC -- -*^'. — --' 117 120 h.. 116 1_ 115 -- 100 ~C 0 114 900( 113 ~ 0 50 100 150 200 250 300 350 400 MASS OF CHCIF2, gm. Figure 6-2. Calibration of the Calorimeter Heat Capacity by the Extrapolation Method Using Chlorodifluoromethane.

123 s122X - X-S He' 121-~,, 120 - 0 119 117~- 0 - 116 _ _ _ ~12_ __ ___ _ ___ __ __ E __ __ __ __ __ A BY THE OLD METHOD 0 "FREON 12" I/ 000, 115 8114 11308 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 0 REON190 200 210 TEMPERATURE, -C / ~7 108~30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 TEMPERATURET,C Figure 6-3. Heat Capacity of the Calorimeter.

"-69of results. (For data see Table 6-2.) It should be noted that the critical temperature of chlorodifluoromethane is 96.01~C and the extrapolation is not very reliable for low temperatures, VI-4 Comparison with the Former Method Before the extensive data for tetrafluoromethane were collected, all tentative calculations of C were based on calibration by the former method as described in Section VI-l* Dichlorodifluoromethane was chosen for this purpose. Cv* was based on Masi's data(32) and the correction was based on the Martin-Hou equation of state. (34 The experimental data are summarized in Table 6-3 and the final results are plotted in Figure 6-33 On the average, the results are about 0.5% higher than those based on the extrapolation methods This would naturally lead to the speculation that all data published by de Nevers and Martin(l3) might be in considerable error. This was not the case, however, since Cv data were only collected over a considerably high density range in which the heat capacity of the contents was generally larger than that of the calorimeters Thus this 0.5% discrepancy can cause only less than 0.5% error in their final results. In the present study, however, the situation is entirely different, since the density range is quite low; in this range at the worst, the heat capacity of the contents is only abo!t 1/5 of the heat capacity of the calorimeter. This means that 1/2o discrepancy in the calibration may result in a 2.5% error in the final Cv data. Thus it was obvious that accuracy of calibration was a requisite to the success of the project. Besides the very good agreement between the experimental Cv* and the statistical Cv* for tetrafluoromethane, the

TABLE 6-3 CALIBRATION OF CALORIMETER HEAT CAPACITY BY THE OLD METHOD USING DIC HLOROD IF LUOROME THAE Run No4 Tmean C: C-C C ~ mC~ Cgross Ccalr R- nNoVgross cair. C. cal/gmroc cal/gmOC cal/gm~C cal/~C cal/ C cal/~C m = 55035 gnmi Dichlorodifluoromethane A25 57,37 0,1505,00544 015537 7456 116,40 109o04 All 43-<6,13516.00322 0,1548 7.42 117.52 110.10 A12 56,10 015344 400279 0,1572 7.55 118,81 111,26 A13 85320 01597.00206 041418 7,80 121534 1153 54 A14 97.07 0,1425.00176 0o1441 7*95 123,10 115,17 A15 111, 45 0.1449 00149 0 o1464 8,06 124,51 116,45 A16 124.55 0,1475,00128 0o1486 8,18 125,58 117.20 A17 157,50 0,1495.00110 0*1506 8,29 125,94 117.65 A18 156,26 0,1525 o00088 0O1552 8.43 127,52 119409 Al9 171,55 0,1544.00075 0,1551 8,54 129,44 120,90 A21 176,06 0,1550 oo0069 0,1557 8.57 129,39 120,82 A22 191,85 0,1570.00057 0,1576 8.67 130.49 121,82

-71dicilorodifluoromethane was again chosen for checking purposes. Experimental Cv was then compared with Masi's Cv* data(32) plus the correction (34) based on the Martin-Hou equation of state.(3 The result is plotted in Figure 7-1. The agreement is within 0.3%.

VII, EXPERIMENISAL RESULTS VII-1 Constant Volume Heat Capacity of Dichlorodifluoromethane No attempt was made to collect extensive Cv data for dichlorodifluoromethane since Masi(32) has published very reliable Cp* (or Cv*) data, A few experiments with this compounds however, were made to provide an appropriate check for the accuracy of Cv data taken on other compounds for which no experimental data are available- This also provided considerable confidence in the new method of calibrating the heat capacity of the calorimeter, as discussed in the preceding chapter. A series of runs were taken all at one medium density, 0,05695 gm/cc or 10,2%o of the critical density, The results are shown in Table 7-1, where the mean temperature, Tmean is an arithmetic mean of the initial and final temperatures of the temperature range over which heat was added. The gross heat capacity, Cgross5 is the mean gross heat capacity over the same temperature range, but is regarded as the true Cgross at the mean temperature, The heat capacity of the calorimeter, etc., designated as Ccalr is the calibrated value at the mean temperature4 The net heat capacity, Cnetg is the difference between Cgross and C alr Constant-volume heat capacity, Cv, is obtained by dividing Cnet by the total mass of contents, To minimize the uncertainty involved in the correction term,_-C*) based (n the 34)rtin-H (34 (C.C ) based on the Martin-Hou3 ) equation of state, and thus to have a better comparison of the experimental data with Masi's published -"72

-73TABLE 7-1 CONSTANT-VOLUME HEAT CAPACITY OF DICHLORODIFLUOROMETHANE (CF2C12) Run No. Tmean Cgross Ccalr Cnet G - Ccal/OC cal/~C cal/"C caCl/gm~C Dichlorodifluoromethane Loading No. 2 251.74 gmi 0.05695 gm/cc. E-1 122425 155 03 116.80 38,23 0,1519 E-2 133*70 155,60 117,18 38,42 0.1526 E-3 144,56 156.90 117.95 38.95 0.1547 E-4 156.62 1583.4 118.85 39.49 0*1569 E-5 162.13 158.62 119,22 39.40 0.1565 E-6 173.57 159.79 120*05 39.74 0.1579 E-7 184.90 160o79 120,80 39.99 0,1589

-74-.165 _ _ _ _ --- _.160 Tc: 112.04 0C - Pc 0.5581 gm/cc.155 - -.. =. = I I(+)- \x,.7 ~t o.150.. ---',.145 --- _.140 - 7 - - - - - - - -- - — (34) * (32) - BY MASI.130 _ 40 60 80 100 120 140 160 180 200 TEMPERATURE, OC Figure 7-1 Constant-Volume Heat Capacity of Dichlorodifluoromethane (CC12F2). methane (CCl~2).

-75data, the temperature was confined to a range above the critical temperature, 233.6~F. The experimental results are plotted on a Cv vs. T plane in Figure 7-1. A smooth curve has been drawn through seven data points. The worst scatter of the data points from this isometric is 0.67 percent, and most of the data points deviate from this curve by less than 0.2 percent. The Cv calculated from Masi's Cv* data plus the correction based on the Martin-Hou equation of state is also shown in Figure 7-1. Comparison of these two curves leads to the conclusion that agreement is within 0.3 percent. Allowing some possible error in the correction term (Cv-Cv*), say 10 percent, the discrepancy still would not exceed 1 percent since the maximum correction is only 4 percent of Cv. VII-2. Constant-Volume Heat Capacity of Tetrafluoromethane Due to the simple and symmetrical molecular structure of tetrafluoromethane, the spectroscopic data, or more specifically the assignment of the fundamental frequencies, are in close agreement among various authors. Therefore the statistically calculated values of C-v* should be more reliable than those of other compounds studied, whose fundamental frequencies were chosen rather arbitrarily. For this reason, comparison of experimental Cv* of this compound with the statistical Cv* was of great interest. The experimental results for tetrafluoromethane are shown in Table 7-2. They are presented in similar form as in Table 7-1, except

-76TABLE 7-2 CONSTANT-VOLUME HEAT CAPACITY OF TETRAFLUOROMETHANE (CF4) T Cgross Ccalr. Cnet Cv 0C cal/ C cal/ C cal/~C cal / C Tetrafluoromethane Loading No. 1 160.70 gmi. 0.03638 gm/cc. 30 131.60 108.00 25.60 0.1469 40 133.00 108.95 24.05 0.1497 50 134.53 109.92 24.61 0.1531 60 135.92 110.90 25.02 0.1557 70 137.31 111.86 25.45 0.1584 80 138.71 112.75 25.96 O.1615 90 140.10 113.63 26.47 0.1647 100 141.,6 114.46 27.00 0.1680 110 142.80 115.30 27.50 0.1711 120 144.06 116.11 27.95 0.1739 130 145.29 116.90 28.39 0.1767 140 146.40 117.64 28.76 0.1790 150 147.52 118.38 29.14 0.1813 160 1 +8.63 119.10 29.53 0.1838 170 149.71 119.80 29.91 0.1861 180 150.80 120.47 30.33 0.1887 190 151.81 121.13 50.68 0.1909 200 152.80 121.78 31.02 0.1932

-77TABLE 7-2 (cont'd) CONSTANT-VOLUME HEAT CAPACITY OF TETRAFLUOROMETHANE (CF4) T Cgross Ccalr. Cnet Cv ~C cal/ C cal/oC cal/ C cal/gmsC Tetrafluoromethane Loading No. 2 257.44 gmi. 0.05822 gm/cc. 30 145.82 108.o0 37.82 0.1469 40 147.49 108.95 38.54 0.1497 50 1493.0 109.92 39.38 0.1530 60 151.09 110.90 40.19 0.1561 70 152.75 111.86 40.89 0.1588 80 154.50 112.75 41.75 0.1622 90 156.10 113.65 42.47 0.1650 100 157.70 114.46 43.24 0.1680 110 159.30 115.30 44.00 0.1709 120 160.90 116.11 44.79 0.1740 130 162.38 116.90 45.48 0.1767 140 163.80 117.64 46.16 0.1795 150 165.20 118.58 46.82 0.1819 160 166.59 119.10 47.49 0.1845 170 167.93 119.80 48.13 0.1870 180 169.25 120.47 48.78 0.1895 190 170.50 121.13 49.37 0.1918 200 171.70 121.78 49.92 0.1939 Tetrafluoromethane Loading No. 3 334.7.72 gm._ 0.07563 gm/cc. 30 157.10 108.00 49.10 0.1467 40 159.07 108.95 50.12 0.1497 50 161.08 109.92 51.16 0.1528 60 163.07 110.90 52,17 0.1559 70 165.07 111.86 53.21 0.1590 80 167.06 112.75 543.1 0.1623 90 168.90 113.63 55.27 0.1651 100 170,73 114.46 56.27 0.1681 110 172.59 115.5 30 57.29 0.1712 120 174.35 116.11 58.24 0.1740 130 176.10 116.90 59.20 0.1769 140 177.70 117.64 60.06 0.1794

-78TAB LE 7-2 (cont'd) CONSTANT-VOLTTME HEAT CAPACITY OF TETRAFLUOROMETHANE (CF4) T I _ gross Ccalr. Cnet Cv "C c.al./C cal/ C cal/lC cal/gimC Tetrafluoromethane Loading No. 3 (Cont'd) —... 334.72 gm. 0007563 gm/cc.o 150 1.79.40 11.8.58 61.o 02 0.1825 160 1.80.93 ii. 10 61.o83 0 o.847 170 182.45 11.9.80 62.65. 1871 180 1.835 97 120.4'7 6350 0.1.897 1.90 185o 38 1.2 1.3 64.25 0 1920 200 186.80 121. 78 65.02 0o1.942 Tetrafluoromethane Loading No. 4 410.69 gm. 0.09290 gm/cc._ 50 3 8.50 16 08 00 60.o30 0.1468 40 170.48 108.95 61o.53 0,1498 50 1.72,80 1.09. 92 6288 0.1531 60 1.75.00 110.90 64.10 0.1561 70 177.20 11.1.86 65.34 0.1591 80 179.35 11.2 75 66.60 0.1622 90 181.52 113.63 6'7.89 0.1653 100 183.61 114 46 69.15 o.1684 110 185.62 11.550 70.52 0.1712 120 187.60 1.16 11. 71.,49 0.1741

-79that Cgr is read from the smoothed gross heat-capacity curve (see gro s s Appendix D) Figures D-1 and D-2) and Cv is calculated at every 10~C interval, Four densities were used ranging from 0.03638 gm/cc or 5.8% of the critical density to 0.09290 gm/cc or 14.9% of the critical density. The temperature range was from 30~C to 200~C for three low densities, but only up to 120~C for the highest density, to keep the pressure within 500 psi. The results are plotted in Figure 7-2. The fluctuations of the gross heat capacity (see Appendix D) were generally less than 0.2% except in three runs at the lowest density in which the maximum fluctuation was 0.35%. Regardless of densities, all Cv data fluctuate along the statistically calculated Cv* line by Chari.(9) The value of the correction term Cv - Cv is practically negligible. The solid line in Figure 7-2 shows a lower limit of confidence for Cv and may be regarded as the experimental constant-volume heat capacity at the zero pressure, This observed line deviates from Chari's statistical calculation by only 0*2%. The dashed line in Figure 7-2 is based on Chari's correlation: Cv = 3.00559282 x 10-2 + 2237043352 x 10 4T - 2.85660077 x 10 8T2 - 2.95338806 x 1o-11T3 (7-1) where T is in ~R and Cv* is in Btu/lbOR,

0.195 0'190 P = 0.6257 gm/cc T = - 45.66 o.. 0o.85 MW - 88.010 ~~~~~~~~~0.1854 0.180 0.175 0.170 - J/ 0.165 L t __t _-_ cv (experimental) ~C (9) __,_ __ 0Cv (statistical) by CHARI 0.- 1. __ _ C*v (statistical) by GELLES and PITZE17 0.160 0 0.03638 gm /cc L/I/~ ~~/ - ~~~A 0.05822 0.155 - / v 0.07563,, o 0.09290 Note: All data points were calculated from 0.150 Q145 40 60 80 100 120 140 160 180 200 TEMPERATURE, ~C Figure 7-2. Constant-Volume Heat Capacity of Tetrafluoromethane (CFi).

The statistical Cv* by Gelles and Pitzer(17) is 0.4^0.6% less than the experiment values. This is also shown in Figure 7-2 for comparison. VII-3. Constant-Volume Heat Capacity of Chlorodifluoromethane The experimental results for chlorodifluoromethane are shown in Table 7-3. They are presented in the same form as in Tables 7-1 and 7-2. Data were taken for five densities, ranging from 0.0378 gm/cc up to 0.1239 gm/cc. These corresponded to 6.85 percent to 22.4% of critical density. The temperature range was from the saturation temperature (approximate) to 200~C for two low densities, and up to 190~C, 150~C and 1100C, respectively, for three high densities to limit the pressure within 525 psi. For three low densities, as in the case of tetrafluoromethane Cgross was read from the smoothed gross heat-capacity curves (see Appendix D, Figures D-3 and D-4.) For two high densities, Cv was calculated for each run of experiments. The results are also plotted in Figure 7-3. A smooth curve has been drawn through data points for each density; the maximum deviation is about 0.8 percent, and, except for two runs, all are less than 0.3 percent. For three low densities, the deviation in the final plot is negligible because data have been smoothed at the gross heat capacity level. Fluctuations of Cgross from the smoothed gross heat capacity curve are less than 0.3 percent except two runs which are up to 0.3.Yo

-82TABLE 7-3 CONSTANT-VOLUME HEAT CAPACITY OF CHLORODIFLUOROMETHANE (CHClF2) Run No. T Cgross qalr. Cnet C gros.s 9. caiC. c/ "C cal/Ccal/ ca C cal/~C cal/gni~C Chlorodifluoromethane Loading No. 1 166.96 gm.. 0.0378 gm/cc. 50 135558 109.92 25.66 0.1537 60 136.70 110.90 25.80 0.1545 70 157.85 111.86 25.99 0.1557 80 139.00 112.75 26.25 0.1572 90 140.15 113.63 26.52 0.1588 100 141.30 114.46 26.84 0.i608 110 142.47 115.30 27;17 0.i627 120 143.63 116.11 27.52 0.1648 130 144.75 116.90 27.85 o. 668 140 145.88 117.64 28.24 0.1691 150 146.99 118.38 28.61 0.1714 160 148.10 119,10 29.00 0.1737 170 149.15 119.80 29.35 0.1758 180 150.21 120.47 29.74 0.1781 190 151.30 121,13 30.17 0.1807 200 152.58 121.78 30.60 0.1855 Chlorodifluoromethanp Loading No. 2 254.10 gm. 0;0575 gm/cc,_ 50 149.70 109.92 39.78 0.1566 60 150.90 110.90 40.00 0.1574 70 152.22 111.86 40.56 0.1588 80 153,40 112.75 40.65 0.1600 90 154.62 113.63 40.99 0.1613 100 155 85 114.46 41.57 0.1628 110 15708 1155,30 41.78 0.1644 120 158.30 116.11 42.19 0.1660 150 159.59 116.90 42.69 0.1680 140 160.84 117.64 43.20 0.1700 150 162.12 118.38 43.74 0.1721 160 163.42 119.10 44.32 0.1744 170 164.71 119.80 44.91 0.1767 180 166.03 120.47 45.56 0.1793 190 167.27 121,13 46.14 0.1816 200 168.55 121.78 46.75 0.1840

835TABLE 7-3 (c.ont'd) CONSTANT-VOLUME HEAT CAPACITY OF CHLORODIFLUOROMETHANE (CHClF2) Run No. T Cgross Ccalr. Cnet C ~C Gcal/~c cal/'C cal/oC calbn'C Chlorodifluoromethane Loading No. 3 346.08 gm. 0,0782 gm/cc,. 60 167.85 110.90 56.95 0.1646 70 168.70 111.86 56.84 0.1642 80 169.67 112.75 56.92 0.1645 90 170.70 113.60 57.07 0.1649 100 171.80 114.46 57.34 0.1657 110 172.96 115,30 57.66 0.1666 120 174.26 116.11 58.15 0.1680 130 175.60 116.90 58.70 o.1696 140 176.95 117.64 593.1 0.1714 150 178.35 118.38 59.97 0.1733 160 179.80 119.10 60.70 0.1754 170 181.22 119.80 61.42 0.1775 180 182.68 120.47 62.21 0.1798 190 184.19 121.13 63.06 0.1822 Chlorodifluoromethane Loading No. 4 447.08 gm. 0. 1011 gmn/ca. A24 73.-32 188.20 112.15 76.05 0.1701 A25 85.68 188.53 113.25 75.28 0.1684 A26 95.91 189.45 114.14 75.31 0.1684 A27 113.62 191.50 115.58 75.92 0.1698 A28 124.58 193.01 116.48 76.53 0.1712 A29 136.57 195.18 117.40 77.78 0.1740 A30 150.09 197-32 118.45 78.87 0.1764 Chlorodifluoromethane Loading No. 5 548.22 gm.. 0.1239 gm/cc. A31 75.63 208.33 112.36 95.97 0.1751 A32 87.85 209.08 113.44 95.64 0.1745 A33 100.19 208.72 114.46 94.26 0.1719 A34 11019 210.78 115.29 95.49 0.1742 A35 84.56 208.32 113.15 95.17 0.1736

It is estimated that a single data point might deviate by as much as 2 percent if the gross heat capacity were not smoothed. Figure 7-4 is a cross plot of Figure 7-3 into the Cv vs. density plane. The isotherms in Figure 7-4 are constructed by plotting the values of smooth isometrics in Figure 7-3, where those isometrics intersect the lines of constant temperature4 None of the points in Figure 7-4 scatters from the smoothed curve by more than 0.3 perGent. This indicates good internal consistency of the experimental data. Each isotherm is extrapolated to zero density to obtain ideal gas heat capacity, Cv*, as a function of temperature. The values obtained by such extrapolation are then cross-plotted as Cv* Vs. temperature on Figure 7-3. The statistical Cv* calculated by Martin et al.26) is also shown in Figure 7-3 for comparison. The experimental values are higher than the calculated values by 0.8-percent on average. The statistical Cv* calculated by Weissman, Meister, and Cleveland(45) is almost the same as that calculated by Gelles and Pitzer.(l7) This is also shown in Figure 7-3 for comparison. Their values are lower than the experimental values by as much as 3.9 pereent at 200~C and 4.5 percent at 80~C. Figure 7-5 is analogous to Figure 7-4, except that each isotherm is translated downward by the amount of Cv* corresponding to each temperature so that all isotherms pass the origin, yielding Cv-Cv* vs. density plot with temperature as a parameter. Figure 7-6 is analogous

-85-.185 P = 0.5247 gm/cc c =96.010C,eo.180 ==== I MW= 86.476.175 -.170 u_7._=_S__ __ _'sd __ __IL._ _ Ao /X/ k -.170.=65 = g r caac 30 50 70 90 1 1 0.1011 170 190 _ _ C _z 0.0782,, -,,F TEM- PERATU 0.RE 055,,, ~150 / _ _.155 4A 0.1011 - -— 730 50 570 90 1 0 13 0 150 75t 190 X 0.0000 (by TEMPERATURE Cion Figure 7-3. Constant-Volume Heat Capacity of Chlorodifluoromethane (CHC1F2).

.185 -.180 170 \ — 180 oc ~~ I. 160 oc 130C oc —0 -0 00 —— Tc-96.010C CP 00.5247gm/cc g -lIO-c ^,.'-" -- ^.'"- /P —- - - - -.160 -J - ^ - 0 —- - fluoromethane ( —) (This is a cross,6155 0 __ / __plot of Figure 7-).150 600c —---.145 --- -- --- 0 —02 026.08.10.12.14

-87-.030.025 Tc= 96.01 ~C PC 0.5247 gm./cc. o.020, eooc, o7.015 U 9 ___I 90C9_ 0,;__ ____ ____ ____ ____ ___ / ___ / / Y1'0 ~^.010 0 02.04.06.08.10.12 DENSITY, gm/c Figure 7-5. Cv-Cv* of Chlorodifluoromethane (CHC1F2) (This is a modified cross plot of Figure 7-3.)

-88-.030 -- --------.025 \ \ ----------- — ___ --— T —96.01 OC - \\ - - - - -'- - - PC =0.5247 gm/cc..020- - --.015 -- -- -------.010 - \ ~' "iX, I. l,_ P <o.ii239 m/c __ _ i I s l8 I I Ipo.1o I gm/cc.005 -, — -.^^,- ----- c ~~~~ —----- ^^^i"" —^^^>^:^^:^o 0.057 gmQn c. 0.0 3 gm TEMPERATURE, ~C Figure 7-6. Cv-Cv* of Chlorodifluoromethane (CHClF2). (This is a modified plot of Figure 7-3)

-89to Figure 7-3 but the isometrics are translated downward as in Figure 7-5, yielding a Cv-Cv* vs. temperature plot, These modified plots are very convenient for checking an equation of state since the PVT data influence only the correction term (Cv-Cv*)and not the absolute value of CvY according to the following relation: CvCvy*= - T V (1-3) v d T 2 VII-4. Constant-Volume Heat Capacity of Dichlorotetrafluoroethane The experimental heat-capacity results for dichlorotetrafluoroethane are shown in Table 7-4. They are presented in the same way as in the case of chlorodifluoromethane. Data were collected for four densities, ranging from 0,0375 gm/cc up to 0,1357 gm/cc, These densities corresponded to 6*45 percent up to 23*4 pereent of the critical density. For all densities, the temperature range was from the saturation temperature to 200~C. The estimated pressure was less than 500 psi for all runs, For low densities, the final Cv data were calculated based on the smoothed gross heat-capacity curves as before (see Appendix D. Figure D-5). For two high densities, the final Cv data were calculated directly from the measured gross heat capacity. These results are plotted in Figure 7-7 on a Cv vs, temperature plane. The gross heat capacity never deviated from a smoothed curve by more than 0*55 percent and most of the data scattered by less than 0*4 percent. The maximum scatter of the final Cv would have been as high as 2,5 percent if gross heat-capacity data were not smoothed, For two high densities, the maximum scatter of the final Cv data is 0.55 percent from the smoothed curve, and most of points deviate from the smoothed curve by less than 0.3%,

O-90 TABLE 7-4 OONSITA.T.-VOLrME HEEAT CAPACITY OF DICHLOROTETRAFLUOROETHANE (GCI~-CClFf) (CCo — coF2) RIm sNo, T Cgross caltr, Cnet 0~ _ "Ccal/~Cc cal/ cal/~C cal/g~C Loading No, 1. 165,67 gmo. 0,0375 gin/cc, 80 1412 - 112,75 28o37 0,1712 90 142,22 1135,63 28,59 0.1726 100 1433553 114,46 28,87 0,1743 110 144,43 115.50 29,13 0,1758 120 145 57 116,11 29 46 0,1778 130 146,70 116,90 29.80 0,1799 140o i 47,78 117,64 30,14 0.1819 150 148, 80 118,58 30,42 0o1836 160 149,83 11901 30,753 0,1855 170 150o,88 119480 31408 0o1876 180 151,90 120, 47 31,45 0,1877 190 152,95 12,143 3182 041921 200 153595 121,78 32o17 0,1942 Loading Noj, 2, 291,05 gir,, 0,0658 gm/cc, 90 164,50 113653 50.87 0,1748 100 165,77 114,46 51o31 0,1763 110 167,02 115,30 51.72 0,1777 120 168,51 11611 52,20 0,1793 130 169,58 116,90 52,68 0,1810 140 170,88 117,64 53,24 0,1829 150 172`20 118,58 53582 0,1849 160 175347 119,10 54.,7 0,1868 170 174,72 119.80 54,92 0,1887 180 176,00 120,47 55.53 0,1908 190 177,30 121,13 56,17 0,1930 200 178,66 121,78 56,82 0,1952

-91TABLE: 7-4' (.cont'd) CONSTANT-VOLUME HEAT CAPACITY OF DICHLOROTETRAFLUOROETHANE (CclF2ccF 2) Run No, T Cgross Ccalr. net C 0C cal/C ~cal/oC cal/~C cal/gm~C Loading No. 35 440,56 gm, 0*0997 gm/cc, B56 108.57 195*33 115*17 80,16 0.1819 B57 11938 197*01 116.05 80.96 0.1838 B58 130.71 197-85 116.95 80.90 0.1836 B59 155*87 201,77 118,78 82.99 0,1884 B60 165.86 202.60 119.50 83.10 0.1886 B61 182441 204,93 120*61 84.32 0.1914 B62 193,64 207353 121*38 85,95 0,1951 B63 145.81 199,88 118,10 81.78 0.1856 B64 174,65 204.16 120.08 84,08 0.1908 Loading No. 4, 600.17 gm, 0.1357 gm/cc. B27 115,29 228*16 115,73 112,45 0,1873 B28 124.87 229,26 116.50 112.76 0.1879 B29 134,84 230,18 117.26 112.92 0,1881 B30 145.77 230*92 118.09 112*83 0,1880 B31 155.98 232,01 118.80 113521 0.1886 B32 166.10 233,65 119*51 114*14 0.1902 B33 177,41 236,22 120.27 115 *95 0*1932 B34 186,34 237*99 120,87 117*12 0*1951 B35 195*77 239*77 121*52 118,25 0.1970

.92Figure 7T8 is a cross plot of Figure 7-7, and is similar to Figure 7.4o The maximum scatter of the cross-plotted data on the Cv vs. density plane is 0,2 percent, Each isotherm is extrapolated to zero density to deetermine the ideal gas heat capacity which is then crossplotted on Figure 7-7, The statistical C~* calcul.ted by Martin(25) is also shown in Figure 7T7 for comparison. The dashed line in Figure 7-7 is based on his equation: C = 0o0175 + 3.49 x 10"4 T - 1,67 x 107 T2 (7-2) where T is in'R, Cv* in Btu/lboR, The values of Cv* calculated from this equation are generally higher than the experimental values in a range of from 100 to 200~Co The maximum difference is about 3.4 percent at 100'C., The statistical Cv* of isomeric dichlorotetrafluoroethane (CF3CFC12) was calculated by Smith, Alpert, Saunders, Brown, and Moran.(42) Their value of C* for CF3CFC12 is 0.1702 cal/gm~C at 400DK, which compares with an experimental value of 0o1767 for CCLF2CCIF2 at 400-K. Figure 7-9 is analogous to Figure 7-8, showing Cv-Cv* as a function of density with temperature as a parameter, It is to be noted that the isotherms of temperature higher than the critical temperature are practically straight, and linear extrapolation has been made insofar as possible6 In Figures 7-8 and 7-9, isotherms have been drawn at 10~C intervals from 110~C to 200~C, Figure 7-10 is analogous to Figure 7-7, showing Cv-Cv* as a function of temperature with density as a parameter,

-93-.200 -- o 0.5818 gm/cc T = 145.7 ~C.195 _ MW = 170.936.190.185 0 E ___ __ _ ___ o =, I 1 1 1 = = Y/.180 u.175 W 4 S W =~~~ — Cv (statisticol) by i U_ __ __ __ __ __ __ _ ^Martin (25) — Q / 0.1357 gm' /A.170 t 50 09957 g /c -.170 - I0.0658 gm/cc-. _ o.oe137S gm/cc --- E- - 0.0375 gm/cN —! = =___=_ = = = = / == X 0.0000 gm/cc. 165 (extrapoloted) Note: These points were calculated from the smoothed gross heat capocity data..160 l 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 TEMPERATURE, ~C Figure 7-7. Constant-Volume Heat Capacity of Dichlorotetrafluoroethane (CC 0F2 CC1F2)

-94-.200 - -- 195 _ 19.10 E W W M____ ____ P 01858 g. /cc 17 0 OC —---.180 1230 OC.175 ~'.. TC = 14 5.7 ~C 1100C Pc = o.es58 gm./cc.170 W.00.02.04.06.08.10.12.14 DENSITY, gm./cc. Figure 7-8. Constant-Volume Heat Capacity of Dichlorotetrafluoroethane (CClF2CClF2) (This is a cross plot of Figure 7-7.)

-95-.016.014 Tc = 145.7 O~C.012 _ _ | -Pc 0.5818 gm/cc oo,/~.012 gmcc — 0 12 -',..006.004.002 0.oo- — ~ 0.02.04.06.08.10.12.14 DENSITY, gm./cc. Figure 7-9. Cv-Cv* of Dichlorotetrafluoroethane (CClF2CC1F2) (This is a modified cross plot of Figure 7-7)

-96-.016,014.014 --- --- ---- --- ---- -- - Tc = 145.7 OC Pc -0.5818 gm./cc.-.012.010 U 0.008 U.006 0.1357 gm/cc.004 - - \ -- 1.!' |0.0997 gm/cc 0.0658 gm/cc.002'^ <> -- ^^^m o0.0375 gm/cc 100 120 140 160 180 200 220 TEMPERATURE, ~C Figure 7-10. Cv-Cv* of. Dichlorotetrafluoroethane. (CC1F2CC1F2) (This is a modified plot of Figure 7-7)

-97VII-5 Constant-Volume Heat Capacity of Chloropentafluoroethane The experimental heat-capacity results for chloropentafluoroethane are shown in Table 7-5. They are presented in the same form as the results for the other compounds studied in this research. Data were collected for five densities ranging from 0.0427 gm/cc up to 0.2219 gm/cc. These corresponded to 7.16% to 37.24 of the critical density. The temperature range for three low densities was from the saturation temperature up to 200~C, and for two high densities it was from the saturation temperature up to temperatures at which the calculated pressure of the gas was between 500 and 525 psi. For threeslow densities, Cv was calculated from the smoothed gross heat-capacity data (see Appendix D, Figures D-6 and D-7). For two high densities, Cv was calculated directly from the observed gross heat-capacity data. The results are plotted in Figure 7-11 on the Cv vs. temperature plane with density as a parameter. The maximum scatter of the gross heatcapacity data is 0.3%, but most of the data deviate by less than 0.2%. If the Cv were calculated directly from the individual experimental gross heat capacity without smoothing, the maximum deviation in the final Cv would have been 1.3%. As a result of smoothing Cgross, the scatter of Cv in Figure 7-11 is practically negligible for three low densities. For two high densities, however, the maximum scatter of Cv is 0.19%. Figure 7-12 is a cross plot of Figure 7-11, which is similar to Figure 7-4. The maximum scatter of the cross-plotted data is 0.2%. Each isotherm has been extrapolated to zero density to determine the ideal-gas heat capacity Cv*. The Cv* thus determined is then crossplotted as Cv* vs. temperature in Figure 7-11. The statistical Cv* of

-98TABLE 7-5 CONSTAhTO-Y0L)OUE SEAT CQAPACIET OF CMLOROPlENITAFLUOROETHAINE (CClF3-CF3) Run No- _ T; Cgross Ccalr., net CV 0c cal~go cal/o _ cal/ C cal/gm C Loadin.g No, 1, 188,86 gmn 0,0427 gm/cc, 50 141,88 109,92 31.96 0o1692 60 143 31 110,90 523,41 001716 70 144,78 171,86 32,92 0,1743 80 146,21 112,75 33446 0.1772 90 147w60 113563 33597 0*1799 100 149<,01 114,.46 3455 0,1829 l10 150350 115*50 35500 0,1853 120 151,58 116,.11 35.47 0,1878 130 152.85 11690 355 95 0,1904 140 15 4 704 1764 36., 40 0.1927 150 155 ~25 118,38 36,87 0.1952 160 156 41 119,10 37*31 0,1976 170 157.58 119,80 37*78 02000 180 158,70 120,47 38,23 0,2024 190 159,80 121,13 38,67 0,2048 200 16o,.88 121,78 39o10 0,2070 Loading No. 2 3935 ll gmn 0,0889 gm/cc, 50 177e55 109,92 67*63 0.1720 60 179.42 llo,90 68,52 0O1743 70 18125 111o86 69o39 0*1765 80 183,15 112,75 70,40 0.1791 90 185oo00 113,63 713.7 0,1816 100 186,81 114.46 7235 0,-1840 110 188460 115 3Q 73 -3 0 o,1865 120 1903,7 116,11 74,26 0,1889 130 192,04 116,90 75,14 0.1911 140 193,70 117o64'76.06 0.1935 150 195*45 118,58 77407 0,1961 16o 197,10 119,10 78,00 0.1984 170 198',71 119*80 78.91 0,2007 180 200,32 120,47 79,85 0,2031 190 202,00 121,-13 80,87 0,2057

-99TABLE 7-5 (Cont'd) CONSTANT-VOLUME HEAT CAPACITY OF CHLOROPENTAFLUOROETHANE (CCLF3-CF3) ~~~~~~~~~~~~~~~~~~~~~Run Noo,~~~~~ T C... Run No, T Cgross calr4 Cnet Cv _________ ~C _ call /~_C cal/~C cal/~C cal/gm"C Loading No, 35 592.52 gnm 0.1340 gm/cc. 60 217889 110,90 106*90 0.1804 70 219*50 111.86 107.64 0.1817 80 221*25 112.75 108,50 0,1831 90 223*05 113.63 109.42 0,1847 100 224.85 114*46 110.39 0.1863 110 226.82 115.50 111,52 0.1882 120 228.80 116.11 112. 69 0.1902 130 230.80 116,90 11390 0.1922 140 232.85 117.64 115.21 0.1944 150 235500 118,38 116,62 0.1968 160 237,12 119,10 118,02 041992 170 239*30 119.80 119.50 0,2017 180 241.52 120,47 121#05 0.2043 190 243 55 121.13 122.42 0.2066 Loading No. 4, 791.79 gm, 0*1791 gm/cc. C14 65,26 259.10 11140 147.70 0*1865 C15 75*65 260,00 112*36 147.64 o01865 C16 86.30 26159 113,31 148,28 0.1873 C17 96,91 263 26 114,21 149,05 0.,1883 C18 108,01 266,11 115.12 150,99 0.1907 C19 117.46 267*90 115.89 152.01 0,1920 C20 129.01 270.04 116*83 153521 0,1935 021 136.90 271.67 117,42 154.25 0.1948 C22 145.33 274,24 118,06 156,18 0.1973 C23 154,27 276*56 118,69 157,87 0.1994 Loading No. 5, 981,10 gmi 0.2219 gm/cc. C24 71.72 300.93 112.00 188,93 0.1926 C25 82.27 300.25 112,96 187.29 0,1909 C26 91.31 301,24 115*73 187,51 0,1911 C27 100.28 302,66 14.)48 188,18 0,1918 C28 109.25 303 90 115,22 188.68 0*1923 C29 121.50 307.41 115.97 191.44 0.1951

-100chloropentafluoroethane was calculated by Martin, Long, and Service,(1) who correlated their results in the following equation. Cv = 0.034157 + 3.17723 x 104T - 1.37593 x 10'7T2 (7-3) where T is in ~R and Cv* is in Btu/lb-~F. This equation is plotted in Figure 7-11 for comparison. The statistical Cv* agrees reasonably well at high temperatures but predict high by as much as 3.2% at 700C, The statistical Cv* calculated by Smith et al, (42) is also shown in Figure 7-11 for comparison. Their values are lower than the experimental values by 1.8% at 400DK and by 2.4% at 4730K, Martin et al.(30) also calculated the Cv* from the measured value of the velocity of sound, which gave 24,40 Btu/lb mole-~F at 79.8~F, This compares with the observed values of 24,62 Btu/lb mole-~F at 79.8O~F However, the velocity of sound measurement was not considered very precise by Martin et al,, and error in the calculated heat capacity could be as great as 6%^ Based on the experimental Cv*, Figure 7-13 is constructed analogously to Figure 7-12, but showing Cv-Cv* as a function of density with temperature as a parameter. On Figures 7-12 and 7-13, isotherms are drawn at 10~C intervals from 60 up to 200~C. Figure 7-14 is a modified plot o Fige - an also across plot of Figure ad a 7-13, showing C -C * as a function of temperature with density as a parameter.

-101-.210 -—.~~205 0~Tc = 79.95 C' Pc =0.5960 gm /cc, ~~__. 2 o0 0 F _ _ _ 1 — — MW: 15 4.4 7 7 _ _.195 0.190 - -' 75 ____ __ __ __, 0.0.___1 __.185!85> 1 w~'%~ - / — - -- -,' \ -- ~ v-cY (stat.) by Martin et ol (31).1801 //' I s l A 0.2219 gm/cc 175i ~ ~o 0.1791 gm /C 0 50.1340 gm/cc'.175 -- - - -- - -- 0.0889_ o.oeee gm/cc, Note // // / 0.0427 gm/cc. X 0.0000 gm/cc (extrapolated) ~170 Note: These points were calculated from the smoothed gross het copacity dto..165 - [ 30 50 70 90 110 130 150 170 190 TEMPERATURE, ~C Figure 7-LU. Constant-Volume Heat Capacity of Chhloropentrafluoroethane (CCIF2CF3)

-102-.210 2000C ~0... -__ ____ 160 CP:.....60 m.19205 -1950 0 140 OC...300C.. _...o -.200 1- -70 --- 0..OC.. 0 29-..'".'A' I - o oj._ -e- " "D-ENSI Y, gm/ L.cc O —Ti' is. aoo-1.) -10ooc _.-~'~ - -~.. —.......Y. gm/cc 00Centafluoroethane (CClFCF) This is a cross plot of Figure 7-11. I 0 PC 0.5960 gm /cc Figure 7-~....tn-Vln et aaiy fCl,75~~~~~~~9enafuoo hn CL2~~ si acospo fFgr 1.

-103-.025 -.-.020 00 Tc= 79.95 oC -600 =:0.5960 gm /cc -- E'~~~~~~~~~~~~~~________Z70.015 C800 o.010 010 //fF.005/ I 0.04.08.12.14.16.18 DENSITY, gm /cc Figure 7-13. Cv-Cv* of Chloropentafluoroethane (CC1F2CF3) (This is a modified cross plot of Figure 7-11)

.025 --.020 Tc =79.95C ___ __ Pc = 0.5960 gm/cc _.0105 0.1791, gm /cc.005 s0.1340 gm/cc 0.0889 gm/cc.005 ^ — -- --- ^q ^ ^ 0*791 0.0427 gm 7cc _,,t..3 gm1 Z 60 80 100 120 140 160 180 60 80 TEMPERATURE00 120 140 160 180 TEMPERATURE, ~C Figure 7-14. Cv-Cv* of Chloropentafluoroethane (CC1F2CF3) (This is a modified plot of Figure 7-11.)

VIII* DISCUSSIONS OF EXPERIMENTAL RESULTS VIII-1 Characteristics of C, as a Function of Temperature and Density In general, Cv increases with increasing density and also increases with increasing temperature at high temperatures, In the vicinity of or below the critical temperature, however, Cv may increase with decreasing temperature if the density is considerably high. Figures 7-3 77 and 7-11 all indicate this tendency, On the other hand, the values of Cv-C* for any isometric always decrease with increasing temperature and approach zero as the temperature increases, Judging from the case of tetrafluoromethane, it seems reasonable to assume that C -Cv is practically negligible at the reduced temperatures T/Tc = 1*3 or higher, This fact has been utilized in the calibration of heat capacity of the calorimeter (see Section VI-2). Mathematically, it means'2 2 Cv, * - - v o or K d (8-1) V (27) Martin and Hou7) also pointed out (based on the state data) /d2P( (TR) = 0 for high temperatures, (18) In other words, the isometrics on the P vs, T plot are practically straight at those temperatures where T/Tc is 1.3 or higher. On the Cv vs. density plots, the experimental Cv data show that, within the density range studied (less than 37% of the critical density), all low-temperature isotherms curve upward slightly but increase so rapidly that they intersect with the high-temperature isotherms at considerably low density, de Nevers(L2) has advanced a tentative conclusion -105

-io6on the tendency of this upward curvature of the isotherms at a lowdensity range. The present research has fully confirmed his conclusion. The upward curvature reduces its intensity gradually with increasing temperature and becomes practically zero at the low density range for isotherms more than 50~C removed from the critical temperature* In the case of dichlorotetrafluoroethane, the isotherm is practically straight only 10C removed from the critical temperature, Thus it is apparent that temperature not only influences the relative position of isotherms but also affects their characteristics. In the Cv-Cv* vs. temperature plots, all isometrics are monotonically decreasing functions of temperature with different upward curvatures. The maximum curvature does not occur at the same temperature for different densities. From the above discussion, it is not difficult to see that, in a pure mathematical sense, Cv-Cv cannot be correlated in the following form: Cv - C = f(T)g(p) (8-2) since Equation (8-2) indicates that the general shape of isotherms is solely determined by density alone, while that of the isometrics is determined by temperature alone. The more complicated form.is probably required to express the experimental data correctly. Nevertheless, a form as represented by Equation (8-2) is usually preferred for its simplicity. While the empirical correlation of the experimental C. data may be used in the calculation of thermodynamic properties, there is another interesting application in connection with the development of an equation of state, based on the exact thermodynamic relation:

-107(dC) 2 (dCv =Tf (8-3) kdV h \dp A.dT2A Supposing C -Cv* is correlated in the certain form with 1 or 2% maximum error, the differentiation once with respect to density (or volume) and subsequent integration twice with respect to temperature would probably shed light on a better form of an equation of state, Although the development of the PVT equation is beyond the scope of the present project, the mathematical procedures are illustrated using a simple example as follows. Supposing C -Cv is correlated as follows: * 1 C2 C3 C4c _ = - - { (v-e-.b + ).. + + V ~ v Th { ( V-b) y 2(V-b)2 3(V-b)3 + (v(8-b where C1, C2 -. —, b, and n are all arbitrary constants, we have QdCv _ C2 Cb C4 C()5 (8-5) d.V /T C2 ~ii ~i~ (v-b)3- (vbt I /~ = [^(V^ (V-b + + (V-b)5 Using Equation (8-3), we obtain / d2P 1 r C2 3 C3 Y(V) / - 2 = (v-b)V+7 T 3 + 7V7 ( V)55 - (8-6) ~. -(V'-b-' +' —-3 v-b)4'(V'b)'5 Tn+l where C2 C C4 C5, ^Y(v) = A + A )+ + (8-7) (v) =(vb) + (V-b)3 + (V-b)4 + (V-b)5) Integrating once with respect to T, we have (fiY) L1 + B(v) (8-8) VT, nTn- (V) where B(V) is a function of V or p alone. The second integration with respect to T yields:

-108Y(/v P n(nll + B)Tn + ((V) (8-9) where A(V) is an integration constant. It is obvious that the forms of B(V) and A(V) cannot be determined simply by correlating Cv data, but the so-called curvature term can be determined. VIII-2 Statistical and Experimental Cv-* For tetrafluoromethane, the agreement between the experimental and statistical Cv is very good on the basis of probable experimental error. This should not be interpreted, however, as a casual coincidence since the independent facts are available to support the results. First, the Cv of dichlorodifluoromethane measured in the same calorimeter agrees tell witheMasis32) C well with Masi's(32) Cv* corrected by the Martin-Hou equation to the same density. Secondly, the tetrafluoromethane molecule is simple and symmetrical, and the set of fundamental frequencies is well established with only a slight differences existing among various authors, These small differences in frequencies do not make appreciable differences in heat capacity. Chari's calculation was based on a set of fundamental frequencies deter(19) mined by Goubeau et al.,(9) plus an anharmonic contribution based on (33) the semi-empirical method presented by McCullough et al.., using assumptions employed by Albright et al, () In Gelles and Pitzers7) calculation, no anharmonic contribution was added. This is why their Cv* is about 0,5 to 0,8 less than that obtained by Chari. The observed Cv lies between Chari's and Gelles and Pitzer's values, but is closer to Chari's values. The difference between the observed values and those given by Chari is actually within the experimental precision of this work,

-109For chlorodifluoromethane, a set of fundamental frequencies is not definitely established. The most questionable point is the selection of one of the fundamental frequencies, Martin et al(26) selected 831 -l (45) cm as a fundamental, while Weissman, Meister, and Cleveland 5) chose 1178 cm for this same fundamental. Weissman et al. maintained that 831 cm-1 is due to the presence of dichlorofluoromethane (CHC12F). It (43) is interesting that, according to Smith et al.,() the Raman spectra of dichlorocluoromethane indicates no absorption band at 831 while chlorodifluoromethane has a fairly strong band at 831. The same authors also indicated that Raman spectra of both compounds showed no marked band at 1178. In fact, even in the infrared spectrum a band at 1178 is merely a medium absorption band comparable to many such bands which are not selected as fundamentals. Besides this, the infrared spectra of CHC12F given by Weissman et al. indicates a band at 831 only as a shoulder of a strong band at 804. The CHC1F2 sample used by the present author has a purity of 999+ % by gas chromatography according to the specification of the supplier, the "Freon" Products Laboratory of E, I. du Pont de Nemours and Company. The infrared spectra of the sample shows a band at 830 cml, but the mass spectrograph indicates only a negligible amount of CHC12F if any. Whether 831 is a fundamental is a controversial point, but in the light of the experimental Cy obtained in this study, it seems reasonable to conclude that the selection of 831 is more reasonable than the selection of 1178 as given by Weissman et al. Table 8-1 shows the list of fundamental frequencies selected by those authors. For dichlorotetrafluoroethane, the statistical Cv calculated by Martin(2) was based on the spectroscopic data of Glockler and Sage( )

-110(43) and of Smith, Nielsen, Berryman, Claasen, and Hudson. 3 The choice of fundamental frequencies was rather arbitrary and the existence of free internal rotation was assumed, The calculated values are generally higher than the experimental Cv* and the slope of the calculated Cv* curve is not as steep as the experimental one, This clearly indicates that too many low frequencies have been selected as fundamentals, Also, the assumption of free internal rotation may be in error, For chloropentafluoroethane, the statistical Cv* calculated by Martin, Iong, and Service(30) was based on the infrared spectral data of Barcelo(4) and the Raman spectral data, A potential barrier of 1750 cal/gm mole was also used by them to calculate the contribution by the hindered internal rotation, The values of their calculation are generally higher than the experimental Cv of this work and the slope of the Cv curve is less than the observed one, This indicates that one or two low wavenumber fundamentals should be replaced by the higher frequency fundamentals. * ((42) On the other hand, Cv calculated by Smith et al.,(4 are generally lower than the experimental data. This indicates that their selection of fundamental frequencies cover too many high frequencies. The fundamental frequencies selected by both Martin et al, and Smith et al* are listed in Table 8-2 for comparisons VIII-3 Comparison of the Experimental Data with the Equation of State As mentioned in Section I-4, the experimental Cv data may be employed to check the equation of state,, Most of the modern equations of state represent the Cv-Cv* as a function of temperature and density which are separable mathematically, ie, Cv - Cv - f(T)g(p) (8-10)

-llTable 8-1. Fundamental Frequencies of Chlorodifluoromethane (cm-l) Pitzer and Gelles(38) Cleveland (45) Martin(26) Weissman, et al. Meister 365 369 369 422 421 415 595 596 596 809 808 799 __... __"U~~~. ~831 1116 1116 1099 1178 1178 - 1131 1312 1310 1347 1345 1350 3023 3025 3035 Table 8-2. Fundamental Frequencies of Chloropentafluoroethane (Wave number, cm-1) Values Used by Martin et al.(30) Values used by Smith et al(42) 75 171? (tortion) 189 186 264 218 316 315 333 331 367 366 448 442 560 454 596 560 648 596 704 648 762 762 984 982 1128 1133 1180 1185 1230 1241 (2-)* 1348 1350 * statistical weight

-112l It is obvious that on the c-CCv* vs. density plane we get a family of similar isotherms, any one of which may be constructed by simply multiplying the ordinates of any other isotherms with a certain factor which is solely determined by the temperature function f(T). Therefore, the comparison of the experimental data with those predicted by the equation of state must be somehow concentrated on the characteristics rather than on their absolute valuesn Similarly, on the Cv-Cv* vs. temperature plane, we have a family of isometrics, any one of which can be constructed simply by multiplying the ordinates of any other isometrics by a factor, which in turn is determined solely by the density function g (p). So, in the course of comparison, the absolute values of Cv-Cv* are not of much interest but the characteristics of these isometrics must be carefully examined. The Martin-Hou equation has been developed for all compounds (8, 25, 26, 34) studied except chloropentafluoroethane. 26 ) Comparisons of experimental data with those predicted by the Martin-Hou equation in the CvCv* vs. density plane are presented in Figure 8-1 for chlorodifluoromethane, and in Figure 8-2 for dichlorotetrafluoroethaneo In both Figure 8-1 and Figure 8-2, the isotherms predicted by the Martin-Hou equation show a slightly downward curvature while the experimental isotherms indicate a slightly upward curvatureo de Nevers and Martin(l3) also drew a similar conclusion for perfluorocyclobutane and propylene in the lowdensity range. Predicted Cv-Cv* values are greater than experimental values in the case of chlorodifluoromethane, but are much less in the case of dichlorotetrafluoroethane. In the case of chlorodifluoromethane, the difference between the experimental and. predicted values of Cv-Cv*

-113/ / / /.030 ---- --- MARTIN HOU EQUATION // / / /o, / EXPERIMENTAL --- - - / /-/ / / /,// / ___ _______ -L —- /. If / / / / / / // / / / / / 7/ / __2/ I / / E___ ___ ___ ___ ___ ___ ___ ___~ ~ ~ ~ ~ ~~~0/ // / /'~ 0 / /// / ~- I~~~~/ / / / / // 0.0204.06 /.08 /./0 E.l/ >//,/ S//T, g/ _ _ _ _ /////^ ^/^O~. OR ^ Figure 8i/./ C.o s /o/ / E m,v, o C. orodifuoromethan // wt s P t y th M/r I /,010,z,~ c~..-,:/0///'/'/ 0i.~.. /..j,~i~:. /4 0.02.04.06.08.10.12 DENSITY, gm/c Figure 8-1.. Comparison of Experimental Cv-Cvx of Chlorodifluoromethane with Those Predictedc by the Martin-Hou Equation.

-114-.015 - --- -.-.- MARTIN HOU EQUATION EXPERIMENTAL O L Ii<? / XX 00.0..10.. -.1..,DENSITY, gm/cc Figure 8-2. Comparison of Experimental Cv-C* of Dichlorotetrafluoroethane with that Predicted by Martin-Hou Equation. (Comparison of Density Function) ______y^^^^^^^:9 0.02.04.06.08.10.1~ ~~2.1 DENSITY, gm/cci~ Figure ~ ~ 5 8-.Cmaio fEprmna C-y fDclrttaloo

-115reaches 0.0070 cal/gmDC, which corresponds to about 5% in experimental Cv. We can see, however, a tendency for both experimental and predicted values to get close at some higher density. In the case of dichlorotetrafluoroethane, the discrepancy between experimental and predicted values reaches as much as 0.0060 cal/gm~C, which corresponds to about 3.5% of the experimental Cv within the experimental range. There is no tendency, however, for both the experimental and predicted values to get closer at any higher density. In view of the fairly good agreement at high temperatures (above 160~C), but poor agreement at temperatures below the critical temperature, it is reasonable to suspect that the temperature function predicts too low for the low temperatures* The adequacy of the temperature function is best examined on the Cv-Cv* vss temperature plot. Comparisons of the experimental Cv-Cv with those predicted by the Martin-Hou equation on the C -Cv vs. temperature plane are presented in Figure 8-3 for chlorodifluoromethane, and in Figure 8-4 for dichlorotetrafluoroethane, In these figures, both experimental and predicted values of Cv-Cv are monotonically decreasing functions of temperature* But the rates of decrease are quite different; the experimental data decrease rapidly at the range below the critical temperature and quickly approach the asymptotical values at 160~C for chlorodifluoromethane and at 190~C for dichlorotetrafluoroethane, while predicted values decrease rather slowly and do not approach the asymptotical values within the experimental range. In general, the experimental temperature functions have a greater curvature than what can be predicted by the Martin-Hou equation, ie.,, -k - f(T) = Te c (8-11)

.030 \ MARTIN HOU EQUATION \..... -- EXPERIMENTAL _-A - \^ \~~~~~~'-^~~~~"\O1-.020 /- N_ \ \N %,N N^^^ >. 575 gm/cc 60 80 100 120 140 160 180 TEMPERATURE, OC Figure 8-3. Comparison of Experimental Cv-Cv* of Chloroiifluoromethane with Those Predicted by Martin-Hou Equation (Comparison of a Temperature Function). Equation (Comparison of a Temperature Function).

-117-.015 -.. \ - - MARTIN HOU EQUATION __ —- EXPERIMENTAL.010 I:\i i\ 0 C)___._ a____ ____ _ sS,- o I=0.0658 gm/cc I....t"- -/ t -. P ~0.0375 gm/cc 0 100 120 140 160 180 200 220 TEMPERATURE, ~C Figure 8-4. Comparison of Experimental C -C,* of Dichlorotetrafluoroethane with Those Predicted by the Martin-Hou Equation. (Comparison of a Temperature Function.)

-1184 The maximum curvature of the experimental isometrics occurs at temperatures around the critical temperature depending on the density. This fact would suggest that the temperature function, independent of density, is not capable of representing the data in the strict sense. And parallel to the argument presented in Section VIII-1, the experimental data would probably require a somewhat complicated functional relation, such as Cv-Cv = f(T) g(p) h (T,:p) (8-12) In the case of dichlorotetrafluoroethane, the experimental data agree with the predicted values quite well above the critical temperature for all densities. Thus it is reasonable to say that the temperature function causes the main discrepancy at the lower temperatures. No Martin-Hou equation has been developed for chloropentafluoroethane, but Martin et al.(30) have correlated the data in the following form. P = A + BT -C/T3 (8-13) The complete equation with its constants is included in Appendix F. The heat capacity predicted by Equation (8-13) has the following form. vCv = gP) (8-14) T4 The density function in Equation (8-14) is quite similar to that predicted by the Martin-Hou equation but is in much simpler form. There is not much to expect from this simple density function but the temperature function is different from that derived from the Martin-Hou equation, For this reason, the experimental data are compared with those predicted by Equation (8-13) on the Cv-Cv* vs. temperature plane. The actual values of Cv-Cv* predicted by Equation (8-13) are all less than

-119any experimental isometrics due to the excessively low values of the density function. Two of these predicted isometrics are shown in Figure 8-5 by dotted lines. For the convenience of comparison (with emphasis on the curvature of the isometrics), arbitrary values are assigned to the density function so as to make the predicted Cv-Cv* coincide with the experimental values at 100~C. Figure 8-5 shows that the curvature of a temperature function is still not enough to represent the experimental data but seems a little better than those derived from the Martin-Hou equation for chlorodifluoromethane and dichlorotetrafluoroethane. Of course, it should be noted that a curvature predicted by the Martin-Hou equation is very much dependent on the value of k. The value of k is 3.75 for chlorodifluoromethane and 3*00 for dichlorotetrafluoroethane, Figure 8-6 shows the effects of values of k on a curvature of isometrics, in which Cv-Cv* is plotted vs. reduced temperature. An arbitrary value is assigned to a density function to raise the curves to a level which is convenient to compare one another. In general, the curvature of isometrics increases with increasing value of k, and it would probably require k = 7*0 or more for the satisfactory representation of the experimental data, Tetrafluoromethane presents another interesting case for test of the equation of state, in which Cv-Cv* is practically zero for all temperatures and densities studied. The Martin-Hou equation which is correlated by Bhada(8) is used. The maximum value of Cv-Cv* should occur at the lowest temperature and highest density in the entire experimental range. The value of Cv-Cv* at 30~C and 0.0928 gm/cc is 0.0002 cal/gm~C, which is practically negligible. It is clear, then, that the Martin-Hou equation predicts the right curvature of isometrics in the P vs. T plot at the temperature range which is 1.3Tc or higher.

-120-.020 P=A+BT-C/T3 00 g(p) 0 80 1 0 1 21 EXPERIMENTAL 9,E "' I.010' Figure 8-5. Comparison of Experimental C+-C * of Chioropenta — fluoroethane with Those Predicted by P = A + T - C/T Type of Equation of State. o P /CC - = 0.0427 grI/CC 0 r E - -P2S l7 -I —--- 60 80 100 120 140 160 180 TEMPERATURE, OC Figure 8-5. Comparison of Experimental Cv-Cv* of Chloropentafluoroethane with Those Predicted by P = A + BT - C/T3 Type of Equation of State.

-121c 1.00 C O 50 I-6~~. ~ of 0.50 _ 0 \.76.84.92 1.00 1.08 1.16 1.24 T T R TFigure 8-6. Effect of k in the Martin-Hou Equation upon the Curvature of a Temperature Function. -- ^ ^ "".r: — ~~~~k the Curvature of a Temperature Function.

-122VIII-4 The Law of Corresponding State and C, Data If two gases obey the law of corresponding state, they must have the same Cv-Cv* (expressed in molar basis) at the same reduced temperature and reduced density. This may be derived as follows. The law of corresponding state maintains that the compressibility factor defined as PV P z P (8-15) RT RTp is a function of reduced temperature and reduced pressure (or reduced density) and independent of the kind of gases. According to Equation (8-15), we have dT D = Rp[T dz + z] (8-16) p) = Rp[{TQ ) Q )] (8-17) VdT2/ - T2/ P \dT/ P Substituting this into Equation (l-3), we have Cv-cv*- [/ ( p +TRp ] (8-18) CCV RT2R R T.R p ]2P (8-19) de Nevers and Martin(13) studied the experimental C -Cv for propylene and perfluorocyclobutane and concluded that, although the law of corresponding state is sufficiently accurate to make approximate generalization of PVT data, it is not sufficiently accurate to generalize Cv-C* data. Since two compounds studied by them are quite different in their molecular structure, the present author wonders whether

-123the law may be applicable even for Cv-Cv* if two gases are somewhat similar in their molecular structures. In Figure 8-7, values of Cv-C* are compared on the reduced basis. For chlorodifluoromethane, dichlorotetrafluoroethane, chloropentafluoroethane, and propylene, the agreement is not too bad. The worst difference is about 30 percent and mostly they agree within 10 percent* Since Cv-Cv* is only about 5 percent of Cv itself, the difference of 10 to 30 percent in Cv'Cv* may be regarded as an experimental error. Obviously, perfluorocyclobutane must be excluded from this generalization for it has a cyclic structure instead of chain structure. It seems reasonable to conclude that for gases of similar molecular structure, the law of corresponding state is applicable to Cv-Cv* as well as to the PVT relations.

3.5 Chlorodifluoromethone - Dichlorotetrofluoroethoane - -- -- -- 3.0 - -- Chloropentofluoroethone - --- (|i) __ / __ - ----- Propylene (by de Nevers ) - -- - --- - - - - -.. - Perfluorocyclobutone ( by de Nevers0) - - 2.5 f,~~~~~P / Z * __ _ __ __ _ _ /0o* ___ _^__ ___ - o0000 E0 - —.-4/ — - -10 E 2.0 -— 00 _I ___ _, __ - __ Z T _ _ _ / / _ _ _ _~~/ ^~ ~ ~ ~~~~_ ___^ZZZ^^Z ~^Z ~^'~^ ~Z 1.0 0~ —— ^ g ^^-V, 0__ __ __ __ __ /> ry ^ >^ __ ^^^'^ ______ Reduced Temperoture 0 0.1 0.2 0.3 0.4 REDUCED DENSITY, P/P Figure 8-7. Cy-Cy* As a Function of Reduced Temperature and Reduced Density.

IX. CONCLUSIONS 1. It has been shown that the thin-wall large-volume calorimeter originated by de Nevers(l2) can be improved to produce constantvolume heat-capacity data at low densities. It is possible to determine the ideal-gas heat capacity, Cv*, by extrapolating such data to zero density. The highest working temperature was successfully raised from 150~C to 200~C. 2. Comparison of the experimentally determined ideal-gas heat capacities, Cv*, with those statistically calculated has revealed the following: a. For tetrafluoromethane, the values calculated by Chari(9) and his Cv* equation in cubic form agree with the experimental C.v within 0.2 percent. Those calculated by Gelles aa.d Pitzer(l7) are lower than the observed values by 0.6 percent on the average. b. For chlorodifluoromethane, the values calculated by Martin et al.(26) are lower than the experimental data by 0.8 percent on the average. It can be expected to have better agreement if an anharmonic contribution is added to their calculations, The values calculated by Weissman et al.,(45) however, are lower than the experimental values by 4.0 percent at 400~K. c. For dichlorotetrafluoroethane, the values calculated by Martin(25) and his Cv* equation in quadratic form agree well with the experimental data at 200~C, but are higher than experimental values by as much as 3.4 percent at 100~C. -125

-126d. For chloropentafluoroethane, the values of Cj* calculated by Martin et al.(^) agree with the experimental data at 190~C but are higher by as much as 355% at 60~C. The values calculated by Smith et al.42) are lower than the observed values by 1,8% at 4000K and 2.4% at 4735K, 3. The experimental data show the following characteristics within the range of experiment, 30-200~C and 100-500 psi: a. For tetrafluoromethane, Cv-C * is practically negligible. be On the C AC * vs. density plot (except CF4), all isotherms V V curve upward slightly. co On the C-C * vso temperature plot (except CF4) all isometrics are monotonically decreasing functions with an upward curvature and approach the asymptotical values at temperatures about 50OC higher than the critical temperature. The maximum curvature occurs at the temperatures around the critical temperature depending on the density. 4. The Martin-Hou equation predicts the downward curvature of the isotherms at the low densities on the Cv-Cv* vs. density plot, which does not represent the experimental data correctly. 5. The temperature function derived from the Martin-Hou equation, which has a form of Texp(-kT/T ), cannot represent the experimental isometrics on the Cv-Cv vss temperature plane with a sufficient curvature if the value of k is less than 7o0. An equation which has a form P = A + BT - C/T3 does not represent the experimental isometrics satisfactorily.

-1276. The Martin-Hou equation predicts the negligible Cv-C~* at temperatures far above the critical, which is in good agreement with experimental results of tetrafluoromethane. 7. The law of corresponding state is applicable to Cv-Cv* if the gases rae similar in their molecular structure. 8. The extrapolation method as developed in this research for calibrating the alorimeter heat capacity is a reliable method.

APPENDIX A DETERMINATION OF THE CALORIMETER VOLUME A-1 Advantages of Using Nitrogen Gas as a Calibration Medium In the previous investigation done by Noel de Nevers,(l2) the volume of the calorimeter was determined by the weight of distilled water which filled up the calorimeter~ Although the principles involved were quite simple, a technical difficulty arose in the course of feeding and removing water from the calorimeters Tiny bubbles could be formed inside the calorimeter in spite of precautions, and the water which got into the motor was rather difficult to remove0 To avoid these difficulties, compressed pure nitrogen (bone dry) was employed in place of water. Nitrogen gas was preferred because it was available in high purity and its compressibility factors were known to the sufficient accuracy, A-2 Basic Principle Let P1 and P2 be two different pressures in which the following quantities are measured0 W1, W2 ---- Gross weights Of the calorimeter plus gas Zl1 z2 ---—. — Compressibility factors PV/RT T1, T2 ~"-. Temperatures w --.. Net weight of the calorimeter V'. —.-.- - Volume of the calorimeter M -a ------ Molecular weight of nitrogen If we assume that the volume of the calorimeter remains practically constant in the vicinity of room temperature and at the moderate range of -128

-129pressures (3-10 atm), we have P1V Wl-w (A-) z1RT1 M P2V W2_w (A-2) (A-2) Z2RT2 M (A-l) - (A-2), we get Z -z 2 j V W- (A-5) lTl 2T2/ R M Hence _ (Wl-W2)RA Pi P2 A4 M / Tl z2 / / Now if P2 - 0, Equation (A-4) reduces to (Wl-W2)R /P1 (Wl-w2) zlRTl V = ---— / — - =............ (A-5) M / z1T1 P Either Equation (A-4) or (A-5) may be used for calculation; zi and z2 can be obtained from the National Bureau of Standards' Circular 564, Novo, 1955. A-3 Measuring Apparatus The measuring apparatus is shown diagramatically in Figure A-1. The nitrogen used was the bone-dry grade by Matheson Co. The pressure gauge was by Heise Co. (0-500#)o The vacumm pump was of the Hyvac 2 type. A-4 Procedures (a) To avoid evacuation of the pressure gauge, the gauge was purged with pure nitrogen several times. The procedure consisted of filling the gauge with compressed nitrogen and the subsequent release of it into the atmospherec The valve V3 is always closed except the external line was filled with nitrogen.

-130Heise V1 Mcleod Pressure Gauge Gauge (0-500 psig) V3 -.r.c,,, V J-J4'2/( / ~ac\ C/6alori- wcuum T meter Pump \ Nitrogen Cylinder Figure A-1 Schematic Diagram of Determining the Calorimeter Volume. (b) After evaculation of the calorimeter (with V3 and V1 closed), V2 was closed and a calorimeter was disconnected for weighing. (c) Before feeding the calorimeter with pure nitrogen, the line was first evacuated Then, with V4 closed, the calorimeter was filled with an appropriate amount of nitrogen. When equilibrium was reached, the temperature and pressure were measured and then the calorimeter was closed and disconnected from the system for weighing, (d) The same procedures were repeated several times for the different pressures. A-5 Results Run No, Temp. ~K abs.Presatm. z gross wt,gm. Volume 1 0.000013 998.72 2 299.96 12.1279* 0.99823 1059.74 4412 cc 3 299.75 11,4345 0.99826 1056.24 4408 4 299.98 10.7066 0.99833 1052.63 4415 5 298.75 9.4685 0.99836 1046.47 4405 6 299.05 8,0263 0.99861 1039.16 4407 Average Volume 4409 cc * The accuracy of pressure measurements was estimated at no better than 0.05%. The extra digits, however, were retained on the conversion.

APPENDIX B CALIBRATION OF RESISTANCE THERMOMETER The standard resistance thermometer is usually certified on the International Temperature Scale, of which the fixed and reproducible equilibrium temperatures are the ice point, steam point, sulfur point, etc., and the specified interpolation formula is as follows: For the range 0 to 630~.C, t = CR0- + ( i' l)t (B-1) devised by Callendar and commonly used in this country. Equation (B-l) may be put in the equivalent international formula, Rt= Ro(l + At + Bt2) (B-2) where Rt is the resistance of the thermometer at temperature t and Ro is the resistance at 0~Co One of the international requirements for a standard thermometer is that a, or R100-R0/lOORo, must be greater than 0,00391, It was found, unfortunately, that the resistance thermometer as described in Section III-2 generally does not satisfy this requirement, For this reason, it was decided to calibrate the thermometer not only at three fixed points but also at several temperatures in the range of interest, and two constants evaluated by a least-square fitting* Because of lack of the available facility, the sulfur point was omitted* The resistance was measured at the ice point a few times with a 24-hour annealing period between two successive measurements to make sure the resistance was stable, The resistance at temperatures other than the -131

-132ice point was measured by Immersing the thermometer into an agitated oil bath whose temperature was in turn measured by the Leeds and Northrup resistance thermometer No. 1227385, for which an NBS calibration dated June 25, 1958, was available4 The temperatures were recorded to 0o001~C although their reliability was definitely less than this, Due to the small capacity of the oil bath and the manual control of the heating element, the temperature fluctuation was estimated to be of the order of 0,010C per minute, and the possible temperature difference between two points in the oil bath might have reached 0o2~0C The ice point, being a fixed point, was not subject to the above difficulties and was considered more reliable than any other measurements. Hence, Ro = 2358257 ohms was used directly in Equation (B-2) and the constants A and B were evaluated by fitting the following data: Leeds & Northrup Temperature, C Thermometer No. 1227385, ohms Calibrated, ohms 25*5205 0o000 23.8257 28.1293 25.749 26,1166 34.7968 92,466 32,1214 3555888 100,481 32,8688 4046941 152.618 57.4662 4511152 198.454 41*4626 The values obtained for two constants were: A = 3*80518 x 10-3; B = -3^6997 x 10-7. The maximum scatter of the data from the calibrated curve was about 0,15% in resistance which corresponded to about 0*3 ~C Most of the data fitted within 0,15 C.

APPENDIX C SAMPLE CALCULATIONS C-1 Volume of the Calorimeter The volume of the calorimeter at the room temperature, 27~C, and 130 psia was calibrated according to the method. described in Appendix A. In the process of experiments, this volume changed gradually due to the thermal and elastic expansion. These changes were estimated as follows: d.(lnV) = dl dT+ (dlnV dp (C-l) \ dT /p dp /Tp (C-l) or dV /dV \ dV \ - = - dT. + ) dp (C-2) V VdTp Vdp/r where (dV/VdT) was a volumetric coefficient of thermal expansion and approximately three times the linear coefficient of thermal expansion. The value of the linear expansion was 5.0 x 10-6 per degree C for the type of steel used according to the ASM Metal Handbook. (3 (dV/Vdp)T was a coefficient of elastic expansion and related to Young's modulus as follows: (V) A (d5 r = (3)(0.25)(diameter) (C-3) Vd.p2T KydpJT (wall thickness)(Yoag's Modulus) For 8-inch diameter, 0.031-inch wall thickness, and 30 x 106 psi for Young's modulus, we obtained (dV) = 0.667 x 105 per psi (C-4) \VdpIT Hence = 1.5 x 10-5 dT + 0.667 x 10O5 dp (C-5) v -15533

134As an example, for chloropentafluoroethane loading No4 5, the temperature range was 717 -121,50C and the pressure range was 335-500 psi4 Hence the average temperature was 97=C -and the average pressure, 418 psi, The mean volume for this particular loading was then estimated at this average condition, using Equation. (C-5), dS - 1-5 x 1005 (97-27) + 0667 x 105 (418-130) = 0,00297 V' y = 4409 x 1 00297 = 4422 cca Therefore the average density was p =98l1 c 0a,2219 gm/cc4 4422 C-2 Gross Heat Capacity As an example, the calculation of Run No, C-24 is illustrated below The primary data are as follows: The heating period star+ted at 2;25 and ended at 2:54. The elapsed time, A., was 31l173 minutes, The power was measured three times during the heating period, which reads Voltage (volts) Current (amp) 18,30 0,4165 18,38 0,4143 18,46 0,4123 The tiemperatures were measured before and after the heating period at the following times, The resistance shown was a sum of the normal and reverse readings which corresponded to exactly twice the true resistance of the thermometer,

-135Time Ohms Before heating 2:07 59*5833 2:12 59*5827 2:17 59,5815 2:22 59.5805 After heating 3:04 61*5482 3:09 61,5468 3:14 61*5454 3:19 61*5435 From the above primary data, the gross heat capacity was calculated, The thermometer resistance at the start of the heating period, R1, was just one-half the total reading at 2:22 (1 min. difference was neglected), i.e., 29.7900 ohms including the bridge zero correction. The change-of total resistance before heating period was -0.0009 ohms in 5 minutes which corresponded to the drift of -0.0009 ohms in true resistance in ten minutes. This value in resistance was equivalent to -0,0010lC/min. and designated as drift1, Similarly, the drift rate after heating period was estimated. The average drift was -0.0015 ohms in ten minutes in the true resistance which was equivalent to -0.0017'C/min. at this temperature. This was drift2. The resistance at the end Of the heating period was determined by extrapolating the resistance at 3:04 back to 2:54 using the value of drift2 (linear extrapolation). The value obtained was 30.7753 ohms including the bridge zero correction. This was R2 * R and R were then converted into temperatures using the calibration formula: R = 2538257 (1 + 0.00580518t - 536997 x 107 t) (C-6)

-136where R is the resistance in ohms and t is the temperature in OC. (For calibration of the thermometer, see Appendix B,) The results were T = 66.2130C and T2 7723500o Hence, LT 11,022'C. The correction for heat leakage was estimated in terms of corresponding temperatuwe change, using the drift rates, ie,, (31o173)= -(042~C d riftl + drift1\ -.(oo00o + 0,s0017) (.l7 =.42C corr.. 2 - a By multiplying the voltage and current, the gross power inputs at various times were calculated, which yielded 7.622, 7.615, and 7,611 watts, respectively, The average was 7o616 watts. Some of this calculated gross power, however. was dissipated in the voltage measuring circuit, which was parallel with the thermometersheater and motor (see Figure 3-9). The voltage-measuring circuit consisted of two standard resistors and one voltmeter whose total equivalent resistance was found to be 2015 + 5 ohms. Hence, the power consumed in this circuit was E2 E2. IE 2 - -- (C-7) R 2015 For this particular run, the average voltage was 18,38 volts and., therefore, the power loss was 0,168 watts according to Equation (C-7). Their difference, 7,448 watts, was then the net power, The gross heat qapacity was then calculated by Equation (5-6) as follows: Cmean AG (7.7448)(31.73 )(l4,340 03 ) gross 1(4 corr,) (11,022 + 0.042) 300.93 ca]/ where 1445403 cal/watt-min, was a conversion factor,

-157The correction for the expansion work done by the gas on the calorimeter was neglected on the basis that for each 10'C interval the volume increase was only about 0,015% of the original volume and the correction would have been less than 0.02% of the total heat inputs C-3 Constant-Volume Heat Capacity of the Gas The mean gross heat capacity as calculated in Section C-2 was then regarded as the true gross heat capacity at the mean temperature. For example, in Run No. C-24, T1 was 66,213~C and T2 77.235~C. Hence, their arithmatic mean was Tmean = 6.2 + 77235 71.72"C 2 At 71j720C, the heat capacity of the calorimeter was read from Figure 6-3 to be 112.00 cal/oC. The difference between Cgo and Ccalr' was designated as Cnet' Hence, Cnet = Cgross- Ccalr.= 300.93 - 112.00 = 188.93 cal/~C and Cnet 187*07 v m 98110 - 0.1926 cal/gm.OC where m is the mass of the gas loaded.

APPENDIX D DETAILED GROSS HEAT-CAPACITY DATA In Tables D-l through D-5, the runs are numbered in chronological order (carrying the same number as the original data sheets), The letters, A, Bg etc,, indicate the compound loaded, (Exceptions are those runs for dichlorodifluoromethane originally intended for the calibration of calorimeter heat capacity, i.e.,, Run No. A-ll through No. A-23.) Those runs which did not suffice for the criteria of acceptable experimental conditions are discarded regardless of the magnitude of their deviation from the smoothed curve. In each table are listed the values of T1, T2, -driftl, -drift2, mean power, AQ, ( -i-orr,) Cgross9 and Tmean The loadings are numbered in the order of increasing density for each compound, For those loadings whose final results were not calculated directly from the individual gross heat-capacity.but were evaluated by the smoothed gross heat-capacity dat;a, the gross heat-capacity data are plotted in Figures D-1 through D-I7 A smooth curve has been drawn through those data points for each loading, Based on these smooth curves, the final constant-volume heat-capacity data were calculated. 138

TABLE D-1 GROSS BEAT CAPACTY WITE DICLORODIFLUORCETEANE LOADING T1 T2 -driftl -drift2 Mean Power A AT-ATcorr. Cgross Tmean Run No. "C ~C'C/min. ~C/min. Watts min. ~C cal/~C ~C Dichlorodifluorcmethane Loading No. 1. 55,03 gin. Recovered 54.70 gm. A-11 374051 49,665.0000.0011 3.847 26,904 12.629 117.52 43.36 A-12 49.658 62,541,0011.0022 3.824 28.012 12.929 118.81 56.10 A-13 75 927 90.465.0045.0050 4.772 25.996 14.661 121.34 83.20 A-14 90.348 103,797.0050.0056 4.795 24,309 13,578 123.10 97.07 A-15 104,803 118.093 o0067.0074 4.703 24.858 13.465 124.51 111.45 A-16 117.909 131,142.0074.0088 4.682 25.090 13.436 125.38 124.53 A-17 130.886 144.112.0088.0102 4.654 25.412 13.467 125.94 137.50 A-18 148.465 164.051.0113.0125 4,640 30.567 15-950 127.52 156.26 A-19 163.760 179.330,0125.0137 4.622 31.205 15.979 129.44 171.55 k A-21 168.768 183.347.0103.0114 4,389 30.656 14.912 129.39 176.06 A-22 185,328 199.336.0137.0149 5.775 24.192 15.354 130.49 191.83 A-23 32,484 42.250 -.0006.0000 3.855 20.551 9.760 116.40 37.37 Dichlorodifluoromethane Loading No. 2. 251.74 gn, Recovered 251.01 gm. E-1 116.983 127.613.0037.0059 5.701 20.344 10.728 155.03 122.25 E-2 127.457 139.937.0059.0074 5.690 24,111 12.643 155.60 133.70 -E-3 138.501 150.615 oo0063.0077 5.704 23.554 12.279 156.90 144.56 E-4 150.378 162.853.0077.0091 5.666 24.715. 12.683 158.34 156.62 E-5 156.408 167.857.0065.0095 5.233 24,616 11.646 158.62 162,13 E-6 167.612 179.542.0095.0112 5.226 26.010 12.199 159.79 173.57 E-7 178.865 190.944,0099.0118 6.724 20.513 12.302 160.79 184.90

-140TABLE D-2 GROSS HEAT CAPACITY WITH TETRAFLUOROMETHANE LOADING T1 T2 -drift1 -drift2 Mean Power AG AT-Torr Cgross Tmean Run No. ~C ~C ~C/min. C/min. Watts min. C cal/C ~C Tetrafluoromethane Loading No. 3. 334.72 gm. Recovered 334.20 gm. D-10 29.080 41.638.0000.0011 7.281 19.009 12.568 157.92 35.36 D-ll 40.832 53.695.000oo6.0017 7.239 19.930 12,886 160.55 47.26 D-12 53.648 67.044.0017.0028 7.234 21.157 13.444 163.25 60.35 D-13 66.624 78.794.0025.0034 7.205 19.643 12.228 165.98 72.71 D-14 86.961 97.812.0037.0045 5.980 21.573 10.939 169.12 92.39 D-15 97.678 108.901.0045,0056 6,015 22.510 11.337 171.27 103.29 D-16 109.362 120.422.0056.0062 5.989 22.631 11.194 173.64 114.89 D-17 120,279 131.651.0062.0074 5.974 23.645 11.533 175.64 125.97 D-18 131.467 142.920.0074.0087 5.969 24.089 11.647 177.04 137.19 D-19 148.993 159.435.0068.0079 5.437 24.547 10.622 180.18 154.21 D-20 159.211 170.357.0079.0097 5.435 26.628 11.380 182.36 164.78 D-21 169.555 180.542.0100.0112 5.119 28.137 11.285 183.02 175.05 D-22 180.969 192.211.0112.0129 7.314 20.273 11.486 185.13 186.59 Tetrafluoromethane Loading No. 1. 160.70 gm. Recovered 159.47 gm. D-23 27.866 41.399.0007.0009 6.322 19,722 13.535 132.09 34.63 D-24 41.347 53.579.0009,0025 6.309 18.219 12.262 134.42 47.46 D-25 53.501 66.812.0025.0038 6.297 20.087 13.374 135.63 60.16 D-26 78.246 92.127.0025.0038 6.221 21.743 13.949 139.06 85.19 D-27 92.031 106.056.0038.0051 6.213 22.352 14.124 140.99 99.04 D-28 113.629 128,423.0045.0057 6.141 24.423 14.919 144.17 121.03 D-29 128.261 140.208.0057.0076 5.408 22,770 12.098 145.97 134.23 D-30 140.566 150.960.0069.0084 4,574 23,612 10.575 146.46 145.76 D-31 152.998 164,615.0069.0084 5.110 23.879 11.800 148.29 158.81 D-33 175.259 186.534.0099.0114 5.117 23.684 11.527 150.77 180.90 D-34 186.074 197.530.0110.0126 5,101 24.380 11.744 151.86 191.80 D-35 30.212 43.600.0010.0009 6.376 19,406 13.387 132.53 36.91 D-36 60.872 73.672.0012.0027 6.335 19.334 12.838 136.81 67.27 D-37 102.615 115.710.0041.0052 5.709 23.061 13.202 143.01 109.16 D-38 146.322 158.505.0074.0084 5.455 23.388 12.368 147.92 152.41 D-39 165.702 177.421.0085.0104 5.417 23.056 11.937 150,04 171.56 Tetrafluoromethane Loading No. 2. 257.44 gm. Recovered 256.68 gm. D-41 25.449 39.259.0000,0016 6.752 20.833 13.827 145.88 32.35 D-42 39.215 52.046.0016.0031 6.758 19.729 12,877 148.48 45.63 D-43 52.180 64.387.0017.0025 6.762 19.029 12.247 150.67 58.28 D-44 64.326 76.525.0025.0034 6.778 19.258 12.256 152.73 70.43 D-45 76.420 88.926.0034.0044 6.710 20.242 12.585 154.76 82.67 D-46 102.198 113.764.0035.0045 5.816 22.243 11.655 159.18 107.98 D-47 113.911 125.873.0049.0058 5.886 23.050 12.085 160.98 119.89 D-48 125.726 137.487.0058 oo0069 5.886 22.991 11.907 162.99 131.61 D-49 136.840 149,039.0073.0081 5.872 24,118 12.385 163.98 142.94 D-51 166.315 177.065.0088.0101 5.436 23.628 10.973 167.86 171.69 D-52 176,129 187.266.0097.0109 54401 24.895 11.393 169.24 181.70 D-53 188.500 199.308.0103.0124 6.811 19.338 11.027 171.29 193.90 Tetrafluoromethane Loading No. 4. 410.69 gm. Recovered 409.33 gm. D-54 32.197 44.612.0004.0011 7.152 20.588 12.430 169.88 38.40 D-55 44,585 57.202.0011.0018 7,224 21.139 12.648 173.14 50.89 D-56 57.121 69.887.0018.0025 7.214 21.736 12.813 175.49 63.50 D-57 69.819 82.829.0025.0034 7,225 22.552 13.077 178.68 76.32 D-58 81.734 93.698.0030.0039 6.718 22.614 12.042 180.92 87.72 D-59 98.411 109,615.0025.0034 6.281 23,040 11.272 184.10 104.01 D-6o 109,601 120.689.0036.0042 6.318 23,056 11.178 186.88 115.14

88 - 186 52 184 X - 1- 50 /. /~ 182 148 I 0 5 7 90 1 10 13 15 17 19 146 0 - -180- — i —r- D1 -pL 176 / 142 174 ---- -' - - - -- -140 U 97Ise 1 134 172 -- - - -- -- --- -- -- -- -- --- --- -- -- -- -- -- _-138 30 50 70 90 110 130 150 170 190 TEMPERATURE OC Figure D-l. Gross Heat Capacity with Tetrafluoromethane Loading. //~,~6~~~~~~~~~~~~~~~~~~~~~~~ /~~~~~_ Figure D.1. Gross Heat Capacity with Tetrafluoromethane Loading.

-142186 - 184 - 174 / 182 172 180 -- - - -- - - - - -- - - - - -- - - 170 178 -- -- - - - -- - - -- - - /- 168 176 -- - - - - - - - - -- 7 ---- - - - 166 174 - 164 172 - 162,168 1t —-—. —-- --- --- 58l 166 70 -' - -- - -- - -- - -- 160 162'152 U / t 168 158 o 158 - 148 156 1- 46 20 40 60 80 100 120 140 160 180 200 TEMPERATURE, ~C Figure D-2. Gross-Heat Capacity with Tetrafluoromethane Loading.

— 43TABLE D-3 GROSS HEAT CAPACITY WITH C0LORODIFLUOROMETHAME LOADING T1 T2 -driftl -drift2 Mean Power A8 ATTcorr, Cgros Tmean Run No. "C "C ~C/min. ~C/min. Watts min. ~C cal/~C ~C Chlorodifluoromethane Loading No. 3. 346.08 gm. Recovered 346.05 gin. A-2 69.567 79.147.0021.0026 4,498 25.263 9.639 169.05 74.36 A-3 88.198 100.462.0024.0037 6.005 24.531 12.339 171.21 94.33 A-4 100.370 112,300.0037.0046 5.973 24.246 12.031 172.62 106.34 A-5 123.358 135.493.0045 0061 6.080 24.644 12.266 175.18 129.43 A-6 135,340 147.819.0061.0065 6.057 25.838 12.641 177.54 141.58 A-7 147.665 159.910.0060 0068 6.037 25.628 12.409 178.80 153.79 A-8 167.286 181.972.0051.0065 6.974 26.941 14.842 181.54 174.63 Chlordifluoromethane Loading No. 4. 447.08 gm. Recovered 446.81 gm. A-24 67,302 79.344.0015.0019 6.461 24.545 12.084 188.20 73.32 A-25 79.675 91.693.0025.0039 6.463 24.607 12.097 188.53 85.68 A-26 90.013 101.807.0037.0038 6,436 24,396 11.885 189.45 95.91 A-27 108.435 118.814.0039.0052 5.937 23.586 10.486 191.50 113.62 A-28 118.685 130.468.0052.0061 6.253 25.674 11.928 193.01 124.58 A-29 129.274 143.873.0055.0068 8.393 23.913 14.746 195.18 136.57 A-30 143.671 156,512.0068.0080 8.384 21.334 12.999 197.32 150.09 Chorodifluorcmethane Loading No. 5. 548.22 gin. Recovered 547.93 gn. A-31 69.543 81.707.0018.0029 6.981 25.437 12,224 208.33 75.63 A-32 81.634 94.060.0029.0037 6.964 26.195 12.512 209.08 87.85 A-33 93.962 106.408.0037.0046 6.922 26.402 12.556 208.72 100.19 A-34 104.134 117.296.0042.0050 8.474 23.014 13.268 210.78 110.72 A-35 79.691 89.434.0022.0022 6.689 21.262 9.790 208.32 84.56 Chlorodifluoromethane Loading No. 2. 254.10 gm. Recovered 254.08 gn. A-36 41.969 55.276.0011..0019 4.774 29.176 13 351 149.61 48.62 A-37 103.258 116.202.0024.0034 6.060 23.440 13.012 156.55 109.73 A-38 115.851 126.884.0045.0056 5.788 21.314 11.141 158.80 121.37 A-39 126.681 139.021.0056.0068 5.752 24.286 12.491 160.37 132.85 A-40 138.839 150.761.0068.0079 5.721 23.754 12.097 161.10 144.80 A-41 167.224 179.202.0074.0103 5.263 26.669 12.214 164.79 173.21 A-42 178.940 192.441.0103.0108 5.266 30.541 13.823 166.85 185.69 A-43 60.477 75.686.0009.0020 6.623 24.337 15.235 151.72 68.08 A-44 90.556 105.449.0031.0043 6.604 24.553 14.984 155.19 98.00 A-47 99.761 111.681.0028.0036 6.152 21.242 11.988 156.32 105.72 Chlorodifluorometbane Loading No. 1. 166.96 gm. Recovered 166.71 gm. A-49 52.993 66.388.0014.0020 6.192 20.664 13.430 136.62 59.69 A-50 66.341 79.472.0020.0031 6.170 20.639 13.184 138.51 72.90 A-51 83.367 96.006.0041.0050 6.165 20.140 12.731 139.86 89.69 A-52 95.921 109.472.0050.0060 6.128 21.978 13.672 141.27 102.70 A-53 109.349 121.956.0060.0074 6.120 20.787 12.746 143.14 115.65 A-54 121.422 134.050.0056.0068 5.500 23.370 12.773 144.31 127.73 A-57 157.773 169.183.0091.0102 5.462 22.105 11.623 148.96 163.48 A-58 168.906 179.512.0102.0120 5.374 21.100 10.840 150.00 174.21 A-60 136.561 148.461.0056.0068 5.210 23.563 12.046 146.14 142.51 A-62 161.991 173.857.0097.0108 5.198 24.113 12.113 148.39 167.92 A-63 173.585 185.170.0108.0125 5.191 23.940 11.865 150.20 179.38 A-64 184.860 196.345.0125.0125 5.181 23.950 11.784 150.99 190.60

-144168 166 164 / / 152 162'I — 7 -- - - -- - - -- - - -^. -- -- r - -- 150 0//.160 o ~ 1o/. -,'0'b 148 Ulb 0 158 / / - 0 04 _ __ 144 154 152 - 140 150 138 136 40 60 80 100 120 140 160 180 200 TEMPERATURE, OC Figure D-3. Gross Heat Capacity with Chlorodifluoromethane Loading.

-145184 182 178 0e/ 180 1746 < — 70 Figure -4. Gross Heat Capacity with Chlorodif/uoromehane Loading. 60 80 100 120 140 160 180 200 TEMPERATURE, ~C

-146TABLE D-4 GROSS HEAT CAPACITY WITH DICHLOROTETRAFLUOROETHANE LOADING Run No. T1 TT2 -driftl -drift2 Mean Power Ag ZrLT-Aorr Cros Tmean ~C ~C ~C/min. ~C/min. Watts min. C cal/~C ~C Dichlorotetrafluoroethane Loading No. 2. 291.05 gm. Recovered 290.85 gm. B-9 82.558 96.182.0023.0029 6.154 25.508 13.690 164.43 89.37 B-10 95.170 107.304.0030.0036 6.160 22.906 12.210 165.72 101.24 B-11 107.215 119.427.0036.0045 6.158 23.414 12.307 168.00 113.32 B-12 119.312 131.600.0045.0054 6.147 23.838 12.406 169.38 125.46 B-13 131.477 142.899.0054.0063 6.132 22.501 11.554 171.26 137.19 B-15 147.233 159.120.0057.0065 6.243 23.123 12.028 172.12 153.18 B-16 158.989 169.948.0065.0074 5.769 23.303 11.121 173.36 164.47 B-17 167.581 178.805.0068.0071 5.753 23.239 11.392 175.54 173.19 B-19 187.007 197.556.0091.0103 5.596 23.873 10.781 177.69 192.28 B-20 115.685 129.163.0021.0029 6.869 23.191 13.536 168.76 122.42 B-21 128.419 140.824.0044.0051 6.388 23.150 12.515 169.44 134.62 B-22 140.712 152.954.0051.0057 6.324 23.465 12.369 172.04 146.83 B-23 152.898 165.793.0057.0066 6.355 24.738 13.047 172.79 159.35 B-24 164.188 175.741.0057 o0068 5.983 23.758 11.701 174.20 169.96 B-25 175.580 186.914.0068.0080 5.784 24.426 11.515 175.94 181.25 B-26 186.712 197.394.0080.0092 5.775 23.340 10.883 177.61 192.05 Dichlorotetrafluoroethane Loading No. 4. 600.17 gm. Recovered 599.97 gm. B-27 110.538 120.047.0034.0035 6.342 24.064 9.592 288.16 115.29 B-28 119.959 129.778.0035.0042 6.333 25.029 9.915 229.26 124.87 B-29 129.675 140.000.00 2.0051 6.296 26.639 10.449 230.18 134.84 B-30 140.568 150.971.00 2.0057 5.942 28.575 10.5 4 230.92 145.77 B-31 150.830 161.138.0057.0070 5.923 28.655 10.490 232.01 155.98 B-32 160.962 171.229.0070.0080 5.908 23.913 10.484 233.65 166.10 B-33 172.375 182.441.0055.0064 7.318 22.967 10.203 236.22 177.41 B-34 181.103 191.581.0069.0080 7.308 24.204 10.658 237.99 186.34 B-35 191.385 200.156.0080.0092 7.313 20.455 8.947 239.77 195.77 Dichlorotetrafluoroethane Loading No. 1. 165.67 gm. Recovered 165.72 gm. B-36 71.605 81.927.0013.0028 4.307 23.683 10.371 141.04 76.77 B-37 81.854 92.257.0028.0039 4.286 24.163 10.484 141.65 87.06 B-38 91.293 105.157.0036.0054 5.879 23.672 13.971 142.85 98.23 B-39 105.021 117.371.0054.0064 5.861 21.457 12.477 144.54 111.20 B-40 117.210 129.056.0064.0078 5.841 20.936 11.995 146.20 123.13 B-41 125.977 139.488.0064.0074 5.457 25.756 13.689 147.24 132.73 B-42 139.312 151.275.0074.0091 5.439 23.231 12.155 149.07 145.29 B-43 151.086 163.584.0091.0114 5.435 24.527 12.749 149.94 157.34 B-45 186.063 193.227.0135.0165 6.501 22.163 13.496 153.10 186.65 B-47 91.354 104.631.0015.0026 5.948 22.314 13.323 142.85 97.99 B-48 137.588 149.872.0066.0075 5.454 23.570 12.450 148.06 143.73 B-53 158.677 170.771.0108.0120 5.383 24.005 12.368 149.83 164.72 B-54 170.414 182.56.0120.0131 5.370 25.006 12.756 150.96 176.64 B-55 186.620 198.392.0131.0149 5.304 24.406 12.114 153.24 192.51 Dichlorotetrafluoroethane Loading No. 3. 440.56 gm. Recovered 440.40 gm. B-56 103.161 113.980.0045.0053 6.231 23.906 10.936 195.33 108.57 B-57 113.848 12..918.0053.0073 6.229 24.758 11.226 197.01 119.38 B-58 124.748 136.692.0073.0087 6.211 27.012 12.160 197.85 130.72 B-59 150.418 161.330.0075.0086 6.199 25.228 11.115 201.77 155.87 B-60 160.570 171.140.0080 0097 6.175 24.681 10.788 202.60 165.86 B-61 176.721 188.074.0091.0109 6.011 27.646 11.629 204.93 182.40 B-62 187.795 199.468.0109.0138 5.996 29.010 12.031 207.33 193.63 B-63 140.575 151.054.0052.0066 5.940 24.934 10.626 199.88 145.81 B-64 169.435 179.873.0092.0103 5.682 26.807 10.699 204.16 174.65

-147178 176 174 172 -' 0 o A 16870 r 152,/ 0 100 120 140 160 180 200 80 10 2 4 TEMPERATURE,C Figure D-5. Gross Heat Capacity with Dichlorotetrafluoroethane Loading. ___~~ TME R TR,__~-C Fgr -5, ros7Het Cpactywit Dihlootera --- ^ —— fuoro thae Loding

-148TABLE D-5 GROSS HEAT CAPACITY WITH CHLOROPENTAFLUOROETEANE LOADING T1 T2 -drift1 -drift2 Mean Power AG A- T orr. Cgross " Tmean Ruw Nod 0C c ~0C/min. 0C/min. Watts min. C cal/~C C Chloropentafluoroethane Loading No. 3. 592.52 gn. Recovered 592.43 gn. C-l 58.293 70.971.0017.0020 6.866 28.253 12.730 218.53 64.63 C-2 70.926 82.227.0020.0028 6.868 25.509 11.362 221.12 76.58 C-3 82.069 92.269.0028.0034 6.835 23.350 10.272 222.81 87.17 c-4 92.185 102.672.0034.0044 6.763 24.494 10.583 224.46 97.43 C-5 102.748 112.834.0037.0045 6.366 25.181 10.189 225.62 107.79 C-6 112.727 123.330.0045.0059 6.385 26.741 10.742 227.94 118.03 C-7 127.944 137.898.0053.0065 6.374 25.571 10.105 231.30 1532.92 0-8 137.749 147.411.0064.0070 6.349 25.232 9.831 233.68 142.58 0-9 147.235 156.987.0070.0080 6.335 25.797 9.945 235.65 152.11 0-10 163.635 172.137.0080.0091 5.546 26.180 8.726 238.61 167.89 C-ll 171.908 180.431.0091.0100 5.557 26.624 8.789 241.39 176.17 C-12 179.558 188.232.0098.0109 5.536 27.5309 8.957 242.05 183.90 0-13 188.109 197.792.0109.0126 7.217 23.496 9.959 244.17 192.95 Chloropentafluoroethane Loading No. 4. 791.79 gm. Recovered 791.40 gn. C-14 59.995 70.527.0012.0017 7.292 26.191 10.570 259.10 65.26 0-15 70.354 80.952.0018.0025 7.293 26.489 10.655 260.00 75.65 0-16 80.890 91.705.0025.0033 7.276 27.313 10.894 261.59 86.30 0-17 91.624 102.191.0033.0043 6.977 28.085 10.674 263.26 96.91 C-18 103.350 112.675.0026.0034 6.554 26.629 9.405 266.11 108.01 0-19 112.595 122.331.0034.0044 6.556 28.054 9.845 267.90 117.46 0-20 124.315 133.710.0037.0046 6.240 28.712 9.514 270.04 129.01 0-21 132.255 141.543.0050.0060 6.222 28.761 9.446 271.67 136.90 0-22 140.822 149.829.0056.0060 6.159 28.479 9.172 274.24 145.33 0-23 149.680 158.855.o6o0.0069 6.150 29.364 9.364 276.56 154.27 Chloropentafluoroethane Loading No. 5. 981.10 gn. Recovered 980.75 gin. 0-24 66.213 77.235.0010.0017 7.448 31.173 11.064 300.93 71.72 0-25 77.192 87.340.0017.0022 7.416 28.809 10.204 300.25 82.27 0-26 86.868 95.744.0016.0022 6.606 28.397 8.930 301.24 91.31 0-27 95.694 104.871.0022.0030 6.605 29.570 9.254 302.66 100.28 C-28 104.796 113.665.0030.0039 6.579 28.890 8.969 503.90 109.23 0-29 117.189 125.814.0036.0044 6.542 28.640 8.740 307.41 121.50 Chloropentafluoroethane Loading No. 2. 393.11 gin. Recovered 392.26 gin. C-50 132.011 144.200.0057.0066 5.958 28.050 12.362 193.87 138.21 0-31 144.006 156.232.0066.0082 5.927 28.597 12.438 195.41 150.12 C-32 156.017 168.052.0082.0099 5.911 28.674 12.294 197.70 162.03 0-33 164.147 176.568.0089.0106 5.925 29.678 12.710 198.39 170.36 0-34 176.297 188.151.0106.0126 5.905 28.937 12.190 201.01 182.22 0-35 187.847 198.556.0126.0149 5.907 26.453 11.073 202.37 193.20 C-36 45.430 58.849.0010.0016 6.407 26.095 13.453 178.22 52.14 0-37 58.811 71.105.0016.0026 6.427 24.173 12.345 180.47 64.96 0-38 71.041 83.204.0026.0043 6.414 24.295 12.247 182.46 77.12 0-39 87.655 100.654.0031.0039 6.376 26.618 13.092 185.90 94.15 C-40 100.559 113.059.0039.0051 6.310 26.168 12.618 187.66 106.82 0-42 111.085 123.318.0038.0047 6.386 25.639 12.342 190.24 117.20 0-43 122.264 134.276.0054.0063 6.272 25.889 12.163 191.45 128.27 0-44 133.518 146.008.0059.0070 6.268 27.287 12.666 193.64 139.76 c-45 55.585 69.372.0004.0015 6.963 24.883 13.811 179.90 62.48 c.46 69.097 82.476.0015.0024 6.960 24.483 13.427 181.99 75.79 Chloropentafluroethane Loading No. 1. 188.94 gin. Recovered 188.86 gm. 0-48 54.796 68.344.0025.0038 6.790 20.022 13.611 143.24 61.57 0-49 68.039 81.038.0023.0039 6.766 19.595 13.060 145.57 74.54 0-50 80.933 93.688.0039.0056 6.727 19.661 12.848 147.62 87.31 0-52 100.790 112.112.0045.0056 5.904 20.163 11.426 149.40 106.45 0-53 111.776 123.002.0056.0068 5.881 20.307 11.352 150.87 117.39 C-54 122.838 134.652.0068.0079 5.860 21.742 11.974 152.59 128.75 0-55 138.327 149.435.0079.0091 5.486 22.145 11.296 154.23 143.88 0-56 149.228 160.826.0091.0102 5.472 235.578 11.826 156.45 155.03 0-57 159.402 170.742.0105.0118 5.452 23.319 11.600 157.17 165.07 0-58 170.390 183.314.0118.0137 5.447 26.846 13.266 158.07 176.85 0-59 182.705 194.476.0137.0155 6.777 19.852 12.o61 159.96 188.59 0-60 37.567 51.516.0006.0022 6.632 20.969 14.178 14o.66 44.44 C-61 51.247 63.684.0017.0028 6.624 18.726 12.479 142.54 57.47

162 -. — 160 158 ~/ 156 154 0 Z 152 150 -' 0 o / 148 146 144 142 40 60 80 100 120 140 160 180 200 TEMPERATURE, ~C Figure D-6. Gross Heat Capacity with Chloropentafluoroethane Loading.

-150204 - 248 2 0 2 -- -- -- --- -- -- -- -- --- -- - --- -- -- -- -- 2 4 6 200 -- - - - - - - - - - -- / 244 198 - - - - -- - - - - - - - - ~ - 242 196 - -- - -- - -- - -- - -- - - — //240 194 - - - -- - - - - - - a - -- f -- - 238 192 - 236 1 (90 -- A _ — 234 ^ o / 190 ~: 188 232: /240 186 230 184 - r —-- -- ----- --- -^ -- -- -- --- -- — ~ —-- -- 228 182 - - - - - - - - - - -- - 226 0 180 I 224 178 -- - - --- - - - - - - - - - - 22 2 220 218 40 60 80 100 120 140 160 180 200 TEMPERATURE. ~C Figure D-7. Gross Heat Capacity with Chloropentafluoroethane Loading -

APPENDIX E C-Cv* DERIVED FROM THE MARTIN-HOU EQUATION OF STATE i=5 V=5 Ai + BiT + Cj exp(-kT/Tc) ~~~~~~~~~~P s= * ---; -- "7 —— (E-l) ^il (V - b)i i=l E-l Derivation of the Basic Thermodynamic Relation For the single phase of pure substance, dA = -SdT - pdV This leads to the following Maxwell relation ~~(58^~~~~) -~= (~ ~(E-2) \.VJT \dT/v Differentiate (E-2) with respect to T at constant V, we have d, dS - (E-3) dTVdVT dVTdT.Vy T2 Since ( dS' = Cv cdTh T We obtain ((vT ) ( ) (E-4) or by substituting V = l/p, we have T(.d )T= - (d (E-5) Integrating with respect to V or p, we obtain 00 Cv-Cv* -= T () l d(V (E-6) V -151

-152or p C-C T 2 ( dp (E7) o' E-'2 - * E-2 Cv-CV Formula for Martin-Hou Equation The second derivative of Equation (E-l) with respect to T is d. k -k T C2 C3 C4 Cc -'(\P) =(-)e 2 k+{+C + (V-b+W +)5} (E-8) \dT2/ - \T/ (V-b)2 (V-b) (V-.b) (V-b)5 Combining this with Equation (E-6) we have T Cv -Cv*k 2 ek T ( + - C4 bC5 } v CVTc( Tl -b (V b) 2((V-b)2 5(V-b)3 p+4(-b) 1 V T - - e (V-b) - 2 (V-b ) + 4(v-b) -) -k Tl[ =eTe (l-bp) + -p2 2+_)3+ If C = O s in case of "the improved Martin-Hou equation," we obtain v v T ()-b 2(V-b)2 (E334), =_k T2 T~ C / v v T( ) _'p) 2(-bp)2 5(l.b)3 4(l.)-bp If C4 = 0O C5 = 0 as in the original Martin-Hou equation, we obtain c - c,-* — T^. ~(}2 -k (_c_

APPENDIX F CONSTANTS AND CONVERSION FACTORS The constants and conversion factors used in this research are summarized here for convenience. 1 calorie = 1 thermochemical calorie = 4.1840 abs. joules = 0 0412917 lit-atm. 1 Btu. = 1055.18 abs. joules = 5.4046 psi-cu ft 1 abs. watt minute = 143.405 calories T~K = t~C plus 273.16~C T~R = T~K multiplied by 1.8 = ~F + 459.69 1 atmosphere = 14.696 psi R (the universal gas constant) = 1.985 Btu/lb mole-~R = 1.98719 cal/gm mole-~K = 0.0820544. lit, atm./gm mole-~K = 10.7315 psia-cu ft/lb mole-~R h = 6.62577 x 10-27 erg sec (mol.)_ c = 2.997902 x 1010 cm sec-1 k = 1.380257 x 10-1 erg (mol.)-1 degree-1 hc/k = 1.43868 Molecular wt. of dichlorodifluoromethane = 120.924 Molecular wt. of chlorodifluoromethane = 86.476 Molecular wt. of tetrafluoromethane = 88.010 Molecular wt. of dichlorotetrafluoroethane - 170.936 Molecular wt. of chloropentafluoroethane = 154.477 -153

-154The Martin-Hou equation's constants are as follows: 1. For chlorodifluoromethane:(26) P in psi, T in ~R, V in cu ft/lb. Tc = 664.5 deg.~R., c = 32 76 lb/ft35 P = 721.906 psia A1 = 0 B1 0.12409802 A2 = -3.7887702 B2 = 1.2827656 x 10-3 A3 = 6.2780387 x 10-2 B = 1.1458314 x 10'6 A4 = -1.0017004 x 103 B4 0 A5 = 358423977 x 10'6 B5 = 3.8881629 x 10'9 1 5 C1 =0 C5 = -7.5862255 x 10-5 C2 = -355797897 b 6.5367861 x 10'~ C3 0 - 99056314 k = 375 C4 = 0 2. For tetrafluoromethane: (8) Unites are the same as above. Tc = 409,50 R, Pc = 543.16 psia, pc = 39.06 lb/cu ft A1 = 0 B1 0*12193362 A2 = -3.1553788 B2 = 3.2480704 x 103 A = 0.05630627 B = -5.6586787 x 10-5 A4 = -3.157538 x 10 4 B4 = 0 A5 -1.5210836 x 10l6 B = 6.6533754 x 10"9 C1 = 0 C5 = -3.5786565 x 10-6 C2 = -21911976 b = 5.7104970 x 10-3 C3 = -0.052630252 k = 5.0 C4 = 0

-1553. For dichlorotetrafluoroethane.25) Units are the same as before* Tc = 753-95:R, PC a 475.187 psia, Pc = 36.32 lb/cu ft. A1 3 O B = 0o627808 A2 -2.3856704 B2 = 00010801207 A3 = 0.034055687 B3 = -53336494 x 10-6 A4 =-3.5857481 x 104 B4 = 0 A5 = 16017659 x 10"6 B5 = 6.263234 x 10-10 C1 -0 C5 = -1*0165314 x 10"5 C2 = -6.564348 b = 0i005914907 C3 016566057 k 5 3.0 C4 0 4. For dichlorodifluoromethane(3 4) Units are the same as before. Tc = 699.35R, Pc 596.9 psia, Pc = 34.84 lb/cu ft A1 = 0 B1 - 0.088734 A2 = *5 49727154 B2 = 1.59434848 x 10lo A3 = 0.06023944654 B3 = -1.879618431 x 10-5 A4 - -5.4873007 x 10'4 B4 - 0 A5 = B5 = 3.46883400 x 10-9 1 = 0 5 = -2.54390678 x 10'5 2 = -56.7627671 b - 0*0065093886 C3 = 1.311399084 k = 5.475 C4 0

"156No Martin-Hou equation has been developed for chloropentafluoroethane. Martin et al, (30) however, correlated PVT data in the following form: 3.1857748 0.028919059 17.4448 x 10-6 V 2 V3 V ro.o6941 +0.00267975 1.18424 x 10"5 1.67627 x 10-7] + T + -2 3 v4 1 8343505 598499031 " T3 L V2'v4

BIBLIOGRAPHY 1, Albright, L. F., Galegor, W. Co and Innes, K, K., J. A, C. S. 76 6017 (1954). 2. Amagat, E. H., Annales de Chimie et de Physique, 5e series, xxii, 353-389 (1881). 3. American Society for Metals, Metal Handbook, Cleveland, 555 (1948). 4. Barcelo, J. R., J. of Research, N. B. So, 44, 521, RP 2099 (1950). 5# Beattie, J. A,, and Bridgeman, 0 C., Proc. Am. Acad. Arts and Sci. 63, 229-308 (1928). 6* Benedict, W. Webb, G. B*, and Rubin, L. C,, J, Chem. Physics, 8, 334 (1940)) and 10, 747 (1942). 7, Bennewitz, K. and Splittgerber, E,, Z. Physo Chem,, 124, 49-68 (1928) 8. Bhada, R. K., The Construction and Operation of a Variable Volume Isothermal Bomb for Determining the PVT Behavior of Gases and Liquids, Ph, D, thesis, Univ. of Mich, (1960). 9. Chari^ N. C, S,, Thermodynamic Properties of Carbon Tetrafluoride, Ph, D. thesis, Univ. of Mich. (1960). 10. Connolly, T. J., Sage, B, H, and Lacey, W. N., Ind. Eng. Chem. 43, 946 (1951)o This is the most recent one in the long series. 11i Curtiss, C. F., Boyd, C, A,,and Palmer, H. B., J, Chem. Phys., 19, 801 (1951). 12. de Nevers, N. H,, The Constant Volume Heat Capacity of Gaseous Perfluorocyclobutane and Propylene, Ph, D, thesis, Univo of Micho (1958), 13. de Nevers, N. H, and Martin, J. J., A. I. Ch. E. J., 6, 43-49,(1960). 14, Dieterici, C., Ann. der Physik, 12, 145-185 (1903)4 15. Dodge, B. F., Chemical Engineering Thermodynamics, McGraw-Hill, N. Y*, p. 167 et seq. (1944). 16. Eucken, A. and Hauck, F*, Za Phys. Chem,, 134, 161-189, (1928). 17. Gelles, E. and Pitzer, K. S., J. A, C. S. 75, 5259-5267 (1953)o 18. Glockler, G. and Sage, C., J, Chem. Phys., 9, 387, (1941). 19* Goubeau, J., Bues, Wo and Kampmann, F, W,, Z. Anorg. Allgem. Chem,, 283, 123 et seq. (1956). -157

W15620, Hoge, H. Jo, J Res. NBS, 44 321 (1950). 21, Hoge, Ho Jo, Review Sci. Instrument, 20, 59-61 (1949), 22, Joly, J., Proc, Roy, Soc,, 55, 390 (1894), 23, Keenan, J, H., Thermodynamics, John Wiley, N. Y,, p. 409 (1941), 24, Kilpatrick, Jo. H and Pitzer, K, S., J, of Res, NBS, 37, 163 (1946). 25, Martin, J. Jo, J, Chem, and Engo Data, 5, 334-336 (1960)o 26, Martin, Jo J^, Gifford. M, J. Welshans, L. M, and Gryka, G, E., Thermodynamic Properties of Chlorodifluoromethane, Univ. of Mich. Res, Inst* Project No, M777, Ann Arbor, Mich, (1953). 27. Martin, J, Jo and Hou, Yo C,, A, I, Cho E. Journal, 1 142-151 (1955), 28. Martin, Jo J,, Kapoor, R. Mo. Bray, B, G, Salive, M, L. and Bhada, R, K,, Data and Equation for the Thermxodynamic Properties of "Freon-C 318" Perfluorocyclobutane, Univd of Mich, Eng, Res, Inst,. Report No. 1777-29-T, Ann Arbor (1956) 29 Martin, J, J,, Kapoor, R, M* and de Nevers, N,, A. I, Ch, E, 5, 159-160 (1959), 30. Martin, J, J,, Long, R, D*, Marks, J, D., Service, W. J*, Jr., Taylor, Ro C, and Weaver, D. E,, Thermodynamic Properties of "Freon115" Univ. of Mich, Eng, Res. Inst, Report, Proj. No. M777, Ann Arbor (1951). 31, Martin, J, J Long, R. D. and Service, WA J,, Jr., physical and Thermodynamic Properties of Various "Freons". Univ, of Mich, Eng, Res. Inst. Report, Proj. No. M777, Ann Arbor (1951). 32, Masi, J. F., JACS, 74, 4738 (1952)o 33. McCullough, J, P,^ Finke, H. L:, Hubbard. W* N., Good, W, Do, Pennington, R. E., Messerly, J. F. and Waddington, G., JACS, 76, 2661 (1954). 34, McHarness, R, C,, Eiseman, B. J*, Jr., and Martin, J, J., Refrig. Eng.63, 31 (1955). 35. Michels, A, and Strijland, J., Physica, 18, 613-628 (1952)* 36. Osborne, N. S,, Stimson, H, F. and Sligh, T. S., Jr,, Sci, Papers of NBS, Number 503 (1924). 37, Pall, D, B., and Broughton, J. W*. Canadian J. of Research, A-16, 230, 449 (1938).

-159384 Pitzer, K, So and Gelles E,, The Vibrational Frequencies of the Halogenated Methanes and the Substitution Product Ruld API Res. Proj. No. 50, Univ, of Calif, (1952). 39, Reinganum, M., Ann. der Physik, 18, 1008 (1905). 40o Schaefer, K., Fortschritt Chem, Forsch,, 1, 61-118 (1949)o 41, Schneider, W. Go and Chynoweth, A., J, Chem. Phys., 19, 1607 (1951). 42. Smith, D. C., Alpert, M., Saunders, R. A,, Brown, G* M. and Moran, N. B,- Infrared Spectra of Fluorinated Hydrocarbons Naval Res. Lab, Report, 3924 (1949), 43 Smith, D, Co, Nielsen, Ji R., Berryman, L, H., Claasen, H. H., and Hudson, R. L.,.Spectroscopic Properties of Fluorocarbons and Fluorinated Hydrocarbons, Naval Research Laboratory Report 3567, ( 1949). * 44. Trautz, M. and Grosskinsky, 0., Ann* der Physik, 67, 462 (1922). 45* Weissman, H. B,, Meister A. G, and Cleveland, F, Fo, J. Chem. Phys,, 29, 72-77 (1958), 46, Young, S., Proc. Phys. Soc. London, 602 (1894-5).

UNIVERSITY OF MICHIGAN II3 9015 03025 144411111111 I 3 9015 03025 1444