T H E U N I V E R S I T Y 0 F M I C H I G A N COLLEGE OF ENGINEERING Department of Chemical Engineering Technical Report CALORIMETRIC STUDIES ON ARGON AND HEXAFLUORO ETHANE AND A GENERALIZED CORRELATION OF MAXIMA IN ISOBARIC HFAT CAPACITY Kwan Y. Kim DRDA Project 003470 Supported by: NATIONAL SCIENCE FOUNDATION GRANT NO. GK-24719 WASHINGTON, D.C. administered through: DIVISION OF RESEARCH DEVELOPMENT AND ADMINISTRATION ANN ARBOR January 1974

To my mother, Mrs. Chong Kil Yi and My wife, Hae Rim ii

ACKNOWLEDGEMENTS I wish to express my appreciation to the following people who contributed to the success of this work: To Professor John E. Powers, the chairman of my thesis committee, for his guidance and encouragement. To Professors Dale E. Briggs, James H. Hand and Edgar F. Westrum, Jr., for serving on the doctoral committee. To Joseph C. Golba who contributed to this work by assisting in all phases of the experiments. To Andre W. Furtado for many suggestions which involved the present work. To Takaya Miyazaki for his help during the measurements of C2F6. To E. Ruke and H. Senecal of the ORA Instrument Shop and D. Connell of the Chemical Engineering Department for their shop services. I also wish to acknowledge the following organizations: The National Science Foundation for support of the research and for provision of fellowships; the E. I. du Pont de Nemours & Co. for the donation of Freon-116 used in this work. Finally, I would like to thank my mother, my wife and my daughter for their faith in me. iii

TABLE OF CONTENTS Page DEDICATION................................................... ii ACKNOWLEDGEMENTS.............................................. iii LIST OF TABLES............................................... vii LIST OF FIGURES.............................................. ix NOMENCLATURE................................................ xiii ABSTRACT...................................................... xvi I. INTRODUCTION............................................ II. PRELIMINARY CONSIDERATIONS.............................. 3 Thermodynamics of Flow Calorimetry...................... 3 Data Interpretation..................................... 8 Thermodynamic Consideration for Basic Data......... 9 Constructing Equal Area Curve...................... 12 Interpretation of Joule-Thomson Data............... 13 Thermodynamic Consistency Checks.................... 14 Error Analysis..................................... 15 Corresponding States Principle.......................... 15 Significance of Cp(T) Maxima............................ 19 Previous Studies on Cp(T) Maxima........................ 22 Choice of Experimental Fluids.......................... 23 Previous Experimental Data for Argon............... 24 Previous Experimental Data for C2F6................. 27 III. CALORIMETRIC DETERMINATIONS WITH ARGON.................. 28 The Recycle Flow System................................ 28 Calorimeters............................................ 31 Experimental Measurements............................... 31 iv

Page Experimental Procedure................................. 40 Material Used.......................................... 41 Region of Measurements............................... 42 Results................................................ 45 Cp and Cp(T) Maxima................................ 48 Isenthalpic and Isothermal Data.................... 53 Enthalpy Changes on Vaporization................... 56 Heat Leak Check.................................... 60 Thermodynamic Consistency Checks................... 60 Enthalpy Table and Diagram......................... 63 Comparison With Other Published Data............. 68 IV. CALORIMETRIC DETERMINATIONS WITH HEXAFLUOROETHANE...... 75 New Recycle Flow System................................ 75 Multipurpose Calorimeter................................ 78 Experimental Measurements............................... 80 Material Used.................................83 Region of Measurements................................. 84 Determination of Liquid Densities...................... 84 Results............................................... 91 Cp and Cp(T) Maxima............................... 91 Isothermal Data................................... 97 Enthalpy Changes on Vaporization....................... 101 Thermodynamic Consistency Checks.................. 101 Enthalpy in the Critical Region.................... 101 Enthalpy Table and Diagram................................. Comparison With Previous Experimental Data......... 1 110 v

Page V. GENERALIZED CORRELATION FOR Cp(T) MAXIMA............... 115 Data for Correlation.................................... 115 Location of Cp(T) Maxima................................. 119 Magnitude of Cp(T) Maxima............................ 119 Discussion of Results................................... 125 VI. SUMMARY AND CONCLUSION................................. 128 VII. RECOMMENDATIONS FOR FUTURE WORK......................... 129 APPENDIX A.................................................... 131 APPENDIX B..................................... 138 APPENDIX C.................................................... 149 REFERENCES............................................. 169 vi

LIST OF TABLES Table Page II-1. A List of Fluids Suitable for Use in the Present Equipment.......................................... 35 III-1. Composition of Argon.............42 III-2. Isobaric Heat Capacities of Argon.............51 III-3. Cp(T) Maxima Data for Argon................53 III-4. Joule-Thomson Coefficients of Argon at -240F....... 55 III-5. Enthalpy Difference of -240~F Isotherm Calculated From the Isenthalpic Data........................... 55 II-6. 0(P) Maxima Data for Argon........................... 56 III-7. Isothermal Throttling Coefficients of Argon......... 58 III-8. Saturation Data for Argon............................* 0 III-9. Tabulated Values of Saturation Enthalpy for Argon.... 65 III-10. Tabulated Values of Enthalpy for Argon........ 66 III-11. Comparison of Isobaric Heat Capacities of Argon..... 69 IV-1. Composition of C2F6..* —** —*** —-- 83 IV-1. Composition of C2F6.................................. 83 IV-2. Isobaric Heat Capacities of C2F6.................... 92 IV-3. Cp(T) Maxima Data for C2F6.......................... 97 IV-4. 0(P) Maxima Data for C2F6..................97 IV-5. Isothermal Throttling Coefficients of C2F6...... 98 IV-6. Comparison of Saturation Data for C2F6.............. 102 IV-7. Enthalpy of C2F6 Near the Critical Point............. 107 IV-8. Critical Constant for C2F6.......................... 110 IV-9. Tabulated Values of Saturation Enthalpy for C2F6.... 112 IV-10. Tabulated Values of Enthalpy for C2F6............... 113 V-1. Sources of Cp(T) Maxima and Cp~ Data............... 116 P P 116~~~ vii

Table Page V-2. Data Used in the Present Correlation.................. 117 V-3. Critical Constants for the Substances Used in This Work...................................... 118 V-4. Comparison of the Data With Values Determined From the Correlation................................ 126 V-5. Mean and Standard Deviations for (TM - TM ).......127 exp caic 127 A-1. Calibration Constants for Platinum Resistance Thermometer........................................... 132 A-2. Calibration Data for Thermopiles...................... 133 A-3. Pressure Transducer (high) Calibrations............... 134 A-4. Pressure Transducer (low) Calibrations................ 135 A-5. Flow Meter Calibrations............................. 136 A-6. Density Data of C2F6 at F........................... 137 B-1. Basic Isobaric Data for Argon........................ 139 B-2. Basic Isothermal Data for Argon.................... 144 B-3. Basic Isobaric Data for C2F6......................... 145 B-4. Basic Isothermal Data for Argon....................... 148 C-1. Cp Values for Argon................................... 150 C-2. p Values of Argon................................. 159 C-3. d Values for Argon................................... 159 C-4. Enthalpy Traverse Data for Argon...................... 161 C-5. Cp Values for C2F6......................163 C-6. Values for C2F6................................... 167 C-7. Enthalpy Traverse Data for C2F6....................... 168 viii * * V 1 1

LIST OF FIGURES Figure Page II-1. A Schematic Diagram for a Flow Calorimeter............ 4 11-2. Schematic Diagram Illustrating the Calorimeter assemblies used in this work....................... 5 11-3. Example of an Isobaric Run............................ 11-4. Example of an Isothermal Run......................... 11 11-5. An Illustration of Cp(T) Curves in the Supercritical Region...................................... 20 II-6. Plot Showing the Location of Cp(T) Maxima............. 20 III-1. Flow Diagram of the Recycle-Flow System Used for the Measurements With Argon.............................. 29 III-2. Pressure Transducer (High) Calibration................ 34 III-3. Pressure Transducer (Low) Calibration................. 34 III-4. A Modified Circuit of Power Input to the Calorimeter.. 36 111-5. Flow Meter Calibration................................ 39 III-6. Comparison of the Present 1ow Meter Calibration with a Generalized One by Furtado.......................... 39 III-7. Chromatographic Analysis of the Argon Sample from the System............................................ 43 III-8. Range of Calorimetric Determination on Argon......... 44 III-9. Isobaric Heat Capacity for Argon at 286 psia......... 47 III-10. Isobaric Heat Capacity for Argon at 457 psia.......... 47 III-11. Isobaric Heat Capacity for Argon at 571 psia......... 47 III-12. Isobaric Heat Capacity for Argon at 1143 psia......... 48 III-13. Isobaric Heat Capacity for Argon at 706 psia......... 49 III-14. Isobaric Heat Capacity for Argon at 950 psia.......... 49 III-15. Isobaric Heat Capacity for Argon at 800 psia......... 49 III-16. Isobaric Heat Capacity for Argon at 1371 psia........ 50 ix

Figure Page III-17. Isobaric Heat Capacity for Argon at 1714 psia........ 50 III-18. Isobaric Heat Capacity for Argon at 2000 psia........ 50 III-19. Joule-Thomson Coefficient for Argon at -240~F........ 54 III-20. Isothermal Throttling Coefficient for Argon at -168.3~F 54 III-21. Isothermal Throttling Coefficient for Argon at -208.9~F 57 III-22. Isothermal Throttling Coefficient for Argon at -191.2~F 57 III-23. Isothermal Throttling Coefficient for Argon at 167~F.. 57 111-24. Isobaric Enthalpy Traverse Across the Two Phase 59 Boundary for Argon at 457 psia..................... III-25. Isobaric Enthalpy Traverse Across the Two Phase Boundary for Argon at 286 psia......................... 59 III-26. Isobaric Enthalpy Traverse Across the Two Phase Boundary for Argon at 571 psia....................... 59 III-27. Heat Leak Test for the Isobaric Calorimeter. Mean Heat Capacity of Argon as a Function of Reciprocal Flow Rate........................... 61 III-28. Thermodynamic Consistency Checks for the Present Calorimetric Data for Argon......................... 62 III-29. H-P-T Diagram for Argon.............................. 64 III-30. Comparison of the Present Isobaric Heat Capacities With Those from Walker60.............................. 73 III-31. Comparision of the PresentIsobaric' Heat Capacities With Those from Michels et al.8, 39................. 73 III-32. Comparison of the Present Isobaric Heat Capacities With Those Calculated from the Equation of State by Gosman et al.,............................7 73 III-33. Comparison of the Present Isobaric Heat Capacities in the High Temperature Region with Those From Michels, et al., 39............. 74 III-34. Comparison of the Present Enthalpies with the Tabulated Values from IUPAC.......................... 74 x

Figure IV-1. IV-2. IV-3. IV-4. IV-5. IV-6. IV-7. Flow Diagram of the New Recycle-Flow System........... Diagram Illustrating the Principle of the Multipurpose Calorimeter........................ Drawing of the Multipurpose Calorimeter Assembly..... Range of Calorimetric Determinations on C2F6......... Diagram Illustrating the Measurement of Liquid Density Arrangement for the Liquid Density Measurement....... Plot of Liquid Densities for C2F6 at 0~F............. Page 76 79 81 85 86 88 90 IV-8. Isobaric Heat Capacity for IV-9. IV-10. IV-11. IV-12. IV-13. IV-14. IV-15. IV-16. IV-17. Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Isobaric Heat Capacity Capacity Capacity Capacity Capacity Capacity Capacity Capacity for for for for for for for for C2F6 at C2F6 at C2F6 at C2F6 at C2F6 at C2F6 at C2F6 at C2F6 at C2F6 at 490 psia.......... 437 psia........... 442 psia.......... 247 psia.......... 432 psia.......... 700 psia........... 839 psia.......... 1049 psia.......... 1398 psia......... 93 94 94 95 95 95 96 96 96 96 99 99 100 100 100 103 103 Capacity for C2F6 at 1969 psia......... IV-18. Isothermal Throttling Coefficient for Argon at F... IV-19. Isothermal Throttling Coefficient for Argon at 67.5~F. IV-20. Isothermal Throttling Coefficient for Argon at 122~F. IV-21. Isothermal Throttling Coefficient for Argon at 176~F. IV-22. Isothermal Throttling Coefficient for Argon at 247~F. IV-23. Isobaric Enthalpy Traverse Across the Two Phase Boundary for C2F6 at 247 psia......................... IV-24. Isobaric Enthalpy Traverse Across the Two Phase Boundary for C2F6 at 432 psia........................ xi

Figure Page IV-25. Thermodynamic Consistency Checks for the Present Calorimetric Data for C2F6........................... 104 IV-26. Plots of Enthalpies at C (T) Maxima and Average Enthalpies at Saturation Points as Function of Pressure (C2F6)..................................... 106 IV-27. Plot of Enthalpies for C2F6 in the Critical Region... 106 IV-28. Plot of the Saturation Line Near the Critical Point, Cp(T) Maxima and 0(P) Maxima........................ 109 IV-29. H-P-T Diagram for C2F................................ 111 V-1. Plot of Cp(T) Maxima Locations in Pr-Tr Coordinates.. 120 V-2. Plot Showing the Correlation for the Location of Cp(T) Maxima.................................. 121 V-3. Plot for the Cp(T) Maxima on zn Pr - in (CpM -Cp)/R Coordinates............................. 122 V-4. Plot Showing a Correlation for the Magnitude of Cp(T) Maxima on Intermediate Coordinates........... 124 V-5. Plot Showing the Final Correlation for the Magnitude of Cp(T) Maxima................................... 124 xii

a, b, a, b, a, b c, d, D c, d A, B, C, D A, B, C, D A', B', C', D' A, B B Cp Cp(T) Maximum M Cp 0 CP UP Cp d E emf f F 9 h H k k m NOMENCLATURE Constants in Equation (V-3) Constants in Equation (IV-1) Constants for the viscosity-density isotherm (Equation (III-4)) Constants in pressure transducer calibration (Equation III-1)) Constants in flow meter calibration (Equation (III-5)) Constants in flow meter calibration (Equation (III-6)) Constants in Equation (V-l) Second virial coefficient Isobaric specific heat capacity Maximum of Cp along isobar Magnitude of Cp(T) maximum Cp at zero pressure Mean value of Cp over some temperature interval Deviation defined in Equation (III-9) Voltage Electromotive force Factor defined in Equation (V-2) Mass flow rate Function defined by Equation (V-3) Plank's constant Specific enthalpy Boltzmann's constant Constant in Equation (III-8) molecular mass xiii * * xl1 1

N pM P Q R T TM V V X1, X2,..., Xn X1, X2,..., Xn Xn x x x Y Y z Avogadro's number Pressure Pressure of the C (T) maximum P Quadrupole moment Rate of heat transfer Gas constant Temperature Temperature of the Cp(T) maximum Volume Volt Rate of work done Variables in Equation (II-16) Variables in Equation (II-17) Variable in Equation (III-6) Variable defined in Equation (V-3) Variable in Equation (IV-1) Variable in Equation (IV-1) Variable in Equation (IV-2) Compressibility factor Polarizability Riedel factor A measure of deviation of intermolecular potential from that of simple fluids Third parameter defined in Equation (11-24) Intermolecular parameter known as minimum energy a TC co xiv

A VP 11 p p a 0 0 0(P) maximum Subscripts C 0 r sat vap Difference Dipole moment Joule-Thomson coefficient Viscosity Micro (106) Mean value of u Density Intermolecular parameter known as collision diameter Summation Isothermal throttling coefficient Mean value of 0 in some pressure interval Maximum of 0 along isotherm Acentric factor Critical point property Reference state Reduced property Saturation property Vaporization Inlet condition Outlet condition Units Used in This Work 1 2 Conversion Factors for 1 atm = 14.696 psia 1 Btu = 1055.87 Joules 1 cu ft = 28317 ml 1 lb = 453.592 g ~R = ~F + 459.67 R = 10.73147 psi ft3/~R - lb mole XV

ABSTRACT CALORIMETRIC STUDIES ON ARGON AND HEXAFLUOROETHANE AND A GENERALIZED CORRELATION OF MAXIMA IN ISOBARIC HEAT CAPACITY by Kwan Young Kim Chairman: John E. Powers The objectives of this research are: (1) To conduct calorimetric measurements on argon and hexafluoroethane. Experimental range for argon covers temperatures between -240~F and 220~F and pressures up to 2000 psia. For hexafluoroethane it covers temperatures between 0~F and 250~F and pressures up to 2000 psia. (2) To develop a generalized correlation for Cp(T) maxima based on the existing Cp(T) maxima and the ones obtained from the present experimental work. The equipment used in the measurements with argon was a recycle flow system utilizing a Corblin diaphragm compressor for recycling the fluid. Two calorimeters, an isobaric and throttling calorimeter, were used interchangeable in the system. The basic calorimetric measurements were interpreted to yield smoothed values of enthalpy, isobaric heat capacities, maxima of isobaric heat capacity, isothermal throttling coefficients, JouleThomson coefficients (with an inversion point at -240~F) and enthalpy changes in vaporization. Enthalpy-pressure-temperature table and diagram are prepared. The data are internally self-consistent to about 0.09%. Measurements with hexafluoroethane were made at the new recycle flow system with double-acting precision metering pumps and a multipurpose calorimeter which can be used for both isobaric and throttling modes of operation. The data obtained were smoothed values of enthalpy, isobaric heat capacities and their maxima, isothermal throttling coefficients. In addition, extensive measurements of enthalpy in the critical region were made and the critical constants were determined from these measurements. Enthalpy-pressure-temperature table and diagram were prepared. The data were internally self-consistent to about 0.03%. Cp(T) maxima data obtained in this research and existing data in the literature were used to develop a generalized correlation within the three xvi

parameter corresponding states principle making use of the Riedel factor, aC' as the third parameter. Correlational effort was divided into two parts: (1) Correlation of locus of Cp(T) maxima and (2) Correlation of magnitude of Cp(T) maxima. The correlation covers satisfactorily the data for substances with widely different physical properties including hydrocarbons, C02, and H20 as well as argon and C2F6. xvii

I - INTRODUCTION Importance of a knowledge of thermal properties for fluids in a wide range of temperature and pressure has been well acknowledged by many engaged both in industrial and theoretical fields. To both designers and engineers in charge of process operation and maintenance, having sufficient thermal property data for their working fluids is essential because it is directly related to the economic and operational concerns. In the field of thermodynamic research, accurate thermal property data are needed in testing theories of fluid behavior or in correlating these data. In the past, however, people in the area of experimental research on thermodynamic properties were mainly concerned with the measurements of PVT behavior of fluids. Consequently, while PVT data are available for many substances in wide temperature and pressure ranges, thermal property data are available only for a few substances, especially at elevated pressures. Obtaining the thermal properties from the PVT, however, requires differentiation and integration steps, which would cause errors and sometimes they are too significant to be acceptable. Therefore, it is desirable to obtain the thermal property data directly from calorimetric measurements. The Thermal Properties of Fluids Laboratory at the University of Michigan has been the source of thermal property data for a number of hydrocarbons, nitrogen and their mixtures for the past decade with a recycle-flow calorimetric facility capable of producing accurate data for wide ranges of pressure and temperature. Recently, a new facility has been developed and tested for its performance in the course of Ph.D. thesis work by Miyazaki.34 The new facility turns out to be simpler and more economical to operate, and it is capable of producing highly accurate data. As noted earlier, thermal property data and Cp data in particular are scarce in the region of elevated pressures and especially in the supercritical region where most rapid changes in Cp occur. This region includes the neighborhood of Cp(T) maxima curve, the loci of Cp maxima on isobars, mathematically those satisfying (aCp/T)p = 0, projected on -1

-2 P-T plane. Therefore, most of the existing correlations for Cp, which are based on the Cp values derived from PVT data, give worse predictions in this region. For example, some Cp values in the vicinity of the Cp(T) maxima curve estimated from the generalized correlation by Edmister 1 (which is based on PVT data for hydrocarbons) differ from the direct C data18' 34 61 by as high as 100%. It is felt that a correlation of Cp(T) maxima will contribute significantly to the improvement of existing Cp correlation and, it can be an important first step to developing a new generalized Cp correlation to be based on the direct Cp data. Therefore the objectives of the present research are (1) to contribute to the existing knowledge of the thermal properties of fluids by obtaining accurate data of some pure fluids (argon and hexafluoroethane) through carefully conducted experiments with the available calorimetric facilities, and (2) to make contributions in the area of predicting thermal property data by obtaining extensive Cp(T) maxima as well as Cp data and correlating them with existing Cp(T) maxima data in the literature.

II - PRELIMINARY CONSIDERATIONS Before undertaking the research, a study was made on the information applicable to the present investigation, and the results are presented in this section. The first part of this section is devoted to a review of thermodynamic relations fundamental to the description of flow calorimeters, such as the ones used in the present experiments. A discussion is also made on the techniques applied to interpreting the basic data to obtain smoothed enthalpy and its derivatives such as Cp, 0 and v. The second part of the section presents a review of the matters relevant to the present goal of correlating the Cp(T) maxima. The corresponding states principle is chosen as the framework of the correlation because it has been recognized as one of the most useful tools in the area of thermodynamic correlations. In a comparative test of calorimetric enthalpy data with existing prediction methods, Powers42 demonstrates that the corresponding states correlations yield highly accurate estimates of enthalpy for CH4, C3H8, N2 and He in most of the P-T region where comparisons are made. In another case Furtado confirms the corresponding states principle as a successful means for predicting and representing the enthalpy of ethane. The last part of the section presents a discussion on the choice of experimental fluids, argon and C2F6, among others. Some other fluids which could be subjected to the experimental investigation in the existing facility are presented as the future reference. It also presents a review of the previous data on argon and C2F6, which are relevant to the present investigation. Thermodynamics of Flow Calorimetry The principle of the flow calorimeters, such as the ones used in the present work, can be illustrated with the following simple schematic: -3

-4 Heat Leak, Q Mass Inlet Stream |> Outlet Stream Flow Rate IF T1 P1 T2, P2 Electrical Energy input Figure II-1. A Schematic Diagram for a Flow Calorimeter At a steady state operation of a nonreacting fluid, the first law of thermodynamics gives the following relation for the calorimeter with negligible potential and kinetic energy effects: H - H = (Q - W)/F (II-1) -2 -l where H = specific enthalpy of the fluid Q = the rate of heat leak W = the rate of electric energy input F = the mass flow rate The schematic drawing for the calorimeter assembly used in the measurements of argon is presented in Figure II-2(a). The calorimeter, C, is encased in a metal container (D) which is evacuated to a few micron vacuum to minimize convection heat transfer between the calorimeter and its container. Differential thermopiles are placed between the inlet (A) and outlet (B) junctions to measure the temperature difference across the calorimeter. Pressure taps are connected to these junctions for inlet and outlet pressure measurements. The calorimeter assembly is immersed in a constant temperature bath maintained at the inlet

(b) I Figure II-2. Schematic diagram illustrating the calorimeter assemblies used in this work.

-6 temperature, T1. The inlet junction is separated from the calorimeter by a mechanical partition in order to prevent the radiation from the calorimeter. The calorimeter and the outlet junction are surrounded by a radiation shield (E) wrapped with heating wire, a so-called guard heater. For nonisothermal operations, electrical energy is added to the guard heater and is adjusted until a differential thermocouple between the shield and the calorimeter, as monitored by a galvanometer, indicates zero temperature difference. In this case Q should be practically zero. A schematic drawing for the calorimeter assembly used for the measurements of C2F6 is presented in Figure II-2(b). In this case, the calorimeter (C) and the outlet junction (B) are surrounded by the coils (E and F) through which the fluid enters the calorimeter. The outlet junction (B) is again surrounded by the coil (G), through which the fluid from the calorimeter flows. Most of the heat radiated from the calorimeter to the coils E and F is absorbed by the fluid stream, which travels to the calorimeter, and consequently heat loss Q should become very small. When the calorimeter is operated in such a way that Q becomes negligibly small, Equation (II-1) reduces to -W H H- - -2 — 1 F (11-2) For the pure fluid, which is the case of the present investigation, in the absence of unusual force fields, H = H(T1, P1) H2 = H(T2, P2) Since H is a point function, Equation (11-2) can be rewritten as

-7 [H(T1 P2) -1)+ H(T2, P2) + H(T1, P 2) (11-3) The first and second square brackets represent respective isothermal and isobaric changes of enthalpy. As Cp and 0 are defined as P Th (PH) C p =aTP P, (II-4) Equation (II-3)can be rewritten as 2 2 ( 0(T, P) dP + Cp(T, P2) dT = (II-5) P1 T1 Equations (11-3) and (11-5) are valid within a single phase. In case of measurements across the phase boundary, it is necessary to use the more general form: P T Psat Tsat 0(T1 P) dP + I Cp(T, P2) dT + AH P1 T1 P T (II-6) + f (Tp3 P) dP + Cp(T, P) dT (I1-6) Psat Tsat where AH is the enthalpy change by vaporization at T and P -vap sat sat It can be seen from Equation (II-5) that the calorimeter can be specified so only one term in the left hand side of the equation is dominant. For example, the pressure drop across the isobaric calorimeter is made as small as possible so that the second term is dominant. Thus, the measurements of electrical energy input, W, and flow rate yield an integral average of Cp between the temperatures T1 and T2. In the isothermal calorimeter a sizeable pressure drop is made as the fluid is throttled

-8 through a capillary coil of fixed length and diameter. An adjustable quantity of electrical energy is added to the fluid stream to maintain T2 as close to T1 as possible. In this case the first term should dominate over the second and the electrical energy input provides us with an integral average of 0 between the pressures P1 and P2. In cases where a pressure drop causes a rise in the fluid temperature, an isothermal operation is not possible as it requires the removal of energy from the throttled fluid. It is then necessary to operate the calorimeter in the isenthalpic mode. No electrical energy is added in this case and the guard heater is heated to bring the shield temperature to that of the calorimeter outlet section so as to reduce Q to essentially zero. Then Equation (11-5) simplifies to T2 P2 Cp(T, P2) dT = - 0(T1, P) dP (11-7) T1 P1 or Cp(T1 T2; P2) * (T2 - T1) = -0(T1; P1 P2) (P2 - Pl). (11-8) Therefore, the measurements of T1, P1, T2 and P2 define the mean adiabatic Joule-Thomson coefficient as T2 - T1 -0(T1; P1, P2) p(T1, T 12; P P2) -P2 - P1 (T1 T2 P2)-9) Data Interpretation Practically it is not possible to avoid pressure changes and temperature changes, however small, completely from the actual isobaric and isothermal operations. During a series of isobaric (or isothermal) measurements inlet pressures (or inlet temperatures) can change slightly from the reference pressure (or temperature) depending on the operation

-9 condition. Therefore, those effects should be compensated from the basic data before Cp or 0 values are determined. Thermodynamic Consideration for Basic Data If the reference pressure for an isobaric run is P0, then every data point in the run at slightly different inlet pressure P1 must be corrected to P0. The small pressure drop (P1 - P2) must also be compensated. The desired enthalpy difference can be expressed as H(T2, P0) -H(T1, P0) = {H(T2, P2) - (T1, P1)} + {H(T2, PO) - H(T2, P2)} + {H(T1, P) -(T1, P0)}. (II-10) The first term is the actual measured enthalpy difference [see Equation (11-5)] and the othersare correction terms. Equation (II-10), when rewritten in terms of the appropriate enthalpy derivatives, becomes P0 Pl H(T2, PO) - H(T1, PO) = l + 0(T2, P) dP + 0(T1, P)dP. (II-11) P2 P0 Therefore, the mean heat capacity over the interval between T2 and T1 may be determined as P0 p(T1, T2;P0) T + 02(T P) dP + { 0(T1, P) dPi P0

-1 0 Similarly, for an isothermal run with TO as the reference temperature, we have ~ 0 H(T, P2) - H(TO P1) i + J Cp(T, P2) dT T, ~T2 + f Cp(T, P1) dT. (II-13) TO0 The mean isothermal throttling coefficient over the interval P2 and P1 may be determined as 0(To; P1' P2) P2- Cp(T. P dT T2 1. T 2 + f C(T, P1) dT. (11-14) As an isobaric run (see Figure II-3) consists of a series of measurements where the inlet conditions are held fairly constant, the corrected basic data may be differenced with additional corrections for small inlet temperature variations. Suppose we choose two data points i and j with inlet temperatures Tli and Tlj, and outlet temperatures T2i and T2j, respectively. If To is the reference inlet temperature of the run, then the mean heat capacity over the interval between T2i and T2j is given by

-11 ISOBARRIC MERN HERT CAPRCITY C2F6 598. PSIR o cU ao 0) 0 CO o co CD - 0 00 O o C') o 0. 60. 75, 90. 105. 120. TEMPERRTURE (OF) Figure II-3. Example of an isobaric run.'/S. 1000. 1iSO. 1500. PRESSURE (PS R) Figure 11-4. Example of anl isothermal runl.

-12 IT -T -(T- TTlj T -|2'i i C(T T P ) + T li'T P T2j T~ii p li' 2i' 0,Tj - Tpi| P li' Tg; 0 -IT j- Cp(Ti Tl; PO). (II-15) The mean heat capacities given by Equation (II-12) are solid horizontal lines while those in Equation (11-15) are dotted lines, as shown in Figure 11-3. A smoothed heat capacity curve is drawn along the entire isobar under the constraint that the area under the horizontal lines is equal to the area under the smoothed curve. The mean isothermal throttling coefficients given by Equation (II-14) are shown in Figure 11-4. A smoothed 0 curve is constructed along the entire isotherm with the same "equal area" constraint that is imposed on Cp. Constructing Equal Area Curve Constructing equal area curves for Cp and 0 from the basic data is the most crucial part of the data reduction since it is the data interpreted from the curves that constitute the result of the whole experimental activity. Several techniques related to this matter appear in the works of previous investigators.3' 18 34, 61 An excellent review on the merits and deficiencies of those techniques are presented in Furtado's work.l8 The most reliable technique at the present time appears to be the one proposed by Furtado,8 and it is adopted for use in the present work. A detailed description of the technique can be found in the original work, and it need not be elaborated here. Instead, an outline of the technique is introduced briefly. This technique, so-called computer aided graphical technique, employs a graphic curve fitting method and machine computation as a tool to check the fittability of a drawn curve to the basic data. A smoothed curve of Cp vs T (or 0 vs P) is manually constructed according to the Simpson's

-13 3 rule technique. The curve is made on a large sized graph of the corrected basic and differenced data plotted as horizontal lines. From the curve, point values of Cp or 0 were selected at proper intervals so these values could adequately represent the shape of the curve. The functional relationship in the interval between any two successive points is represented by successive five point Lagrange interpolation polynomials.6 The desired interval is arranged to lie between the third and fourth of the five points whenever possible. The integral over each interval is computed to obtain enthalpy differences using Gauss-Legendre quadrature. The area under the curve is also computed over the intervals corresponding to the basic and differenced data and compared with the experimental ones. These comparisons provide a check on the graphical technique and indicate regions where adjustments are necessary. In this work, the final curves are made to fit the corrected basic data within 0.2% deviation. Though all the integrations and interpolations over the curve were done by machine computation, the repeated manual construction of the curves and preparation of the input data to the computer alone made this procedure one of the most time consuming procedures in this work. Interpretation of Joule-Thomson Data In this investigation only a single run of isenthalpic measurements is made with argon, which is illustrated in Figure (III-19), where the average value of Joule-Thomson coefficient, p, is plotted over the pressure interval for each data point. It should be pointed out that the successive data points do not lie on the same isenthalpic curve when the inlet pressure is changed and the inlet temperature remains constant throughout the run. Strictly speaking, the point value of u cannot be obtained from the equal area curve through the data points. However, as Yesavage1 suggested, if the temperature difference, T2 - T1, is small and u is not a strong function of temperature, which is the case with the present measurements, the plot of u vs P may be approximated by an equal area curve as shown in the figure.

-14 The isenthalpic data can be interpreted to yield an enthalpy isotherm corresponding to the inlet temperature of the run. From Equation (II-9) W(T1; P1, P2) can be obtained from an experimental determination of i and an estimate of Cp(T1, T2; P2). Then the point values of 0(T1, P) can be determined by constructing the equal area curve through 0 data using the technique described earlier. Thermodynamic Consistency Checks When the experimental isotherms and isobars form a network of closed loops, as shown in Figure (111-28), for example, then the isothermal and isobaric data obtained over a loop can be checked for self-consistency. We chose the enthalpy loop from -58~F to 167~F and from 286 psia to 1143 psia for explanation on how the loop check is accomplished. The enthalpy changes between the grid points are obtained from the integrals of the Cp or 0 curves discussed earlier in this section. For example, f167~F 35.09 = |C C(T, P = 1143 psia) dT J-58~F r1143 psia -3.27 = | 0(T = 167~F, P) dP J 286 psia As enthalpy is a state function, the algebraic sum of all enthalpy differences around the loop, I AH;, should be exactly equal to zero. In practice, it is a finite value (in this case -0.09 Btu/lb when the sum is taken along the clock-wise path). The actual sum divided by the sum of the absolute values of the enthalpy differences, percent deviation AHi / JAHil x 100, can serve as a measure of the thermodynamic consistency of the data. In this case inconsistency of the loop is -0.09/76.81 x 100 = -0.117%. It is necessary to adjust enthalpy differences between grid points optimally so that the percent deviation of each loop becomes exactly zero. In the particular case examined, the final enthalpy change from -58~F to 167~F at 1143 psia needs an addition of 0.096 Btu/lb to the original 35.09 Btu/lb. Adjustments for the other arms of the loop are also given in the parenthesis.

-15 In order to avoid a concentration of errors in the small end loop, the largest loop (-240~F to 167~F, and from 286 psia to 2000 psia) is balanced first and bounds are established on the total acceptable variations for the individual arms. Then, the smaller constituent loops are balanced within these constraints. The bottom loops are fabricated with zero pressure enthalpy differences calculated with the ideal gas heat capacity, CO, from the literature. Particularly for argon, the zero enthalpy changes can be obtained exactly as Cp is (5/2)R, in accordance with the kinetic theory of monoatomic molecules. Therefore, the bottom loops can provide an opportunity to check the data with the exact values. As the entire network is balanced, the smoothed Cp and 0 values for the individual arms are now readjusted by increasing or decreasing uniformly to conform to the final enthalpy adjustment assigned to the given arm. Error Analysis A comprehensive error analysis of the basic measurements and reduced 25, 36, 37, 18 data has been undertaken by the previous investigators. 2 As pointed out by Furtado,18 estimation of the accuracy of the basic enthalpy data based on the errors involved in the major experimental measurements is at best approximate in view of the highly variable dependence of the enthalpy on temperature and pressure. Furthermore, the precise contribution of unsteady state and mass leakage is almost always uncertain. It is suggested61' 18 that the most reliable index for the accuracy of the results is the observed discrepancy between the original and adjusted values of the enthalpy difference for each arm of every enthalpy loop for any given system. Corresponding States Principle The corresponding state principle has been stated in many ways by many people, although the basic theoretical idea behind each statement is the same as the one introduced by Van der Waals about one hundred years ago. We may here adopt the one from Reid and Sherwood,48 that "all substances would have the same equation of state when expressed in terms of dimensionless (or reduced) system variables". Let

-16 F(X1, X2,..., Xn) = 0 (II-16) be a universal function with n system variables describing the state of all pure fluids (we purposely restrict to pure substances only for the present discussion). These variables should be external thermodynamic variables as P, V and T and also internal variables pertaining to molecular or atomic properties. Now suppose we render dimensionless X1 to Xn by dividing them by X1,... Xn, respectively, where X1,..., Xn are some arbitrary constants. Then we may rewrite Equation (II-16)as -' X F,..., nl 0 (11-17) x X1 I As for those dimensionless variables Bird and Brock4 suggested the following: - j NkT) 2 2 PV V kT 2 Q2 o' h F NkT' 3 o 3, h = 0 (II-18) NclrL EL EI JL 33 b e =1 (11-18) * NkT9 NG 35 c05COG 35 coa9a3!1 Gi(mcO) 1 where k = Boltzmann's constant h = Plank's constant m = molecular mass a= intermolecular potential parameter known as collision diameter Co =intermolecular potential parameter known as minimum energy u = dipole moment Q = quadrupole moment = a measure of deviation of intermolecular potential from that of simple fluids a= polarizability N = Avogadro's number

-17 Since e0 and a are usually unknown, they are conveniently replaced by experimentally measurable quantities; o~/k by critical temperature, TC, and Na3 by VC, critical volume. There are theoretical grounds for those replacements. Since TC is a measure of the kinetic energy at the state when liquid and vapor states are identical, we may expect proportionality between TC and minimum energy of a molecule, cO. As a is a distance parameter, we also expect proportionality between a and VC. The dimensionless group, h/a(mc0)1/2, is for the quantum effect. Except for such quantum gases as Ne, He, H2, etc., this effect is accounted for only at very low temperatures; therefore, we generally exclude this group from the equation. Through the preceding arguments, Equation (11-18) reduces to 2 2 PV V, T. 5 = 0 (-19) F NkjT' -' T VC VkT VC (1-19) It is desirable to replace V/VC by P/Pc' as PC data are generally more 48 reliable than VC data.8 Introduction of P/PC in place of V/VC, however, is accompanied by ZC, critical compressibility factor, since V Z T C (II-20) VC ZC TC * where Z = PV/NkT. Therefore, we must add to Equation (11-19) one more variable as a price for V/Vc elimination. Hence, we have Equation (11-21), 2 2 F( Z P- T Q -) = (II-21) F 5' \ v-' C *PTC T VCkTC V ckTc C which expresses a basic relation for the corresponding states principle (CSP) with eight dimensionless variables as parameters. For convenience, we may rewrite Equation (11-21) in the Z explicit function as

-18 2 2 Z = Z(T P, Z,, ) (11-22) Z(T Pr' ZCr VCkTc V 5kT VC Note that Pr = P/PC, T = T/TC Although it is desirable that either Equation (11-21) or (11-22) be an analytical expression, it can be instead a tabulation of data or a generalized chart drawn from smoothed data. In practice, however, all of the variables in Equation (11-22) are seldom accounted for. The simplest form of CSP has only two parameters Z = Z(P, Tr) (11-23) which implies the compressibility factor as a function of Tr and Pr only. A certain group of molecules called simple fluids such as Ar, Kr, Xe, CH4, which have spherically symmetric structures, was experimentally observed to conform to Equation (11-23). In an attempt to improve two parameter CSP in such a way to cover more than simple fluids, people in the field of thermodynamic correlations have worked out three parameter CSP by introducing the third parameter, y, as Z = Z(Tr, PrY) (11-24) Comparing Equation (11-24) with Equation (11-22), we may see that y should be equivalent to lumped contribution of the five parameters in Equation (II-22). Efforts have been made by a number of researchers to fit y to some macroscopically measurable quantities. Riedel related the third parameter to measured values of the slope of the reduced vapor pressure at the critical point. His parameter, designated as aC, is expressed as

-19 d an Pr1 C= d n Tr) (II-25) PT 1 r where P = reduced vapor pressure. Pitzer and coworkers43 introduced a third parameter called acentric factor, w, as (II-26) W = -1 - (log Pr,) (1-26 Tr = 0.7 Although addition of the third parameter significantly improved the performance of the two parameter CSP, it is not satisfactory enough to cover the fluids with polarity or appreciable asymmetry in their intermolecular force fields, such as H20, NH3, alcohols, etc. A few attempts have been made to improve the three parameter CSP through the addition of parameters. An excellent review on the multiparameter CSP appears in 30 an article by Leland and Chappelear.3 However, as indicated by Leland and Chappelear, the current state of the extent and accuracy of the measurements related to the potential parameters makes it difficult to generalize CSP beyond the three parameter correlation. Significance of Cp(T) Maxima For pure substances the isobaric heat capacity may be expressed as Cp = Cp(T, P) (11-27) If a Cp vs T plot is made along an isobar in the supercritical region, it exhibits a peak called Cp(T) maximum. The peak becomes sharper as the pressure is closer to the critical pressure, PC, and eventually becomes infinite when the pressure equals PC. Figure II-5 illustrates some of Cp vs T plots for argon in the supercritical region. As shown in the figure, Cp(T) maximum is characterized by the magnitude, Cp,

LL 0 I.0:3 4a. OI 2000 1800 1600 1400 a' 1200 o u c) o 1000 J.0 c 800 Li w D () Wz 600 0. )F H I I ) { ARGON o Location of Cp maxima, (aCp/T) = O * Critical Point 400 0 Saturation Point I I I I I, I I. I, I TEMPERATURE, ~F 240 260 280 300 320 340 360 380400 TEMPERATURE, ~R (Log Scale) Figure 11-5. An illustration of Cp(T) curves in the super critical region. Figure 11-6. Plot showing the location of Cp(T) maxima.

-21 and location, TM, for the peak of a given pressure. If TM vs P plot is made on a P-T plane, as shown in Figure 11-6, the plot demonstrates a curve similar to the vapor pressure curve in the subcritical region. 26 25 It was suggested by Kaganir and Jakob and later substantiated by the experimental results of Sirota, et al.51 that the slope of the vapor pressure curve at the critical point is the same as that of the curve formed by the loci of Cp(T) maxima (called Cp(T) maxima curve). Therefore, they once regarded the Cp(T) maxima curve as an extension of the vapor pressure curve into the supercritical region. The existence of rapid changes in Cp along the Cp(T) maxima curve made a few researchers speculate that there might be a structural change in fluids at the supercritical region, and the Cp(T) maximum curve might be the boundary between "vapor-like" and "liquid-like" phases51' 52 However, there is insufficient information on the physical nature of the maxima and the existence of phase transition is still questionable. Nevertheless, the knowledge of location and the magnitude of Cp(T) maxima would be of great importance to the formulation of any Cp correlation. There are several existing correlations for (Cp - Cp~) by several 27 investigators. Lydersen, et al.27 established generalized charts for (Cp - Cp0) from their generalized compressibility table. Sherwood53 established (Cp - Cp~) correlation from the generalized enthalpy tables by Curl and Pitzer. There are generalized (Cp - Cp ) charts by Edmisterl4 and by Weiss and Joffe.59 All these correlations are based in PVT data, not Cp data. The thermodynamic relation, as described by Equation (11-28) P Cp(T, P) - Cp~(T) = T ( 1) dP (11-28) 0 shows that in order to obtain Cp data, PVT data should be differentiated twice, followed by an integration either numerically or graphically, which would introduce sometimes significant errors. Especially in a Cp(T) maxima region where rapid changes in Cp occur, reliability of Cp s derived from PVT's are quite questionable. Even for the regions

-22 excluding the neighborhood of critical point, according to Weise and 59 Joffe, errors encountered may be as high as 50 to 100%. Therefore, direct determinations of Cp as well as Cp(T) maxima in this region of poorest definition would contribute significantly to the improvement of existing correlations as well as to the development of new generalized Cp correlations. Previous Studies on Cp(T) Maxima Because of experimental difficulties involved in the measurements of calorimetric data, direct Cp data in the supercritical region are available for only a few substances. Consequently Cp(T) maxima data are found among only those substances. Most of the data are from several researchers in the U.S.S.R. and the previous workers of the Thermal Properties of Fluids Laboratory (TPFL) at the University of Michigan. Sirota and his coworkers51' 52 report Cp(T) maxima of H20 from their extensive work on Cp measurements in the supercritical region. Cp(T) 47 maxima of CO2 were obtained by Rivikin and Gukov. The data obtained through experimental measurements at TPFL include Cp(T) maxima for 25 18, 34 61 35 CH, C2H, C3H, and N In addition, the data have been 638- T18 18 obtained for a number of binary mixtures of CH4 - C2H6, C2H6 - C3H8 CH4 - C3H86, and CH4 - N2, and a ternary mixture of CH4 - C2H6 - C3H8. There are few investigations related to correlations for Cp(T) maxima. Sirota, et al.51 observed from their experimental Cp(T) maxima data of water that the location of the peak could be expressed in the simple expression In Pr = C(1 -) (11-29) r C Tr where Pr = reduced pressure Tr = reduced temperature at which the peak locates

-23 Powers45 has suggested, based on his study of the Cp(T) maxima data obtained from the University of Michigan, the following equation for the location of Cp(T) maxima: In Pr = aC In Tr (11-30) Choice of Experimental Fluids It was felt that for a fluid to be suitable for the experiment planned at TPEL it should meet the following criteria: 1. It should be nontoxic and physiologically inert. 2. It should be chemically stable. 3. Its critical temperature and pressure should lie well within the operating range of the equipment. 4. It should be available as a relatively pure material. The first criterion is the concern of life hazard to persons engaged in the experiments in case of mass leaks from the equipment. Since the measurements usually take a long period of time, there could be a chance of prolonged gas exposure to the human beings involved. Therefore, even at a low level of concentration, a toxic gas can inflict injuries to the human body. It was decided that the fluids belonging to, or are equivalent to, groups one through four of Underwriter's Laboratory Classifica58 tion5 be excluded from further considerations. For example, fluids otherwise suitable for our investigation, such as SiF4 and BF3, were rejected. The second criterion concerns possible decomposition of a fluid within the system. This may result in erronous data and, furthermore, lead to such dangerous situations as explosions, line pluggings, etc. The third criterion aims to eliminate the fluids with critical constants out of the operating range of the present equipment (temperatures between -240~F and 300~F and pressures up to 2000 psia). With such

-24 fluids, measurements cannot be made both in the subcritical and the supercritical regions. Among the fluids satisfying this criterion, those with relatively low critical constants are preferable because the measurements in the supercritical region will be emphasized in the present work. The fourth criterion concerns the impurity level in the sample to be used for the experiment. It would be ideal to use a sample free of impurities. Practically, however, every commercially available sample contains impurities varying from the level of less than 0.001% to as high as 10% depending on the substances. It is desirable to choose the sample with an impurity level lower than 0.1%; however, up to 0.5% impurity could be acceptable if the content of impurities is known and the corrections could be made. Table II-1 gives a list of some of the fluids which were considered for our use. Excluded from the table are the ones already used in the previous works at TPFL (such as CH4, C2H6, C3H8 and N2). The list consists of the simple molecules (Ar, Kr, Xe), fluorocarbons, a couple of olefins and CO2. It was intended that one simple molecule and one fluorocarbon be chosen for the present investigation, and argon and C2F6 (Freon-116) were finally chosen among them. The choice of C2F6, among other fluorocarbons was in accordance with the interest of the du Pont de Nemours & Co., which donated C2F6 with high purity (99.9%). It is to be noted that while argon is a simple fluid with aC = 5.98, C2F6, the fluorine analog of ethane, is a substance with aC = 7.19, a comparatively high value. Therefore, the choice of the substances with widely different aC values for the calorimetric measurements may furnish information which could help establish the third parameter effect on the Cp(T) maxima correspondence. Previous Experimental Data for Argon A comprehensive literature search for the thermodynamic data pub23 lished up to 1964 is found in a publication of NBS. It includes more than 400 sources for the data not only of thermodynamic but also

-25 TABLE II-1 A LIST OF FLUIDS SUITABLE FOR USE IN THE PRESENT EQUIPMENT Mole c ular SubstanceM Tc (OF) Pc (psia) Weight Ar 39.94 -188.6 705.4 Kr 83.7 - 82.8 798 Xe 131.3 - 38.1 853 CC12F (Freon-12) 120.93 233.6 596.9 CC1F3 (Freon-13) 104.47 83.9 561 CBFrF5 (Freon-13B1) 148.9 152.6 575 (F'J4I (TFreon-14) 88.1 - 50.2 514 (C FCi1F' ( i'reon-22) 86. 48 24.8 71.9 CIlnl3 (Freon-23) 70.02 78.6 o71 CC1F2-CF3 (Freon-115) 154.48 175.9455 C2F6 (Freon-116) 138.02 67.1 1437 C4F8 (Freon-C318) 200.04 239.6 403.6 C2H4 28.05 49.9 742 C3H6 42.08 197.5 668 CO2 44.01 87.9 1071

-26 mechanical and transport properties. There are only a few cases in which direct measurements of thermal properties have been made. Roebuck 49 and Osterberg49 have determined the Joule-Thomson coefficients with the highest initial pressure being 200 atm and initial temperatures ranging from -150~C to 300~C. The specific heats of the saturated solid and liquid have been reported by Eucken5 16 and Clusius78 who conducted low temperature calorimetric measurements. They have determined the latent heats of fusion and vaporization at the triple point and normal boiling point. Walker60 has determined Cp of argon for pressures from 10 to 40 atm and temperatures from -240~F to -140~F from calorimetric measurements with a bomb-type nonflow calorimeter. Reliability of Walker's data are somewhat questionable because the measurements involved heat capacities of the calorimeter which were usually higher than those of the sample except for the peak region. According to his analysis, the overall accuracy of data was ~0.7%. Compilations of thermodynamic properties of argon may be traced back 39 to the work of Michels, et al.39 who calculated and tabulated Cp, H and S as well as other thermodynamic properties at temperatures between 0 and 150~C and pressures up to 1050 atm. Later Michels and coworkers38 extended the compilation to temperatures down to -140~C. DinO has prepared thermodynamic tables and a Mollier diagram from the data published up to 1952. His work covered temperatures between 90 and 240~K and pressures up to 5000 atm. A similar work has been done by 24 Hilsenrath, et al. The most recent compilation is the one prepared by Angus and Armstrong under the auspices of the International Union of Pure and Applied Chemistry (IUPAC), covering temperatures from 85 to 1100~K and pressures up to 1000 bar. It is a collation of two recent 22 tables, one by Gosman, et al. of NBS and the other by Vasserman, et al.56, 57 of Odessa Institute of Marine Engineers, U.S.S.R. The two sets of tables are to a large extent based on the same data. Angus and Armstrong noted that agreement between the values of the properties listed in the two tables, with the exception of the heat capacities, is within the range comparable to the experimental errors.

-27 Previous Experimental Data for C2F6 A literature survey reveals few sources for the thermodynamic properties of hexafluoroethane. Pace and Aston41 have determined the heat capacity of saturated solid and liquid from 11.2 to 195.0~K from calorimetric measurements. They have also measured the vapor pressures of the solid and the liquid to the normal boiling point (194.87~K) as well as the heat of vaporization and saturated vapor density at 273.16~K. A compilation of thermodynamic properties of hexafluroethane has been issued by Freon Products Division of E. I. du Pont de Nemours & Co.17 The ranges of the compilation are temperatures from -150~F to 460~F and pressures up to 460 psia. Values of the ideal gas heat capacity determined from spectroscopic analysis are found in the literature.9' 54 from spectroscopic analysis are found in the literature.

III - CALORIMETRIC DETERMINATIONS WITH ARGON This section presents the descriptions of the experimental equipment and procedure and presentation and discussion of the results. The equipment used in the present work was originally designed and constructed by 19 Faulkner. It has been subjected to improvements and modifications by previous workers25' 35, 36, 37, 61, 18 and is well documented in their Ph.D. theses. Therefore, the facility is described here only briefly. Emphasis is put on the modifications and calibrations of measuring instruments which were done during the present investigation. Experimental results are presented in the form of tabulation of the basic data H, Cp, 0, and v as well as the smoothed values of Cp, 0 and p. Plots of Cp, 0 and U along the isotherms and H-P-T diagram are presented. These data are checked for thermodynamic consistency and compared with values from the literature. The Recycle Flow System A flow diagram of the system is shown in Figure III-1. It is fundamentally a recycle flow system designed to supply a fluid at a constant measured rate to a calorimeter at a designated temperature and pressure. The fluid is compressed to a pressure higher than that at which measurements are to be made (usually 4 ~ 500 psi higher than the calorimeter inlet pressure) by means of a two-stage Corblin diaphragm compressor operating at a constant volumetric rate (~4 SCFM). The fluid, after passing through the scavenger bomb containing heated copper fillings which absorb any oxygen in the stream, is throttled approximately to a preselected pressure through the compressor throttle valve (CT). The flow is then divided into two streams: one stream bypasses to the inlet buffer through the bypass throttle valves (BT) and the other (called the main stream) proceeds to the calorimeter. Eventually these two streams merge at the inlet buffer at about 80 psig and recycle to the compressor. The main stream enters a cylinder called the high pressure buffer which serves to stabilize the fluctuation of the flow pressure. The fluid then either passes through the cooling water coil (when the desired temperature -28

Figure III-i. Flow diagram of the recyle-flow system used for the measurements with argon.

-30 is lower than room temperature) or proceeds directly to the dry ice bath. The dry ice bath contains 175 feet of 3/16 in. O.D. copper tubing which serves to bring the fluid temperature down to about -100~F, if necessary, when the bath is filled with a dry ice-acetone mixture. The stream next enters the heat exchanger bath containing 325 feet of 3/16 in. O.D. copper tubing immersed in a bath fluid which is maintained to within ~1~F of the calorimeter inlet temperature using a controlled immersion heater. It then enters the calorimeter bath containing 100 feet of 3/16 in. O.D. copper tubing for a final temperature conditioning for the calorimeter. Originally both the isothermal and isobaric calorimeters were placed in the bath and the stream was directed to either one of the calorimeters depending on the type of the measurements by manipulating the four cryogenic valves inside the bath. However, it was found out after Furtado's measurements that a small portion of the stream could bypass to the inactive calorimeter as some of the cryogenic valves failed to shut completely. Since it was difficult to prevent the bypass completely during the run, it was decided that the inactive calorimeter be removed from the bath and inlet and outlet lines to the calorimeter were plugged. The calorimeter bath is well stirred and temperatures are controlled to within ~0.05~F of a desired temperature. Isopentane (temperatures below -50~F) and Dow-Corning silicone oil (temperatures above -50~F)are used as bath fluids for both the calorimeter and heat exchanger baths. At below ambient temperatures, the bath fluid is cooled by liquid nitrogen passing through the cooling coil immersed in the bath. The liquid nitrogen is supplied from externally located 160-liter dewars and its flow is regulated by adjusting a valve located in the nitrogen vent line outside the bath. The measurements of the inlet pressure and temperature, the changes in temperature and pressure across the calorimeter, and the electrical energy input are made as the fluid passes through the calorimeter. After leaving the calorimeter, the condensed part of the fluid, if any, is completely vaporized as it passes through the hot oil bath and returns to the control manifold where it is throttled to 80 psig through the calorimeter throttle valve (9T).

-31 The fluid then enters the flowmeter bath where the flow meter is located. The bath is filled with water and the temperature is maintained at 27 ~0.05~C by a 100 watt tubular heater controlled by a mercury contact switch. The fluid passes through 50 feet of 3/8 in. O.D. copper tubing for the temperature conditioning before entering the calibrated Meriam flow meter. Micron filters are located on the inlet and outlet side of the meter to remove entrapped particles from the stream. The fluid passes through another 50 feet of copper tubing after the flow rate is measured and returns to the compressor via the inlet buffer. Two bypassable absorbent beds are located in the bypass stream to the inlet buffer and in the inlet stream to the flow meter bath. These beds, designated to remove oil and moisture in the stream, consist of layers of molecular sieves 3A and 4A, activated charcoal and drierite. A twelve foot double pipe water cooling coil is placed in the flow meter stream before the absorbent bed. There are five storage tanks located in a heated air bath. These tanks serve to adjust the pressure for the recycling system. Calorimeters The isobaric and, isothermal calorimeters used in this work are the same ones used by Furtado.18 The isobaric calorimeter was originally designed by Faulkner19 and it is modified by previous workers.25, 61, 18 37 The isothermal or throttling calorimeter was designed by Mather and it also has been subjected to modifications by previous workers.61' 18 An excellent description of the original design and modifications to those 18 calorimeters can be found in Furtado's thesis.8 Experimental Measurements Detailed descriptions for the experimental measurements and the 25 36 measuring instruments are found in the theses of Jones, Manker,6 and Mather37 and are discussed here only briefly with an emphasis on the changes made during the present investigation. The major measurements in this experiment can be listed as the following:

-32 1. Temperature at the inlet to the calorimeter. 2. Temperature rise through the isobaric calorimeter. 3. Temperature difference between the isothermal calorimeter inlet and outlet. 4. Pressure at the inlet to the calorimeter. 5. Pressure drop through the isobaric calorimeter. 6. Pressure drop through the throttling calorimeter. 7. Electrical energy input to the calorimeters. 8. Mass flow rate. (1) The temperature at the inlet to the calorimeter is assumed to be the calorimeter bath temperature, which is measured using a platinum resistance thermometer. The calibration of the thermometer was made by NBS (June, 1968) and the calibration constants are given in Table A-1 of Appendix A. The accuracy of the bath temperature measurement is 0.04~F. (2) The temperature rise through the isobaric calorimeter is measured with duplicate six-function copper-constantant thermopiles calibrated by NBS. Calibration data are fitted to fourth degree polynomials by the least square method. The calibration data and the constants of least square fits are given in Table A-2 of Appendix A. (3) The temperature difference between the isothermal calorimeter inlet and outlet is measured with a 15 junction copper-constantan thermopile calibrated by NBS. The calibration equation for the thermopile was obtained by Furtadol8 and its constants as well as the calibration data are shown in Table A-2 of Appendix A. (4) Pressures at the inlet to the calorimeter are measured by the Mansfield and Green (M & G) dead weight gage (with a gas to oil pressure transmitter and an electronic null detector) which is sensitive to imbalances as low as 0.05 psi. The resolution of the dead weight gage is 0.2 psig. According to FurtadoS8 who tested the instrument against a calibration standard Model 2400 Ruska dead weight gage, discrepancies between the two sources are within 0.1% over the pressure range from 250 to 2000 psia.

-33 (5) The pressure drops through the isobaric calorimeter are measured using a 40 inch high pressure mercury manometer enclosed in a heated air box to prevent liquid holdup in the lines in case of low temperature operation. Normally the pressure drops never exceed 1 psi. Accuracy of the measurement is ~0.05 inches of mercury. (6) The pressure drop through the throttling calorimeter is measured using two strain gage type absolute transducers installed on the inlet 18 (high pressure) and outlet (low pressure) pressure taps by Furtado.8 Originally a strain gage differential transducer (Sensotec Model ZD) with an operating range from 0 to 250 psid up to 2000 psia line pressure was installed for the measurement. However, at the beginning of the isothermal run a significant mass leak was detected through the metal gasket which was deteriorated by corrosion due to prolonged immersion in the flow meter bath. As a result, the differential transducer was sent back to the manufacturer for repair and in the meantime all of the isothermal runs had to be made with the absolute transducers. Each pressure transducer was calibrated against the M&G dead weight gage three times, at the beginning, middle and last period of the isothermal measurements. The results are plotted in Figures III-2 and III-3. For both high and low pressure transducers the following equation well fits the data: E = A + BP + CP2 + DP3 (III-1) where E = EMF transduced by the transducer, pV P = gage pressure, psig. The constants A, B, C and D for each transducer as well as the calibration data are presented in Tables A-3 and A-4 of Appendix A. Average deviations for the equations from the data are 0.025% for the low pressure transducer and 0.020% for the high pressure one. (7) The electrical energy input to the calorimeters is supplied by a DC power supply (KEPCO Model SM325-2MX) capable of delivering up to 2.0 amps at 325 volts within 0.01% voltage regulation. The power input

-34 2500.2000 0 0 - 1500- Calibration U 1000 2 u_^ 0o 3 500 400 600 800 1000 1200 1400 1600 1800 2000 PRESSURE (psig) Figure III-2. Pressure transducer (high) calibration. 2500 2000 o 0. 1500 2~~ ~ ~~~E j^^I/~ ~Calibration LL_ CJ Series E f o 1 L 1000 A 2 o 3 500 400 600 800 1000 1200 1400 1600 1800 2000 PRESSURE (psig) Figure III-3. Pressure transducer (low) calibratior.

-35 is measured by a K-3 potentiometer using standard resistors to scale down the voltage to the range of the potentiometer. A wiring diagram for the power measurement circuit appears in Yesavage's thesis.61 During isothermal measurements it is necessary to make fine adjustments to the power input of the calorimeter heater so that the temperature difference between the inlet and outlet of the calorimeter can be maintained as small as possible. However, it was found from past experience that maintaining the outlet temperature within +0.02~F (51V) of the inlet temperature by manual adjustment of a potentiometer attached to the power supply alone was difficult. To accommodate this, the circuit for the isothermal calorimeter was modified by adding a 40-turn Helipot for fine adjustment of its power input. The modified circuit is shown in Figure III-4. The coarse adjustment of the power is made with the potentiometer attached to the power supply (not shown in the drawing). Then the fine adjustment is done by regulating the R4 setting. The switch S2 serves as a bypass if necessary. The power input to the calorimeter heater, RC, is determined by simultaneous measurements of E1 and E3. According to Yesavage61 the accuracy of the power input determination is within ~0.05%. (8) The mass flow rate is calculated from the pressure drop across the Meriam flow meter, the density and the viscosity of the fluid at the flow meter. The pressure drop is measured to ~0.001 inches by a 20-inch precision water manometer. The density of the fluid is estimated at the flow meter inlet pressure, as measured to ~0.01 inches by a 180 inch mercury manometer, and the flow meter bath temperature using the virial equation truncated after the second virial coefficient: = 1 + B/V (III-2) where V = molar volume of the fluid P = flow meter inlet pressure T = temperature of the flow meter bath B = second virial coefficient of the fluid. The second virial coefficient, B, for argon at temperatures close to the flow meter bath temperature (27~C) can be expressed, based on the data

LEGEND OuRply | —-- 3 Re S lS2,S Switches | | | — t R4 40-turn Helipot, 250 P R0 Resistor, 10 R1 Standard resistor, New Installation R2 Standard resistor, R Standard resistor, 100 Q R Isothermal calorimeter heater, 250 w c -1c, El EMF across Rl (measured with K-3 potentiometer) E3 EMF across R3 (measured with K-3 potentiometer) I Cl) Figure III-4. A modified circuit of power input to the calorimeter.

-37 12 by Dymond and Smith, as B = 55.73 - 21534.6/T (III-3) Here B is in cc/g-mole and T is in ~K. The viscosity of argon was estimated from the correlation for the viscosity-density isotherm reported by Flynn et al.20 as = a + bp (III-4) where p = mass density of argon a and b were obtained from their data as a = 0.6671 (T-298.16) + 225.3, b = 0.100 (T-298.16) + 109.0. Here T is in OK, a in ppoise, and b in ppoise - cc/g. The flowmeter is calibrated by a direct method involving the weighing of the condensed fluid collected in a liquid nitrogen cooled sampling tank in a specified time interval. The apparatus and procedure of the calibra25 tion have been described by Jones25 and a modified version for the procedure is later described in detail by Furtado.18 The flow rates used in the present experimenta are between 0.04 and 0.30 lb/min; however, for most of the cases flow rates are around 0.2 lb/min. As a calibration equation, the following form is used in the present work: P P A + B F + C + D F3 (III-5) BQ( )c()+DQ) (111-5) where AP = pressure drop across the flow meter F = mass flow rate. This equation has been used by previous workers at the Laboratory.25' 35, 36, 37, 61, 18 Furtado18 discussed the following alternative to the equation.

-38 -lOF 2 3 FTp = A + BX + C'X2 + D'X3 (III-6) where X = in (P x 103) He observed from his calibrations for ethane, ethane-propane and methane-ethane mixtures that at low flow rates [F/p < 0.002 (lb/min/ p poise)] Equation (III-5) was preferable to Equation (III-6), while Equation (III-6) was better at intermediate and high flow rates. Flow meter calibration results for argon were found to be satisfactorily fitted to Equation (III-5) as the upper limit for F/p was only 0.0012 (lb/min/p poise) due to the high value of argon viscosity (roughly twice as high as that of ethane). The plot of calibration data (Table A-5 in Appendix A) is shown in Figure III-5. The standard deviation of the data is 0.14%. It is interesting to compare the present calibration with those for other systems since the calibration should be independent of system fluids if their densities and viscosities are accurately estimated, assuming 18 there is no change in the flow meter characteristics with time. Furtado8 reported that a single curve could represent the calibrations for his ethane and all of the binary systems of methane-ethane and ethane-propane within 0.25% deviation for the range up to F/p = 2.2 x 10-3 (lb/min/ micropoise). A comparison of the present calibration with his generalized one is made in Figure III-6. There is, however, a uniform discrepancy of 2.2% between them which indicates errors involved in the estimation of viscosity and/or density. It is unlikely that this discrepancy is due to the errors in density estimation since both for argon and hydrocarbons density can be accurately estimated at the flow meter condition (27~C at 85 psig). Therefore, it is concluded that the discrepancy is due to incorrect estimations of viscosity either of argon or the hydrocarbons (or both). The viscosity of argon, however, is determined from Equation (III-4) which was derived from the direct experimental data while that of hydrocarbons was estimated from the prediction method of Lee, et. al.31 Assuming that there is uniform error in the estimation

-39 1.30 0) (A 0 o' - 2 1.25._ E 4 c EI 1.20 ~L N$ 1.15 Q1 1% T ARGON o May, 1973 \_~ o^8/ A, October, 1972 ~LF^ % ~o a February, 1973 H I.IOh I I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 F//' 104 (Ib/min/micropoise) Figure III-5. Flow meter calibration. 1.6 () 0 CN ) c u. C 4CE N 0 Q F/y -103 ( Ib/min ~F/p^ *0 Imicropoise Figure III-6. Comparison of the present flow meter calibration with a generalized one by Flrtado.18

-40 of viscosity of the hydrocarbons, the generalized calibration is adjusted with uniform increase of 2.2% in viscosity, which lifts the original curve to a new one (see Figure III-6). The agreement between the argon and the adjusted calibrations is well within 0.1%, which is remarkable since it is better than fitting abilities of both equations to their calibration data. All of the electrical or electrically transduced measurements are made on a K-3 potentiometer (Leeds and Northrup Co.) using standard resistors to scale down voltages to the range of the potentiometer. The circuit for the potentiometer and calibration data for the resistors 25 are essentially the same as the ones given in the Jones' thesis.25 During the present investigation 2-volt rechargeable storage cells which had been used for the power source to the potentiometer were replaced by a Leeds and Northrup power supply (#099034). This replacement eliminates the need for recharging the cell and frequent standardizations to compensate for the voltage drop of the cells due to depletion. In addition emf of the standard cell for the potentiometer was carefully checked by the procedures suggested in the manual and the standard cell setting on the potentiometer was adjusted accordingly. Experimental Procedure An excellent procedure for the acquisition of the basic data is pre18 sented in Furtado's workl and is applicable to the present work. Therefore, the operating procedure is not described in detail here. Instead, a brief discussion is made on some careful measurements taken during the present experiment. (1) Usually the first data point of an experimental run is measured when it appears that the flow system reaches its steady state. This is judged by the indications of the dead weight pressure balance and the calorimeter thermocouple emf when other control elements were functioning properly. Nevertheless, past experiences showed that the first data points were frequently subjected to errors due to unsteady state effect. To remedy this, every first point was repeated again 30 minutes later to check the unsteady state effect. If the result shows

-41 an appreciable change in the values, which indicate an unsteady state behavior of the system, then the same procedure is repeated again until the consecutive values reproduce each other within experimental uncertainty. (2) After the first point consecutive measurements are spaced at least 45 minutes apart so that a period of more than ten minutes is allowed from the time the system shows steady state to the final measurement. (3) Mass leaks from the system are checked at the beginning of the equipment operation. During the measurements, if a leak is suspected, further measurements are postponed until the source is found and the leak stopped. (4) An average calorimeter bath temperature variation over a given run is controlled within the variation of +0.05~F (as compared to +0.1~F shown in previous investigations37 61, 18). Inlet pressure variations for a run are regulated within ~1.0 psia (as compared to ~2.0 psia reported by previous investigators37'61, 18) and they are further regulated within +0.3 psia for the measurements in the vicinity of Cp(T) maxima. P Material Used The material used in the present investigation is UHP grade argon (99.999%) of Matheson Gas Co. Before the sample is charged, the entire recycle system is first evacuated (the last fluid in the system was a ternary mixture of 85% CH4 - 10% C2H6 - 5% C3H8) to about 100 micron of vacuum. It is then filled with technical grade argon (99.9%) up to 200 psia and the gas circulated through the system for 24 hours. The system is evacuated again to about 100 micron of vacuum before the sample is charged to the system. Once the sample is charged it is circulated through the system about 24 hours and a portion of it is taken into a standard cylinder for composition analysis. As a primary check for possible impurities, the sample from the standard cylinder was subjected to a gas-solid chromatographic analysis. A specific column capable of separating argon, N2

-42 and CH4 was made with six foot 1/4 in. O.D. copper tubing filled with Linde molecular sieve 5A, which was dried at 600~F for an hour in a furnace as suggested in the literature.33 The result of the analysis using the column (the column and a thermal conductivity detector are immersed in the flow meter bath at 27~C and helium is used as a carrier gas) is presented in Figure III-7. As shown in the figure, no impurities are detected through the chromatographic analysis. Later the sample is analyzed by mass spectrometry at the University of Michigan and its analysis is in Table III-1. TABLE III-1 Composition of Argon CO2 0.002% N2 0.003% CH4 0.005% Ar(by difference) 99.990% 100.000% Molecular weight of sample 39.945 Region of Measurements The range of experimental determinations is shown on a P-T plane as Figure III-8. The horizontal and vertical lines represent isobaric and isothermal runs. Each run is numbered in the chronological order of the investigation. The numbers with "R" designate isothermal runs and one isenthalpic run (48R). The vapor pressure curve is drawn in the diagram to indicate the phase corresponding to each run. The dotted line drawn from the critical point represents an estimate of the locus of Cp(T) maxima. Some of the isobaric runs are designated with more than one number as they are subjected to more than one measurement. In some cases the measurements are repeated for the entire temperature ranges, in others they are repeated only for specific temperature ranges where the accuracy of the data is in question. Since the primary interest

-43 1.5 Chromatographic Analysis of Argon Sample from the System Argon Peak (Attenuation Disturbance At Sample Injection 1.0 128) Direction of Chart Movement I *9 I 5L I 0.5 w CL > (Attenuation 1) _~~ -a I1 -- - A a a 5 a~~~~~~~~~~ I I I I I I I i FM - 5 4 3 2 TIME, min. I I 0 Figure III-7. Chromatographic analysis sample from the system. of the argon

u) 0. a: LLJ:D (f) Uf) LuJ a: 0L! TEMPERATURE, ~F Figure III-8. Range of calorimetric determination on argon.

-45 was in Cp measurements in the region of Cp(T) maxima and vapor pressure curve, as many isobaric runs were planned as possible in this region. In the supercritical region isobaric runs are made at 706, 800, 950, 1143, 1371, 1714 and 2000 psia. In the subcritical region measurements were made at 286, 457 and 571 psia. Except for 950 and 2000 psia, those pressures were chosen in such a way that their reduced values are the same as those of the propane runs conducted by Yesavage,61 thus forming a set of corresponding states between two systems. As will be seen later, the pressure levels for the measurements of C2F6 are also made in the same way. Extensive measurements were made in the gas region at 286 psia and in the supercritical regions at 1143 psia and 2000 psia. In all, seven isobaric runs were made for seven Cp maxima determinations and three isobaric runs were made across the two phase boundary which gave the enthalpy changes on vaporization as well as the heat capacity of liquid and gas phases. One isenthalpic run at -240~F and five isothermal runs at -208.9~F, -191.2~F, -168.3~F, -58~F and 167~F were made to obtain isothermal changes of enthalpy. Those runs are designed to establish a network of enthalpy loops with the isobaric runs so that the thermodynamic consistency of the data could be established. It should be mentioned here that because of the experimental difficulty encountered during isothermal measurements across the two phase boundary, the isothermal run at -208.9~F (49R) could not be extended to the gas phase region. The basic data for argon are presented in Tables B-1 (isobaric) and B-2 (isenthalpic and isothermal) of Appendix B. Results Cp and Cp(T) Maxima From the isobaric measurements of enthalpy, Cp values were determined by the method described in Section II. For the 286 psia isobar (see Figure III-9), measurements were extended to a higher temperature region (up to 220~F) where the thermodynamic behavior of argon is closer to that of ideal gas than any other region of the present measurements.

-46 For the isobars at 457 psia (Figure III-10) and 571 psia (Figure III-11) Cp values for both liquid and gas phases were determined. A typical isobar in the supercritical region (1143 psia) is illustrated in Figure III-12. The data extend from -250~F to 190~F. The Cp value increases sharply as the temperature approaches the location of the peak (designated TM), where Cp reaches the maximum value (designated CpM) and then decreases rapidly as the temperature increases. At higher temperatures Cp changes only slightly with temperature. In this case T is determined as 165.0~F with uncertainty of +0.2~F and CpM as 0.935 ~0.003 Btu/lb-~F. Figure III-13 shows an isobar at 706 psia which is less than 1 psia above the critical pressure (PC = 705.4 psia from Grigor and Steele21). The Cp(T) curve, as shown in Figure III-13, forms a very sharp peak exceeding 10 Btu/lb-~F (cf. Cp 0.1244 Btu/lb-F). T for this curve is -188.6~F with an uncertainty of ~0.2~F (the critical temperature 21 M by Grigor and Steel2 is -188.61~F). T was determined by repeated measurements with small outlet temperature increments between successive data points as represented by the short dotted lines in the vicinity of the peak. The plot of the isobaric run at 950 psia (Figure III-14) clearly defines an equal area curve in the vicinity of the Cp(T) maximum. This run was made particularly to determine the peak. The temperature increments between successive measurements were made smaller than 2~F. Cp(T) curves at 800, 1371, 1714 and 2000 psia are also shown in Figures III-15, III-16, III-17 and III-18, respectively. Cp values for each isobar are tabulated in Table III-2 and Cp(T) maxima data are listed in Table III-3 Cp values are listed in Table C-1 of Appendix C.

-47 ISOBARIC MEAN HEAT CAPACITY ARFGON (AS) 286.- PSIA a o 0 -; a4u. -180. -120. -60. 0 80. 120. TEMPERATURE (~F) Figure III-9. Isobaric heat capacity for argon at 286 psia. ISOBARIC MEAN HEAT CAPACITY ARGON 457.. PSIR 10O. LL -' L.-. Xi: i..._.~ I_ ----- ---'-25. -229..00. -t17. -150. 125. -100. -75. -SO. TFMPERATURE ("F) Figure Il1-10. Isobaric heat capacity for argon at 45r7 psia. ISOBARIC MEAN HERT CAPRCITY ARGON 571.' PSIA LL. i, O - cM' "t a. ig s I-t lm ~~asl _- --. —r ~~~~~~~~~~_;..'-O. -22S. -200. -17t. -1SO. -12S. -100. -7S. -SO. TEMPERATURE (~F) Ii.'i Iv,, [lI-.l.. Is,,batie leoat oapac it.y 0or Itl'.. It.,''l.(1 p.lot.

o ISQOBRIC RRGON MERN HEAT CRPRCrTY 1143 — PSIR,8 OT 0Ca' ~n in~1 i 00 --- - z. ";-,z i; _q,.'._._........... -........ -'260. -..,6..1LO. -60. -L0. TEMPERATURE (~F) 410. 90. ILO. I90. Figure III-12. Isobaric heat capacity for argon at 1143 psia.

a co r,.4 ISOBRRIC MERN tERT CRPRCITY RRGON 950. PSIR ISOBRRIC MERN HERT CRPRCITT RRGON 800. PSIR 3 o o. a 2 - lb -4 II I 9 c2 CM in 8 a o Q. 0 a a I a 1 9p l0 a9 C M.,.. I - - -190. -18I. -178. -172. TEMPERRTURE (~F) -41B. -I0. -.LO. -160. -11L. TEMPERATURE (~F) -60. 7ig-ere III-_. ICs iari? heart capa-;ity for argon at 706 psia. Figu-re III-14. isobaric heat capacity for argon at 95, psia. T-igure III-15. Isobaric heat capacit~y for argon -=:_,, — 7_

-50 ISOBRRIC MEAN HERT CRPRCITY RRGON 1371., PSIr o 00 a 3 |O CY ~ 8; ('1-.n e0. -'30. -200. -70. -140. -110. -80. TEMPERFTURE (OF) Figure III-16. Isobaric heat capacity for argon at 1371 psia. ISOBARIC MERN HERT CAPRCITY RRGON 1711. PSIR _ = - ~ - ~~ -60. -0. r In U' -- I. 0 oQ * CO Ca z - N ---- -- ^ —-'0 -'2,0, I. -'60 -230.'-00.'-70. -ti0, -'10. -70 -. TEMPERATURE (~F) Figure III-17. Isobaric heat capacity for argon at 1714 psia. -so. -0. -eO. -1SO. -t10. -60. 0 SO. 100Q TEMPERATURE toF) Fipure I Ii-l1. IBobarie heat capacitv t'or ar'ol at f2000 psia.

TABLE I1-2 ISOBARIC HEAT CAPACITIES OF ARGON Pressure = 286. psia Pressure = 457. psia Pressure = 571. psia Pressure = 706. psia Pressure = 800. psia Temperature Cp Temperature C Temperature Cp Temperature C Temperature C (~F) (Btulb-~F)t (~F) (Btu/b-~F)_ (~F)_ (Btu/lb-~F) _ (oF) (Btu/lb-~F) _ (~F) (Btu/lb-~F) -230. -220. -210. -200. -190. -180. -170. -160. -150. -140. -130. -120. -110. -100. - 80. - 60. - 40. - 20. o. - 20. 0. 20. 40. 70. 100. 130. 160. 190. 220. 0.2922 0.2457 0.2152 0.1923 0.1787 0.1705 0.1640 0.1586 0.1544 0.1510 0.1482 0.1460 0.1441 0.1424 0.1598 0.1378 0.1359 0.1344 0.1333 0.1324 0.1316 0.1306 0.1295 0.1288 0.1283 0.1281 o.1278 -240. -250. -220. -215. -210. -209. -208.5 -206. -202. -198. -194. -190. -185. -18o. -170. -160. -140. -120. -100. - 80. - 60. 0.3090 0.5578 0.3880 0.4250 0.4750 0.5000 0.7250 0.5575 0.5620 0.3020 0.2717 0.2528 0.2389 0.2276 0.2100 0.1961 0.1759 0.1638 0.1551 0.1508 0.1475 -240. -250. -220.. -210. -205. -200 -199. -198.5 -197.5 -196. -194. -190. -18o. -170. -16o. -140. -120. -100. - 80. - 60. 0.5044 0.3281 0.3691 0.4362 0.5159 0. 9558 o.,358 2.2660 1.0600 0.7620 0.5216 0.4360 0.3112 0.2544 0.2270 0.1983 0.1794. 1680 0.1594 0.1515 -250. -240. -230. -220. -210. -200. -195. -195. -191. -190. -189. -188.6. -187.9 -187. -185. -185. -180o. -175. -170. -160. -140. -120. -100. - 80. - 60. - 40. 0.2924 0.3055 0.5236 0.5558 0.3970 0.5226 0.7004 0.8255 1.0750 1.3410 2.7590 10.1000 9.0450 1.9400 1.2170 0.7862 0.5800 0.4274 0.3691 0.2899 0.2214 0.2050 0.1850 0.1745. 1620 0.1530 -250. -2L0. -250. -220. -210. -200. -195. -190. -188. -186. -184. -183. -182.6 -182. -181. -18o. -178. -175. -170. - 160o. -150. -140. -120. -100. - 80. - 60. - 40. 0.2705 0.2946 0.5204 0. 5435 0.5850 0.4793 0.6072 0.8000. 9095 1.1500 2.1950 3.7600 4.0570 3.2560 2.4120 1.6780 1.1510 0.7930 0.5515 0.3600 0.296( 0.2660 0.2187 0.1945 0.1740 0.1614 0.1650 I!

TABLE III-2 (Concluded) Pressure = 950. psia Pressure = 1143. psia Pressure = 1371. sia 2000. psia Temperature C Te-perature C Temperature CTemperature C Temperature C (~F) (Btu/b-~F) (~F) (Btu/lb-F) (~F) (Btu/~b-~F) (~F) (Btu/b-~F) (~F) (Btu/b-OF) -18o. -178. -176. -174. -172. -170. -168. - 16. 0.9640 1.1260 1.3520 1.6270 1.4400 1.2140 1.036o 0.8444 -250. -230. -210. -200. -190. -180. -170. -167. -165. -163 5. -16o. -150. -140. -130. -120. -100. - 80. - 60. - 30. 0. 30. 60. 90. 120. 150. 18o. 0.2846 o. 3025 0..5466 0.3863 0.4437 0.5477 0.8150 o.8995 0.9350. 9004 0.8587 0.5905 0.4294 0. 35464 0.3000 0.2400 0.2101 0.1935 0.1763 0.1637 0.1562 0.1518 0.1468 0.1441 0.1409 0.1587 -250. -250. -210. -200. -190. -180. -170. -160. -158. - 156. -154. -150. -140. -150. -120. -100. - 80. - 80. 0.2714 0.2959 0.3270 0.3538 0.3898 0.432L 0.5354 0.6295 0.6490 0.6624 0.6490 0.6171 0.5344 0.4335 0.3638 0.2800 0.2370 0.2224 -250. -230. -210. -19o. -18o. -170. -16o. -150. -146. -144. -142. -140. -130. -120. -100. - 80. - 60. 0.2626 0.2866 0.3107 0.3447 0.3712 0.4037 0.4463 0.4830 0.4929 0.4947 0.4929 0.4890 0.4572 0.4155 0.5296 0.2714 0.2580 -250. -230. -210. -190. -180. -170. -16o. -150. -140. -136. -13L. -130. -120. -100. - 80. - 60. - 40. - 20. 0. 50. 90. 120. 150. 18o. 0.2608 0.2797 0.2994 0.5225 0.3585 0.3532 0.5745 0.3958 0.4185 0.L235 0.42L8 0.L217 0.4086 0.3512 0.2932 0.2565 0.2319 0.2121 o.,1988 0.1851 0.1715 O.1365 0.1580 0.1534,.1497 I lO!

-53 Pressure (psia) 706 800 950 1143 1371 1714 2000 TABLE III-3 Cp(T) Maxima Data For Argon TM (~F) (Btt -188.6 ~0.2 >10 -182.6 +0.2 4 -174.0 +0.2 1 -165.0 ~0.2 0 -158.9 ~0.5 0, -144.0 +0.8 0, -134.0 +1.0 0 C M /p u/lb-~F).0.057.627.935.649.4947.4248 ~0.014 +0.004 ~0.003 ~0.002 ~0.0015 ~0.0010 Isenthalpic and Isothermal Data One isenthalpic run was made at -240~F and the basic data were plotted (see Figure III-19) to obtain the values of p. It is observed that the curve goes through the inversion point (0 = O at P = 425 psia). The values are listed in Table III-4. Table III-5 presents isothermal enthalpy changes at -240~F which were obtained from the isenthalpic data using the method discussed in Section II. A typical isothermal run -168.3~F) is illustrated in Figure III-20. The equal area curve is drawn through the basic isothermal data using the method discussed in Section II. Note that all the 0 values are negative. This curve is extrapolated to the zero pressure value calculated from the thermodynamic relation 0 (T, P = 0) = B - T (d) ( I I I -7) where B is the second virial coefficient. 21 B from Gosman, et al.21 (expressed in an equation form) was used for the calculation. The -0 value increases sharply as the pressure approaches the peak location (P a 950 ~25 psia), where -0 reaches its maximum (0.06915 ~0.00069 Btu/lb-psid), and then it decreases rapidly as the pressure passes the peak. At higher pressures 0 changes only slightly

-54 JOULE-THOMSON COEFFICIENT RRGON -240.OF 0 0 -p -:- a n3: a_ sm -j %-IPa:6 bI' Inversion at 425 1t psia b aso. 500. 750 1000. 1S0 0. PRESSURE (PSIR) 1500. 1750.. 200. Figure III-19. Joule-Thomson coefficient for argon at -240~F. rSOTHERMRL THROTTLTNG RRGON -168.3~F COEFF CIENT o cE; a m a_ t.p^ ^ F Figure III-20. Isothermal throttling coefficient for argon at -168.3~F.

-55 TABLE III-4 JOULE-THOMSON COEFFICIENTS OF ARGON AT -240.~F Pressure D x 100 (psia) ( F/psid) 250. 0.0700 500. 0.04o54 400. 0.0033 500. -0.0245 600. -0.0471 800. -0.0850 1000. -0.1140 1200. -0.1427 1400. -0.1722 1600. -0.1992 1800. -0.2248 2000. -0.2515 TABLE III-5 ENTHALPY DIFFERENCE OF -240. F ISOTHERM CALCULATED FROM THE ISENTHALPIC DATA Pressure H (psia) (Btu/lb) 2000. 0 1714. -0.18 1571. -0.57 1143. -0.47 800. -0.58 706. -0.60 571. -0.62 457. -0.63 286. -0.62

-56 with pressure. The other isotherms at -208.9~F, -191.2~F and 167~F are also illustrated in Figures III-21, III-22 and III-23, respectively. Another 0(P) maximum was determined from the -58~F isotherm as shown in Figure II-4 (-d = 0.01073 +0.00005 Btu/lb-psid at P = 1200 ~50 psia). Values for 0(P) maxipm are listed in Table III-6. The 0 values of the isotherms are presented in Table III-7. Values for 11 and 0 are listed in Tables C-2 and C-3 of Appendix C. TABLE III-6 0(P) Maxima Data for Argon Temperature Pressure -0 x 100 (~F) (psia) (Btu/lb-psid) -168.0 950 +20 6.915 ~0.069 - 58.0 1200 +50 1.0725 ~0.0054 Enthalpy Changes on Vaporization A typical plot of enthalpy vs temperature across the two phase boundary (457 psia) is shown in Figure III-24. Enthalpy change on vaporization is determined from the enthalpy difference between the upper and lower break points. It was observed that the phase transistion is isothermal within ~0.02~F (note that the sample used in the measurement is 99.9% argon). Enthalpy traverses for 286 and 571 psia appear in Figures III-25 and III-26. The data for these plots are presented in Table C-4 of Appendix C. The latent heats and saturation temperatures determined in this work are presented in Table III-8 together with literature values for comparison.

-57 ISOTHERMRL THROTTLING COEFFICIENT RRGON -208.9 F $^' s CA =3 a o 4 CXa.(n I _ tCO b 2S. SOO. 7S0. 1000. 1250. tS00. 17S. O000. PRESSURE (PSIRA Figure III-21. Isothermal throttling coefficient for argon at -208.9"F. ISOTHERMRL THROTTLING COEFFICIENT PRESSURE (PSIR) Figure III-22. Isothermal throttling coefficient for argon at -191.2"F. THROTTLING COEFFICIENT I 167.0~F'.'igure 111-25. Isotlhermal tllottlilKg coetffieint I'or arg'ot, at. t)'lY"F.

TABLE III-7 ISOTHE-R.;r T-iOTTLING COEFFICIENTS OF ARGON U-emerature = -209.~F Temperature = - 191.~F Tempereture = -168.~F Temperature = -5.mF Tempereture = 167.~F Presure - ~ x 100 Pressure - e x 1C Pressure - 0 x 100 Pressure - ~ x 100 Pressure - x 100 -i s e ) (Btu/lb-ps id) (psia) (Btu/1b-msid) ( {si ) (Btu/lb-psid) (psia) (Btu /lb-psid) (r si ) (B-tu/lb-psid) _.~~~~~~~~~~~~~~~~~~~~~~~~~~B d)Bt / —b _j S/-0A.00..,_,-co. 200:. 2IC3. 2vvt 0.3690 0.3284 0.2646 0.2180 0.1739 O.1474 0.0994 0.0605 0.0297 0.0078 0.0077 0. 100. 200. 300. 400. 500. 580. 660. 740. 780. 820. 900. 1000. 11C0. 1200. 1400. 1600. 1800. 2000. 1.8900 2.0800 2.3400 2.640GO 5.1400' 4.1700 6.o510 8.282C 2.0400 1.6230 1. 030 0.9002 0.6355 0.46355 0. 5657 0.23590 o.166o 0.1054 0.0,5485 100. 200. 4r0..00. 700. 800. 900. 930. 950. 98-5. 1100. 1200. 1800. 2000. 1.6410 1.7620 1.8990 2.o840 2.2950 2.5670 2.9740 3.5890 4.5280 6.2000 6.8070 6.9150 6.7 040 6.4700 3.7500 2.2100 1.3650 0.9940 0.5841 0.4071 0.2964 0. 200. 400. 600. 800. 900. 1000. 1100. 1200. 15300. 14oo. 1400. 1600. 1800. 2000. 0.9450 0.9741 0.9953 1.0220 0.0510 1.0600 1.0670 1. 0710 1. 0725 1.0670 1.050 1.0270 0.9928 0.9620 0. 200. 400. 600. 1200. 1LO0. 6o00. 1800. 2000. 0.4037 0.4105 0.3969 0.5863 0.5761 0.3668 0.5572 0. 3475 0.3373 0. 3280 0.3207 I o, 00

ISOBRRIC ENTHRLPY TRRVERSE 8 RRGON 457. PSIR C 3x3 I. 8 o <1 8o -l20.00 -21.00 -20.00 -202.00 -19.00 -190.0 TEMPERRTURE OF Figure 1II-24. Isobaric enthal p;raverse across -rhe two spase bo'':iary for argon at 457 psia. ISOBRRIC ENTHRLPY TRRVERSE 8 RRGON 286. PSIR ISOBRRIC ENTHRLPT TRRVERSE ~! RRGON 571. PSIR o. 8 CD o. ~ U2 Ck r aoD u( a:8 =11 o Cl 9 P. o ^- 0 2 r~ a* o om ~ < o ao 8o o cu C~ 9 vxC. 19 I Ql!J p08'- 0.00o -21.00 -228.00 -222.00 -28.00 -20o.00 TEMPERRTURE ~F 7zre III-25. Isobaric enthalpy traverse across the two phase bo —ary for argon at 286 psia. "-210.00 -. -o -200.00o -19S.00 -190.00 -18S.00 TEMPERRTURE ~F Figere Ir-26. Isobaric enthalpy traverse across the two t_. - bo-ro ary for argcr. a, 571 psia.

-60 TABLE III-8 Saturation Data for Argon Pressure Latent Heat (Btu/lb) 22 Saturation Temp. (~F) 22 (psia) This Work Gosman et al. This Work Gosman et al. 286 47.66 ~0.05 47.53 -226.74 ~0.02 -226.75 457 36.57 ~0.05 36.66 -207.97 ~0.02 -207.94 571 27.68 ~0.05 27.55 -198.00 ~0.04 -198.17 Heat Leak Check As discussed in Section II, the calorimeters used in this work are designed and operated in such a way that the heat leak from the calorimeters Q can be reduced to an insignificant level during the non-isothermal operation. Accordingly, Q is neglected from the enthalpy measurements. A series of isobaric enthalpy determinations were made at four different flow rates with the same inlet and outlet conditions to 40, 36, 37, 61, 18 establish whether or not the calorimeter was adiabatic. As the result (AH/AT) vs 1/F plot is made on Figure III-27, where AT is the temperature difference across the calorimeter. The plot indicates that the mean heat capacity is independent of the flow rate, which confirms Q is insignificant if not zero. Thermodynamic Consistency Checks The consistency checks between isobaric and isothermal measurements of argon are presented in Figure III-28. Isobaric and isothermal enthalpy differences between the experimental isotherms and isobars appear on each of the related intervals (all the values are in Btu/lb). Numbers in parentheses represent the adjustments required for every loop to be balanced. (A more detailed explanation is in Section II). The average and maximum inconsistencies in terms of the percent deviation are 0.09 and 0.34, respectively. Accuracies of the present isobaric and isothermal data are estimated at 0.2% and 0.4%, respectively.

LL oi 1.352 u. o 1.348! 1.344 w I - - - - - - - - 1.3492o 8 +0.15% o 0 -0.15% Pressure: 290 psia Inlet Temp.: -50.7~F Outlet Temp.: 82~F I I.... _.....I__.......... I I z 2 0 5 10 15 20 25 INVERSE OF MASS FLOW RATE I/F (min/lb) Figure III-27. Heat leak test for the isobaric calorimeter. Mean heat capacity of argon as a function of reciprocal flow rate.

-62 8.87 5.51 7.74 39.37 40.96 Oc 00 + O 6 (+0.044) -0.06 -0. 537% 9.12 (+0.028) H O 0 0 oI v -0.02 -0.1741o CM 0 0 0 d v3 (-0.029) +0.01 +0.056% I I 5.77 8.55 (-0.016) (+0. o8) O1 1371 o0 0 ~ v -0.01 -0.055 9.45 o i o o 6, \_ +0.00 +0.00% Go 0 o! (-n.019) tO. 07 +0. 321.2 6.28 10.24 0 N4 I r-q II D -i CM 0 o _7 (-0.006) -0.11 (N -0.'12x5 K I 0 0 (+0.049) -0.05 H41.165 41.16 1 42.42 I i (+0.106) n 0 EAH. -0. 1 -1 0o H 0 6d + + I I - (-0.026) -0.01 -0.0527 9.76 (+0.008) (0.039) (o.013) 0 0 I6 v - -o.04 -0.284% -t0 C- 0 66 I f -0.01.-0.0355 1 A.% r C 0 0 + d i EAH. l ~1 = — o.011%, -- 0 0 Cj +O d c0 ro 1-4 35.09 +o. o4 2 +0.04 W +0.045% C I 6.86 1143 40.80 (-0.0o6) (-0.032) (+0.010) (-0.04) - r'0 o ~ +o.04 +0. 19% o 0 O o 6. +0.01 +0.05x3 o 0 6 cv I +0.02 +0.0351% I C( I" o 0 0 v +o.o4 +0.045 +o. 04%o GO I 10.37 8.94 29.48 25.80 c. CM aU CM (U (+0.004) (-0.022) (+0.0o) (+:. 0). o~ -0.04 ~ -0.04 c o+0.05 o oc -o.189%, s -0.047%,, +0.094% o 7 10.66 42.0o3.22.93 6 (-0.056) /(-0.046) (+. 064) co o -0.02 H-'o / -0.08 c NM -0.02 oc o 6. -0.091% / -0.086% -0.04, H ~ oI 11.11 58.65 7.39 20.02 (-0.056) (-0.146)/ (+0.00' (+0.071) 3 o +0.06 CM/ o -0.04 0.7 + 0 +0.055 / O + -0.191% 0 ~ -0.164% H 454.90 5.2218.24 I I I I I cI I L o o d (3 _/ (+0.096) 0 I v c0 -o.09 -0. 117% CoW D I II -N C C C ( - I 0 0 0 \0 0 H o o0 00.. o o, (-0.167) / -O. 01 -0.01 -0.008% -o. oo ~ / 60.03 r<^ C-1 iA I oN o 0 C; (+0.00) +0.00 +0.00% IC I' 3.92 IM _, o, (-0.008) -0.05 -0. 125% Ci 16.16 (-0.194) I (+0.00) o 0 0 1 (-0.03) 0 C 0 g +0.00 +0.00% 2.85 Kr C IT 0 o co -0.01 t-0.026% C 15.72 To 29.60 (-0.022) -t 1 o. +0.05 0.049g oN rH I 27.98 (+O.OQ) (+.o00) (+0.00) -240 -208.9 -191.2 -168.3 -58 167 Temperature (~F) Figure III-28. Thermodynamic consistency present calorimetric data for argon. checks for the

-63 Enthalpy Table and Diagram The enthalpy diagram presented in Figure III-29 represents the enthalpy of argon at any point within the region of the present measurements as defined in Figure III-8. The diagram is prepared mainly by the data obtained from the present investigation and the zero enthalpy value calculated from the knowledge of Cp (= 5/2R). Saturation enthalpies 22 were obtained by smoothing the values given by Gosman with the ones determined from the present experiment. Table III-9 lists those smoothed enthalpy values at saturation. Table III-10 tabulates enthalpy values at regular intervals of temperature and pressure, including those for the measured isotherms. The reference selected for the enthalpy of argon is H = 0 for the perfect crystal at 0~R. This reference has been taken by 10, 22 several investigators' as calorimetric data for solid argon are available down to a low temperature. Din10 calculated the enthalpy of the saturated liquid at 1 atm (87.28~K) from the ideal crystal at zero temperature to be 2972.46 J/mole (32.011 Btu/lb). This value was obtained by integrating and summing the calorimetric data of Clusius extending from 10~K to the normal boiling point (87.28~K) and adding to it a value based on the Debye relationship: C = kT3 (III-8) between 0~K and 100K, K being a constant evaluated from the Cp values close to 100K. Gosman22 later set the enthalpy for the ideal gas at 87.28~K to be 237.9316 J/g (102.355 Btu/lb) based on Din's value. In this work, the enthalpy values along the 0 psia isobar were obtained by adding to the Gosman's value zero enthalpy changes from 87.28K based on Cp~ = 5/2R. Those values, then, specified the reference enthalpy for every experimental isotherm at 0 psia. Therefore, the enthalpy of the ideal gas at -240~F is obtained as in the following:

eI 1 I co CI.......E E-;1 1'T 1-11TLWI.... _.... 1 _ 2 0 t 4. t t t tt m 4 t t t 2 2 |;rS_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... [ Ig g S -g e 0 1 S m - X: S m e~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~IIIFIII 11L I —Lj ~ ~ I 09t. OZ Z;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ S S + = o~~~~~~~~v ~~~ -tt-~~~~~t 09~~~~~~~~i E!- _!i~~Ht Oa-+. t e i-F tt n 09 i _ I~~~~~~~~~ ~~~~~~~~~~~ I I1 fil I Bs'~~~~~I l W-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~E I ms~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~m I~~~~~~ ~ ~~ ~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ imH wFilt Xm4# ~ ~ ~ ~ ~ ~ ~~~~~~il"rt $tt~tt -f l Ht 7..m+-7L- ~~~~~~'891-~~~~~~~~~~~~~tf Ul1 14 r - t t~~~~~~~~~~~~~t!tt I- L, — L -# IV V1 1~11-1-'' -!-Ct-!-i li- tF CI'' i''''i-f.q liCtti flfit: c -I- i-i7! —j i(.L FI-~~~~~~~t Ob~~~~~~~~~~~14 -,TT OT-!arii -,et Aa ~~~~~~~t4 MMM~~~~~~~~~~~~i:.. -— ticiI~-~j: F 0 o Q tbD q-q k O _ g Cd cr H > I a. P1 K1. r N z1 w Hr H h0 ril PC, I |k, 3LUni 8 d~~i 31i C Cg4,, f i || 4f jj Il,lfj.i, jfj,!5 ifflW p'4t$! t I <'1'0 t i J I 4I - t 1 i I I i O I < Ii 2 ~~~~~~~~~~~~~~~~~~~~I IA: I I LL CU Z - -------— t ii L it ~ iC O:i~~~~~~~~~~~~~~~~~~~~~~~ D C) lil!..i.itt -i "tt' 1 (9) t r ~~~~f I d~~~~~~~~~~IIII, I 8 N~ 8 -8 0 o (oisd) 3nS o So (oisd) 3UnSS3Ud w w 0^ ~t %O

TABLE III-9 TABULATED VALUES OF THE SATURATION ENTHALPY FOR ARGON Saturation Saturated Latent Pressure. s Temperature Liquid Vapor Heat (psla) __ (~F) (Btu/lb) (Btu/lb) (Btu/lb) 100 -261.6 44.1 103.9 59.8 200 -239.6 50.7 103.5 52.8 286 -226.74 54.8 102.5 47.7 300 -225.0 55.4 102.2 46.8 400 -213.6 59.9 100.3 40.4 457 -207.97 62.3 98.9 36.6 500 -204.1 64.2 97.6 33.4 571 -198.0 67.4 95.1 27.7 600 -196.0 69.2 93.8 24.6 700 -189.0 79.8 86.0 6.2 Not e: H = O for the perfect crystal at O.~R

-66 TABLE III-10 TABULATED VALUES OF ENTHALPY FOR ARGON Temperature Pressure (psia) (~F) 0 100 200 300 400 50 600 700 800 00 1000 -240. 110.14 107.08 0.12 50.10 50.09 50.09 50.11 50.12 50.14 50.17 50.20 -230. 111.38 108.71 105.25 530 53.25 53.23 53.15 53.04 53.20 53.03 53.10 -220. 112.63 110.23 107.78 103.51 6. 56.50 56.48 56.46 56.47 56.37 56.28 -210. 113.87 111.52 109.00 10578 101.52 0.73 60.32 60.23 60.10 59.96 59.80 -208.9 114.00 111.70 109.23 105.98 101.76 61.1 60.75 6053 60.49 60.30 02C -200. 115.11 113.03 110.70 107.95 103.70 100.03 65.74 4.90 64.31 63.87 63.51 -191.2 116.21 113.95 111.28 109.60 106.71 102.99 97.85 87.40 69.45 68.17 67.50 -190. 116.36 114.20 112.00 109.75 106.97 103.42 98.43 90.15 70.48 68.73 67.90 -180. 117.60 115.71 113.67 111.44 108.98 106.15 102.67 97.83 89.20 76.50 74.1C -170. 118.84 117.02 115.22 113.10 110.94 108.48 105.70 102.23 98.05 91.50 85.27 -168.3 119.06 117.30 115.55 113.51 111.28 108.97 106.21 102.80 98.30 92.77 86.7r -160. 120.09 118.45 116.71 114.79 112.79 110.55 108.09 105.31 102.36 98.80 94.5, -150. 121.33 119.93 118.27 116.48 114.69 112.73 110.54 108.22 105.63 102.73 Q0.72 -140. 122.58 121.28 119.80 118.22 116.42 114.50 112.50 110.48 108.45 106.22 103.78 -130. 123.82 122.49 121.01 119.51 117.95 116.25 114.55 112.75 110.99 109.10 107.0' -120. 125.06 124.98 122.62 121.23 119.72 118.04 116.50 114.84 113.27 111.47 109.60 -110. 126.31 125.13 123.78 122.48 121.08 119.72 118.24 116.73 115.39 113.72 112.10 -100. 127.55 126.30 125.15 123.82 122.10 121.28 119.98 118.60 117.40 115.97 114.5C - 90. 128.79 127.15 126.49 125.28 124.09 122.82 121.67 120.45 119.29 117.80 l1'.50 - 80. 130.04 128.94 127.90 126.76 125.11 124.49 123.28 122.17 121.08 119.74 118.52 - 70. 131.28 130.24 129.21 128.12 127.03 126.00 124.95 123.90 122.78 121.53 120.45 - 60. 132.52 131.50 130.48 129.49 128.48 127.45 126.43 125.39 124.42 123.26 122.21 - 58. 132.77 131.71 130.78 129.80 128.80 127.80 126.78 125.76 114.75 123.70 122.6' - 50. 133.77 132.90 131.93 130.95 129.99 129.01 128.00 127.00 126.02 125.08 1.24.05 - 4.0. 135.01 134.05 133.17 132.22 131.77 130.44 129.49 128.56 127.63 1.26.72 125.80 - 30. 136.25 135.42 143.50 133.68 132.75 131.92 130.Q9 130.15 129.32 128.43 127.52 - 20. 137.50 136.18 135.81 135.00 134.20 133.39 131.51 131.70 130.80 130.05 129.22 - 10. 138.74 137.97 13. 17 136.41 135.52 134.77 134.00 133.22 132.43 131.67 ]130.85 0. 139.99 139.23 138.49 136.72 136.98 136.20 135.47 134.70' 133.45 133.20 132.96 10. 141.23 140.49 139.24 139.00 138.29 137.55 136.81 136.15 135.43 134.72 133:-A 20. 142.47 141.72 141.02 140.41 139.70 138.99 138.28 137.60 136.91 136.25 135.53 30. 143.72 143.02 142.41 141.72 141.04 140.45 139.74 139.08 138.39 137.77 137.18 40. 144.96 144.24 143.59 143.01 142.43 141.76 141.10 140.50 139.85 139.23 138.0 7 50. 146.20 145.51 144.95 144.32 143.73 143.12 142.51 141.96 141.30 140.70 140.17 60. 147.45 147.83 146.25 145.67 145.05 144.50 142.43 143.30 142.73 142.18 141.56 70. 148.69 148.05 147.50 147.00 146.45 145.79 145.27 144.72 144.15 143.58 143.03 80. 149.93 149.30 138.74 148.18 147.67 147.08 146.58 146.03 145.57 145.00 144.50 90. 151.18 150.57 150.06 149.59 149.10 148.53 148.06 147.04 146.97 146.52 146.02 100. 152.42 151.82 151.32 150.82 150.32 149.90 149.42 148.95 148.36 147.94 147.4'7 110. 153.66 153.03 152.55 152.09 151.70 151.21 150.72 150.25 149.75 140.30 148.90 120. 154.91 154.40 153.96 153.46 152.95 152.47 151.99 151.50 151.13 150.55 150.21 130. 156.15 155.71 155.22 154.75 154.29 153.82 153.30 152.83 152.50 152.00 151.55 140. 157.40 157.00 156.50 156.04 155.64 155.20 154.72 154.22 153.87 153.47 153.02 150. 158.64 158.23 157.78 157.41 156.98 156.50 156.01 155.63 155.23 154.75 154.35 160. 159.88 159.35 158.99 158.52 158.20 157.76 157.43 156.99 156.59 156.10 155.72 167. 160.75 160.25 159.95 159.50 159.00 158.62 158.23 157.80 157.48 157.05 156.70 170. 161.13 160.68 160.28 159.93 159.51 159.15 158.75 158.40 157.95 157.08 157.23 180. 162.3( 161.99 161.53 161.12 160.73 160.43 159.98 159.53 159.29 158.81 158.50 190. 1653.61 163.18 12.80 162.48 162.02 161.68 161.30 16o0.98 160.63 160.30 159.o9 200. 164.86 164.50 164.07 163.77 163.48 163.05 162.72 162.43 161.97 161.68 161.28 210. 166.10 165.(5 1.65.30 164.99 164.70 164.32 164.00 163.72 163.31 168.00 162.70 220. 167.34 167. 00 166.59 166.28 165.99 165.57 165.35 164.94 164.64 1'09.27 164.00 WAT'I'UM: H1 0 f'or perfect cryst; 1 nt;t 0~H., Unit f'or H In Btu/lb.

TABLE III-10 (Concluded) Temperature Pressure (psin) (~F) 1100 1200 1.300 1400 1500 1600 1700 18(X) L0()0 2000 -240. -230. -220. -210. -208.9 -200. -191.2 -190. -180. -170. -168.3 -160. -150. -140. -130. -120. -110. -100. -90. - 8o. - 80. - 70. - 60. - 58. - 50. - 40. - 30. - 20. - 10. o. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 16o. 167. 170. 180. 190. 200. 210. 220. 50.25 50.30 53.10 55. 20 56.24 56.24 59.70 59.52 60.02 59.98 63.25 63.00 67.00 66.51 67.98 67.98 72.67 71.70 80.55 77.22 81.98 78.98 89.84 85.80 96.05 92.62 101.16 98.22 104.95 102.33 106.73 105.72 110.49 108.71 113.00 111.97 115.17 113.68 117.27 116.00 119.27 118.18 121.10 120.02 121.55 -120.48 123.07 121.07 124.90 123.99 126.68 125.80 128.43 127.58 130.06 129.33 131.70 130.99 133.25 132.53 134.94 134.22 136.35 135.80 i38.00 13'y. 45 139.55 139.00 141.23 140.51 142.52 142.01 143.99 143.50 145.52 145.02 146.98 146.50 148.42 147.95 149.80 149.30 151.18 150.77 152.62 152.23 153.98 153.58 155.30 154.98 156.32 155.98 156.82 156.49 158.23 157.92 159.60 159.27 161.01 160.63 162.40 162.00 163.72 163.47 50.32 50.37 53.23 53.26 56.25 56.25 59.48 59. 45 59 92 59.77 62.78 62.60 66.20 65.93 66.77 66.48 70.95 70.34 76.22 75.10 77.20 76.00 82.96 80.85 89.60 87.01 95.42 92.98 99.95 97.73 103.20 102.72 106.78 105.08 109.81 108.22 112.18 110.75 114.70 113.28 116.98 115.76 118.99 117.95 119.30 118.26 121.10 120.05 123.05 122.20 124.98 124.04 126.75 125.98 128.52 126.78 130.23 129.49 131.90 131.17 133.55 132.95 135.22 134.56 136.80 136.23 138.44 137.82 139.99 139.45 141.50 141.01 142.98 142.48 144.52 144.03 146.00 145.04 147.50 147.01 148.95 148.50 150.33 149.95 151.34 151.48 153.20 152.80 154.61 154.23 155.70 155.33 156.17 155.82 157.52 157.23 158.96 158.55 160.32 160.01 161.22 161.47 163.18 162.85 50.43 53.28 56.26 59.42 59.78 62.50 65.66 66.23 69.95 74.46 75.08 79.45 85.12 90.78 95.72 99.93 103.50 106.68 109.44 112.01 114.15 116.87 117.30 119.00 121.24 123.22 125.18 127.01 128.74 130.48 132.24 133.99 135.60 137.25 138.92 140.48 142.00 143.55 145.10 146.57 148.01 149.50 151.01 152.51 153.47 155.00 155.49 156.95 157.76 159. 72 1(1.12 162.57 50(.48 53.30 56.26 59.40 59.75 62.48 65.50 66.01 69.55 73.82 74.50 78.27 83.58 88.96 93.84 98.22 101.97 105.15 108.05 110.82 113.48 115.80 116.32 117.78 120.34 122.36 124.32 126.22 128.02 129.82 131.60 133.35 135.04 136.70 138.82 139.97 141.50 143.05 144.62 146.15 147.57 149.08 150.60 152.08 153.52 154.70 155.09 156.55 157.99 159.45 160.83 162.28 50.54 50.60 50. 66 50.(2 53.42l 53.46 53.14 53. 53 56.2'7 56.27 56.28 5l. 3 59.43 59.38 59.35 50.30 59.77 59.72, 59. 7'2 5- ).75 62.47 62.47 62.44 62.35 65.46 65.28 65.30 65.20 65.92 65.73 65.57 65.57 69.40 69.20 69.00o 8.82 73.28 72.92 72.51 72.28 74.03 73.53 73.05 72.80 77.48 76.80 76.26 75.66 82.30 81.32 80.50 79.81 87.32 85.95 84.72 83.90 92.07 90.66 89.40 88.13 96.55 95.03 93.68 92.28 100.48 99.02 97.61 96.26 103.80 102.95 101.10 99.91 106.78 105.55 104.42 103.27 109.70 108.52 107.44 106.33 112.30 111.22 110.15 10q.13 114.83 113.80 112.77 111.75 115.40 114.45 113.48 112.45 117.00 116.05 115.20 114.23 119.48 118.52 117.18 1(..62 121.49 120.54 119.72 1.18.89 123.50 122.70 121.00 121.05 125.47 124.68 123.92 123.1.4 127.29 126.56 125.94 125.1 129.10 128.47 127.73 127.1.2 130.95 130.25 129.62 120.02 132.72 132.15 131.50 130.08 134.49 133.7 133.28 1.32. 6 136.08 135.52 134.08 134.44 137.78 137.24 136.72 13(. 17 139.55 138.93 138.85 137.8(. 141.00 140.50 140.03 130.53 142.57 142.10 141.63 141.15 143.19 143.80 143.30 142.77 145.70 145.23 144.35 144.37 147.19 146.76 146.45 145.95 148.67 148.25 147.82 147.51 150.23 149.86 149.49 14o. o1 151.24 151.90 151.00 150.61 153.23 152.89 152.51 152.11 154.37 154.00 153.20 153.30 154.83 154.49 154.11 153.77 156.25 155.97 155.60 155.27 157.19 157.43 157.05 156.74 159.05 158.82 158.50 158.22 160.52 160.24 160.00 159.68 162.00 161.70 161.48 161.14 DATUM: II = O for perfect crystal nt 0~R. Unit for It is Btu/lb.

-68 H (Btu/lb) Perfect Crystal at 0~R 0 Saturated liquid at 1 atm and -302.57~F 32.011a b Latent heat at -302.57~F 69.671 Pressure effect on enthalpy (from 1 atm to 0) 0.673 Ideal gas enthalpy (-302.57~F to -240~F) 7.781C 110.136 aEstimation made by Dinl b 22 Calculated by Gosman et al. CBased on Cp~ = 5/2R Comparison With Other Published Data In order to make a comparison between the isobaric heat capacity, data of this work and those of Walker,60 the latter was smoothed to obtain the values along the isobars of the present measurements. Thirtyfive points were compared covering a temperature range from -250~F to -140~F and a pressure range from 286 psia to 1371 psid. A comparison 385 39 was made against the smoothed values of Cp which Michels et al.38' 39 derived from their accurate PVT data. One hundred thirty three points were compared covering temperatures from -229~F to 220~F and pressures up to 2000 psia. Finally, a comparison is made with Cp values, which were calculated from the equation of state proposed by Gosman, et al.22 Since Gosman, et al.22 did not compile C values in their table, the P writer had to carry out the computation for those values using an expression for Cp derived from their equation of state. Values of 155 points are included in the comparison of temperatures ranging from -240~F to 60~F and pressures up to 2000 psia. Results of these comparisons are presented in tabular form in Table III-11. Tabulations of such comparisons are useful but are difficult in assessing the overall trend for the comparisons. Therefore, topographical deviation diagrams, as shown in Figures III-30, III-31 and III-32,

TABLE III-11 COMPARISONS OF ISOBARIC HEAT CAPACITIES OF ARGON Pressure = 286. osia __ Pressure = 457. psia ^ Pressure = 571. psia Temperature Cp (Btu/lb-~F) Temperature Cp (Btu/lb-~F) j Temperature __ (Btu/lb-~F) Ter(-Derature Thiserature Temperature T empe tu/ F FWalker Michels Gosrmani Walker Michels Gosman Walker Michels Gosman Work Work 4 Work ii ii -220. 0.2457 0.2310 0.2321 -240. 0.3090 0.310 i -230. 0.3281 0.525 -210. 0.2152 0.2050 0.2062 -230. 0.3378 0.336 -220. 0.3691 0.363 -200. 0.1923 0O.1890 0.1897 -220. 0.3880 0.380 -210. 0.4362 0.433 0..L292 0.L285 -190. 0.1787 0.1770 0.1790 -215. 0.4250 0.417 -200. 0.6649 0.680 1.5765 -180. 0.1705 0.1700 0.1703 -210. 0.4750 0.474 0.5406 -196. 0.7620 0.720 0.6616 -170. 0.1640 0.1650 0.1644 -202. 0.5620 0.382 0.2419 0.3519 -190. 0.4360 0.486 0. 1337 -160. 0.1586 o.1566 0.1587 -190. 0.2528 0.275 0.2662 0.2639 -180. 0.3112 0.355 0.3128 -150. 0.1544 0.1528 0.1556 -185. 0.2389 0.246 0.2447 -170. 0.2544 0.297 0.2607 -140. 0.1510 0.1481 0.1515 -180. 0.2276 0.219 0.2302 -160. 0.2270 0.261 0.2760 0.2308 -130. 0.1482 0.1498 0.1487 -170. 0.2100 0.2079 0.2092 -140. 0.1983 0.1977 0.1975 -120. 0.1460 0.1472 0.1466 -160. 0.1961 0.1952 0.1948 -120. 0.1794 0.1790 0.1790 -110. 0.1441 0.1445 0.1440 -140. 0.1759 0.1170 0.1761 -100. 0.1680 0.1676 0.1677 -100. 0.1424 0.1427. 145' -120. 0.1638 0.1646 0.1644 0 o. 0.154 0.1589 0.1596 - 80. 0.1398 0.1397.1401 -100. 0.1551 0.1569 0.1567 60. 0.1515 0.1534 0.1537 - 6 0.0.13 00.1375 0.1371 - 80. 0.1508 0.1506 0.1512 - 40. 0.1359 0.1355 0.1349 - 60. 0.1475 0.1466 0>.1465 - 20. 0.1544 0.1342 0.1351 } 0. 15.i335 0.1331 0.13555 20. 0.1324 0.122 0.1325 40. 0.1316 0.1314 0. 134 70. 0.1506 0.130 0.1294 i 100. 0.1295 0.1294 130. 0.1288 0.12357 i 16. 0.28 0.128.1282 190. 0.1281 0.1278i 220. 0.1278 0.1274 I!

TABLE III-11 (Continued) Pressure = 706. psia Pressure = 800. psia Pressure = 114. psia Cp (Btu/lb-~F) Cp (Btu/lb-~F) Cp (Btu/lb-~F) Temperature Th Temperature Temperature -Te(~F) Walker Michels (~F) This Gosman (This Walker Michels GThis (CF) Walker Michels Gosa (F) Walker Michels Gosman (F) Walker Michels Gosman Work Work Work -250. -240. -230. -220. -210. -200. -190. -185. -18o. -175. -170. -16o. -140. -120. -100. - 80. - 60. - 40. 0.2924 0.5035 0.3236 0.5558 0.3970 0.5226 1.341 1.217 0.5800 0.4274 o.3691 0.2899 0.2214 0.2030 0.185o 0.1745 0.1620 0.1530 0.297 0.316 0.348 0.599 0.527 0.545 0.455 0.544 0.3400 0.3910 0.5110 0.6057 0.3923 0.2454 0.2014 0.1821 0.1699 0.1622 0.1557 0. 276 0.2904 0.3102 0.3401 0.3925 0.5151 1.6075 1.081 0.6057 0.4541 0.3780 0.2987 0.2310 0.2002 0.1820 0.1705 0.1623 0.1561 -240. -220 -210. -200. -19o. -184. -180. -175. -170. -160o. W150. -140. -120. -100. - 80. - 60. - 40. 0.2946 0.3435 0.3850 0.4793 0.8000 2.195 1.678 0.7930 0.5513 0.3600 0.2960.2660 0.2187 0.1945 0.1740 0.1614 0.1630 0.3230 0.5660 0.4500 0.5760 0.3810 0.3090 0.2680 0.2213 0.1937 0.1784 0.1689 0.1609 0.2870 0.33145 0.3746 0.4614 0.7622 2.5414 1.745 0.7976 0.5527 0.3753 0.5020 0.2616 0.2174 0.1935 0.1787 0.1683 0.1611 -250. -230. -210. -200. -190. -18o. -170. -165. -160. -150., -140. -130. -120. -100. - 80. - 60. - 30 0 50 60 90 120 150 180 0.2846 0.3025 0.3466 0.3863 0.4437 0.5477 0.8150 0.9350 0.8387 0.5905 0.4294 0.3464 0.3000 0.2400 0.2101 0.1935 0.1765 0.1637 0. 1562 0.1518 0.1468 0.1441 0.1409 0.1387 o0.3300 0.5650 0.4300 0.5210 0.7850 0.9079 0.7771 0.57',5 0.4545 0.5670 0.519) 0.2475 0.2147 0. 1963 0.1760 0.16-7 0.1571 0.1515 0.1471 0.1359 0.1413 0.1589 0.2670 0.2903 0.3528 0.3709 0.o,558 0.5667 0.8221 0.8864 0.8129 0.5785 0.4326 0.5508 0. 008 0.2L43 0.2135 0.1942 0.1762 0.1648 0.156> 0.1511 I — 4 O! -------------------- _ _ _ _ - ---------------------- _ ____________________if^ _ __ _ _ I,

TABLE III-11 (Concluded) Pressure = 1371. psia Pressure = 1714. psia _Pressure = 2000. psia Cp (Btu/Ib-F) = (Btu/lb-~F) C = (Btu/ C (Btu/lb-~F) Temperature TiTemper e i Temperature Temperature h- p (~F) Wor chs Gos () Walker Michels Gosan s Work Walker Michels Gosman _-_t_1___- -- - Work Worke ich o m nWork -250. -210. -200. -190. -180. -170. -160. -158. -156. -154. -150. -140. -130. -120. -100. - 80. - 60. 0.2959 0.3270 0.3538 0.3898 0.4524 0.5534 0.6295 0.6490 0.6624 0.6490 0.6171 0.5544 0.4333 0.3638 0.2800 0.2370 0.2224 0.290 0.326 0.557 0.595 0.429 0.545 0.640 0.757 0.587 0.5100 0.3360 0.3750 0.420 0.5570 0.6562 0.6680 0.6652 0.6477 0.6126 0.5251 0.4484 0.3852 0.2884 0.2413 0.2159 0.2827 0.5157 0.5418 0.3804 0.4405 0.5547 o.6350 0.6447 0.6481 0.6453 0.6236 0.5248 0.4310 0.5654 0.2827 0.2592 0.2182 -250. -230. -210. -190. -180. -170. -160. -150. -146. -144. -142. -140. -130. -120. -100. - 80. - 60. 0.2626 0.2866 0.3107 0.3447 0.3712 0.4037 0.4463 0.4830 0.4929 0.4947 0.4929 0.4890 0.4572 0.4155 0.5296 0.2714 0.2380 0.2840 0.3280 0.3610 0.4050 0.4490 0.4780 0.4800 0.4810 0.4820 0.4831 0.4648 0.4174 0.3362 0.2774 0.2441 0.2577 0.2738 0.2977 0.5564 0.3656 0.4036 0.4482 0.4844 0.4910 0.4918 0.4910 0.4887 0.4580 0.4125 0.3500 0.2751 0.2599 -250. -250. -210. -190. -i8o. -180. -170. -160. -150. -140. -136. -134. -130. -120. -100. - 80. - 60. - 40. - 20. 0. 50. 60. 90. 120. 150. 18o. 0.2608 0.2797 0.2994 0.5225 0.3383 0.3532 0.3745 0.5958 0.4185 0.4255 0.4248 0.4217 0.4086 0.5512 0.2952 0.2565 0.2319 0.2121 0.1988 0.1851 0.1715 0. 1636 0. 1580 0.1554 0.1497 0.2840 0.3080 0.3200 0.3253 0. 195 0.3362 0. 625 0. 731 0.3768 0.3752 0.2712 0.3473 0.2968 0.2627 0.2327 0.2140 0.1987 0.1852 0.1719 0.1643 0. 584 0.1536 0.1493 0.2541 0.2677 0.2867 0. 146 0.5336 0.5565 0. 824 0.4072 0.4226 0.4244 0.4241 0.4213 0.4055 0.3475 0.2957 0.2580 0.2314 0.2121 0.1979 0.1822 0.1719 I1 il _

-72 are prepared for summarizing the results. The deviation, d, in the diagrams are defined as Cp (This Work) - Cp (Literature) d = This Work)x 100 (III-9) Lines corresponding to zero percent deviation are sketched in much the same manner one might draw a contour line from survey determinations on a topographic map. In a similar manner contour lines corresponding to ~1%, ~5% and +10% deviation were sketched in. Suitable coding was developed to distinguish these regions as illustrated in the figures. Comparisons, as shown in these diagrams, reveal that in the lower temperature region the present data agree better with Walker's values than those from the other two sources. In the region of temperatures higher than -70~F the deviations of both Gosman and Michels show less than 1%. In temperatures higher than 0~F a comparison of the present data with the values from Michels is presented more specifically in Figure III-33. In the lower pressure region agreements are excellent (deviations are less than 0.2%). Smoothed values of the present enthalpy data (Table III-8) are compared with tabulated values by IUPAC.1 IUPAC values are also based on H = 0 for perfect crystal at the absolute zero temperature (H of saturated vapor at 87.28~K coincides with that of Din's compilation (237.543 J/g) which is based on the perfect crystal at 0~K). Comparisons were made at ninety-four points covering the temperature range from -240~F to 220~F and the pressure range from 0 to 2000 psia. Care was taken to include points near the two-phase and critical regions. The results of comparisons are illustrated as a topographical diagram in Figure III-34. Discrepancies between two sources never exceed 0.5 Btu/lb and for more than half of the region they are less than 0.2 Btu/lb. The average absolute deviation of all 94 points is 0.2 Btu/lb. Finally, the present heats of vaporization are compared with those from Gosman, et al.22 (see Table III-8). The latter, according to Gosman, et al. were calculated using their vapor pressure equation and equation of state. The discrepancies in the latent heats between two sources are within ~0.5%, while the present saturation temperatures agree within experimental errors with Gosman's values.

-73 150C o IOOC a 50C ) ), + \/''!'^. |J /.'?:;,' LEGEND.. / -.,:. Not Applicable in --— d 0% ~%;X /'~: This Region d] d< %..i:l; t%<d<5% ~;..^^ -: 5%<d< 10% +'.:,,.....:-:'i d > 10% I I L. I -200 -100 0 TEMPERATURE, ~F 100' 200 Figure III-50. Comparison of the present isobaric heat capacities with those from Walker.00 1500 O a 1000 "<-: ~:~~.;.:..,/ /.:~ ^^-'~?:i:x'i *~' ~ —..::;..'".2/ |~~ I c.,',,...,~..'"'","/'::~....../.* -.u ~,::~:.,:'?.'."~:: i./ I I \ I \ I \ / \ I -— d 0% + I d i; %<d<5% ^: >; 5%<d<10% d >,10% El d <1 500 -200 -100 0 TEMPERATURE, ~F 100 200 Figure III-31. Comparison of the present isobaric heat capacities with those from Michels et al. 5 2000f \:i'::;ri';:f -" ".~ *.: / ~':'/ + 1500 -f;..'''- * / Comparison not made. //-' /'*^ / in this region... (' / ) LEGEND: - I / % —-d.% ~::::;.;....'.:':..; "d<1%:N,:': I // G%<d<5%:.,.'. /. ~a 000..' TEMPERATURE, ~F Fl'tlIur,'' 1 ti-5;. Coinplrisolll of tile preseott isol)a.rc' ai t'npacities witil tHlose cal.alte.tii'frOll the O'quatioIJ ot' sate by (oslIni it elt a..'

-74 C7 1000 ------— " a (, a x zzi LEGEND, 0II 0%<d<0.2% ~~500 a~ / //,, 0.2%<d<0.5% > f 0.4%<d< 1% 100 200 TEMPERATURE, OF Figure III-33. Comparison of the present isobaric heat capacities in the high temperature region with those from Michels et al.38539 2000 I500 a. f,,,. -100 0 TEMPERATURE, OF Figure III-34. Comparison of the present enthalpies with the tabulated values from IUPAC.

IV - CALORIMETRIC DETERMINATIONS WITH HEXAFLUOROETHANE As the new recycle flow system, designed and constructed by Miyazaki,34 has been successfully operated with ethane, it was decided that calorimetric measurements with C2F6 be conducted at the new system. The operation of the new facility is simpler and more economical than that of the existing one as the new facility has a single calorimeter which can be used both for isobaric and isothermal (and isenthalpic) modes of operation. In addition the flow rate of the system fluid is maintained constant during the operation by a pair of double-acting precision metering pumps which provide a constant flow through the system. Detailed descriptions of the facility and important aspects of 34 equipment design can be found in Miyazaki's thesis.34 Therefore, only a brief description of the experimental equipment will be presented in the first part of this section. The rest of the section is devoted to presentation and discussion of the experimental results. New Recycle Flow System A schematic diagram of the the existing facility described designed to supply a fluid at a a predetermined temperature and tem fluid is provided by a pair (P-1A and P-1B), one of which di as a precisely machined plunger other takes in the fluid as the stant speed. When the plungers system is shown in Figure IV-l. Like before, it is a recycle flow system constant flow rate to a calorimeter at pressure. The constant flow of the sysof identical precision metering pumps scharges the fluid in the liquid phase moves down at a constant speed while the other plunger moves up at the same conreach the ends of the cylinders (upper and lower ends, respectively), the so-called "switch-back" system reverses the moving directions of the plungers and the discharging pump becomes the in-take pump and vice versa. The flow direction of main stream to the calorimeter is, however, maintained constant with a set of four solenoid values (V1, V2, V3, and V4). When the pump P-1A is discharging, V1 and V4 are open, while V2 and V3 are closed; when P-1B is discharging V2 and V3 are open and Vl and V4 are closed. In order to prevent possible bypass flow in case there are leaks through the closed valves due to -75

P-LA and P-1B Metering pumps — T - Solenoid valve < Check valve -><X — Shut-off valve B-1 Pump bath B-2 Pre-conditioning bath B-3 Calorimeter bath B-4 Post-conditioning bath A-ll Air box F-ll, F-12, F-13 Bellows LG Level gage P-12, P-13 Oil pumps (manual) P-1l Water circulation pump P-31 Vacuum pump P-32 Diffusion pump Pi, PO Heise pressure gages D.W.G. Ruska dead weight gage C Calorimeter C-3 Calorimeter vacuum pot CDPT Calorimeter differential pressure transducer LDPT Line differential pressure transducer SV Safety valve T1 Inlet thermometer T2 Outlet thermometer C-1 Helium cylinder CDPT LDPT Figure IV-1. Flow diagram of the new recycle-flow system

-77 incomplete closing of stems, a check valve is installed in a series with each of those solenoid valves. All the valves and the pump cylinders are immersed in the pump bath (B-1) fluid which maintains a constant temperature by a pair of controlled immersion heaters. Throughout the present measurements the bath temperature is maintained at 0 ~0.05~F (Dow-Corning silicon oil is used as the bath fluid). The system fluid, discharged from the pump bath, enters the preconditioning bath (B-2) containing 1/8-in. O.D. stainless steel tubing immersed in the bath fluid, which is maintained to within ~1~F of the calorimeter bath temperature using a linear temperature controller (Bayley Instrument, Model 21). Then it enters the calorimeter bath (B-3) containing a coil of 1/8-in. O.D. tubing for a final temperature conditioning for the calorimeter. The calorimeter bath temperature is controlled by Thermotrol 1053 (Hallakainen Instrument) within +0.02~F of a desired temperature. The measurements of the inlet temperature and pressure, and the changes in temperature and pressure across the calorimeter and the electric energy input are made as the fluid passes through the calorimeter. After leaving the calorimeter, the fluid enters the postconditioning bath (B-4), which is identical to the preconditioning bath (B-2). Passing through the bath, the fluid is conditioned to within ~1~F of the pump bath temperature and finally enters the pump bath and one of the metering pump cylinders. One of the distinguished features in the system is a pressure controlling mechanism employing a set of bellows and a buffer cylinder (C-l) filled with helium. One of the bellows (F-ll) serves to balance the system pressure with the helium pressure of the cylinder (C-l). The bellows is filled with oil and the oil-helium interface is visualized by a reflection type high pressure level gage (LG). The cylinder (C-l) is immersed in a controlled water bath which serves to maintain the helium temperature constant. Generally the valve V5 is closed when the system is not in operation. It is also closed when it is necessary to change the system pressure. In this case another bellows (F-12) is used to set the fluid pressure by compressing or expanding by way of the manual oil pump, P-12. Adjustment of helium pressure to that of the

-78 system is made by introducing higher pressure helium from the He Bomb or venting it out through V8, if necessary. Fluctuation in the system pressure during the operation is compensated by a slight movement of the bellows (F-ll). Thus, the system pressure is maintained the same as the helium pressure of the cylinder (C-l). The other bellows (F-13), together with the manual oil pump (P-13), is to be used when it is necessary to increase the helium pressure above the pressure of the bomb. The position of each of the bellows is monitored by a reading of emf transduced from linear displacement transducers. A specially designed safety valve, SV, serves to prevent excessive expansion of F-ll caused by mass leak from the system during the operation. When the bellows expands to a certain point, the safety valve closes by itself and thus prevents further depletion of the fluid pressure from the shell side of the bellows. The valve, V-13, serves either as an entrance or a vent for the system fluid. Multipurpose Calorimeter The calorimeter used in this experiment is the one Miyazaki devel34 oped in the course of his thesis work.34 It is designed to operate in both isobaric and throttling modes. Figure IV-2 schematically illustrates the principle of the calorimeter. The calorimeter consists of 3/16 in. O.D. tubing (1) and a coaxial capillary tubing of about 0.03 in. I.D. (2). This small tubing is surrounded by electrical heating wire with glass fiber insulation (3). The heating wire extends a length of 30" (A). The shut-off valve (5) is connected by a 1/16 in. O.D. tubing (8) in which 0.02" piano wire (9) is inserted. One end of the wire is attached to an externally located adjuster (11) which can thrust down the wire to make the shut-off valve closed. When the valve is closed, the path of the stream is restricted to the capillary tubing which causes a pressure drop of between 25 psid and 150 psid depending on the flow rate and condition of the flow. Thus, the isothermal or isenthalpic measurements can be made in this way. In the isothermal measurements, electrical energy is transferred from the heating wire to the stream in the capillary tubing to maintain the temperature of outgoing fluid the

-79 12 13 1 3/16-in. O.D. tubing 20 2 22 BWG capillary tubing 3 Electric heating wire 4 1/8-in. O.D. tubing 19 9 5 Shut-off valve \- " / 6 Plunger.'" 8 7 Spring 8 1/16-in. 0.D. tubing = 9 0.020-in. piano wire^ 10 Turning handle 18. / JL 11 Wire adjuster I i 12 Stem 4 i1; ~~~4 15 t [ll81 | 1/ 2 A \ 1'n 1 3 14 L 13 Spring,2 A B..I 14 Electric heater lead 14 Electric heater lead j1 — _ 6 ~ 15 1/8-in. O.D. tubing 16 Voltage measurements tap >'5 ~ 17 3/16-in. O.D. tubing 18 Lead wire seal unit 19 Wire seal fitting 20 Pressure tap A Heating zone B Mixing zone Figure IV-2. Diagram illustrating the principle of the multipurpose calorimeter 6 17

-80 same as that of the incoming one. When the valve is open, most of the stream passes through the annulus and pressure drop across the calorimeter becomes smaller (order of 0.1 psid). In this case, the calorimeter can be operated in the isobaric mode. After the heating section (A), the stream passes through the section B of 20" length filled with twisted lead wires for the heater, which serve as baffles for mixing the stream. The mixed stream then leaves the calorimeter through the outgoing line (15). The lead wires and the voltage measurement taps (16) are led to the outside through the sealed unit (18). The actual calorimeter assembly is shown in Figure (IV-3). For easier understanding of the drawing in Figure IV-3, the reader is advised to refer to Figure II-2(b) as well as Figure IV-2. Comparing Figure II-2(b) and Figure IV-3, one can see that A and B in Figure II-2(b) correspond to T1 and T2 in Figure IV-3. E, F and G in Figure II-2(b) are the coils wrapped by radiation shields R1, R2 and R3, respectively, in Figure IV-3. The calorimeter and shut-off valve, which have been explained in Figure IV-2, are shown in Figure IV-3 as items 5 and 6. Radiation shield R4 on the coil leading to the exit is installed to reduce the conduction heat loss along the calorimeter outlet pressure tap, 4. Y is a small piece of metal which serves as a thermal contact between the pressure tap and the outgoing tube to reduce the temperature gradient on the pressure tap. Similarly, a thermal contact is made at X between the inlet tube and the piano wire lead, which was explained in Figure IV-2. The broken line (2) indicates a radiation shield with guard heater. It was installed as an additional guard in case the heat loss could not be satisfactorily prevented by the inner shields. It was observed in most cases that the temperature difference between the guard shield and R1 was small (less than 0.1~C) without adding power to the guard heater. Experimental Measurements For a detailed description of experimental measurements and accuracies involved in the measuring instruments, the reader is referred to Miyazaki's 34 thesis. The major measurements of the experiments are as follows:

-81 OUT - 1 Vacuum pot 2 Guarded radiation shield 3 Calorimeter inlet pressure tap 4 Calorimeter outlet pressure tap Shut-off valve 6 Calorimeter section 7 Piano wire lead tubing IN Y -R 4 I, P Inlet pressure tap junction R1 Radiation shield R2 Radiation shield \\ R3 Radiation shield R4 Radiation shield Tl Inlet thermometer well T2-~ r J- 2 T2 Outlet thermometer well X Thermal contact = j - Y Thermal contact 1 R I R3 [. qT 1 0l Ii,~-~ —-- _Z=~ID ~ TiScale, inch Figure IV-3. Drawing of the multipurpose calorineter assembly

-82 1. The calorimeter inlet and outlet temperatures are measured by a quartz crystal thermometer (Hewlett-Packard, Model 28D1A). Corrections were made on the thermometer readings as suggested by Miyazaki.4 The thermometer has a resolution of 0.0001~C and a factory calibration gives accuracy of ~0.02~C. In addition a six junction copper-constantan thermopile is placed between the inlet and outlet measuring points to make independent measurements of the temperature differences. Accord34 ing to Miyazaki,4 for measurements of the outlet temperatures, the thermopile readings are more reliable than the quartz thermometer readings, especially when the temperature differences are small across the calorimeter. Therefore, the outlet temperatures were determined from the thermopile readings and the inlet temperatures were measured with the quartz thermometer. The emf of the thermopile is measured using a K-5 potentiometer. A calibration equation for the thermopile is given in 34 Miyazaki's thesis. 2. The electrical energy input to the calorimeter is supplied by a DC power supply (KEPCO Model PVS100-IMG) capable of delivering up to 1 ampere at 100 volts. It is measured by a K-5 potentiometer using standard resistors to scale down the voltage to the range of the potentiometer. 3. The calorimeter inlet pressure is determined from the measurement of helium pressure of the cylinder, C-l, (refer to Figure IV-1) using a dead weight gage (Ruska Instrument, Model 2400), with a resolution of 0.1 psi. The gage actually measures the oil pressure balanced by the helium pressure exerted by the bellows, F-13. In order to compensate for the spring effect of the bellows, it is adjusted to its equilibrium position, as monitored by the null indicator, before the measurement. A small inbalance in pressure between the system fluid and helium, as indicated by the position indicator for the bellows, F-, is corrected using the calibration made by Miyazaki34 In addition F-11, is corrected using the calibration made by Miyazaki. In addition,

-83 the line pressure drop between the bellows (F-ll) and the inlet to the calorimeter is measured using a differential pressure transducer (LDPT) so that the calorimeter inlet pressure can be calculated accurately. 4. The pressure drop across the calorimeter is measured using a differential pressure transducer. A calibration was prepared by 34 Miyazaki. According to Miyazaki, the data fit the calibration equation within ~0.15%. 5. The volumetric flow rate is determined by the pump displacement speed together with a knowledge of the cross-sectional area of the plunger, which is corrected for the thermal contraction at the pump bath temperature. In the present investigation the pump speeds are set at values corresponding to 12 and 14.2 c.c./min. Material Used The material used in the experiment is an extra pure grade donated by the Freon Division of du Pont de Nemours and Co. Before the sample was charged, the system was evacuated to 100 micron pressure. The system was flushed with the sample several times in a similar method as described in Section III. A sample, after the experiment was finished, was taken from the system and sent to a Freon Products Laboratory of du Pont Co. for analysis. The result of the analysis is presented in Table IV-1. TABLE IV-1 Composition of C2F6 C2F6 99.980% Air 0.014 Freon 12 (CCI2F2) 0.003 Others* 0.003 100.000% (*Possibly, CO, CF4, C2F5H, C2C13F6 and H20) Molecular weight of the sample: 138.01

-84 Region of Measurements Calorimetric studies on C2F6 covered the temperatures from 0~F to 250~F and pressures from 247 to 1969 psia as shown on a P-T plane in Figure IV-4. Each run is numbered in the chronological order of investigation. The vapor pressure curve is drawn in the diagram to indicate the phase corresponding to each run. In the supercritical region emphasis is placed on isobaric measurements in the Cp(T) maxima region, which includes the runs at 490, 598, 700, 839, 1049 and 1398 psia. Extended measurements are made at 247 and 1969 psia. The pressures, except for 598 and 1969 psia, were chosen in such a way that their reduced values are the same as those for the experimental isobars in the argon measurements (and propane measurements 61). An isobaric run was made at 432 psia, which according to du Pont Co., is the critical pressure. An enthalpy vs temperature plot constructed from the measurements (Figure IV-24) shows a significant enthalpy change indicating the pressure was significantly below the critical pressure. In an attempt to locate the true critical point, a series of isobaric enthalpy traverse runs in the critical region were added to the original plan. These are presented in Figure IV-4. The pressure levels selected for those measurements are (in descending order) 442, 437, 436, 433.5, 432, 427 and 418 psia. In addition, enthalpy traverse runs were made at 376 and 247 psia. Isothermal changes in enthalpy were measured along the five isotherms: 0, 67.6, 122, 176 and 247~F. The basic data for C2F6 are presented in Tables B-3 (isobaric) and B-4 (isothermal) of Appendix B. Determination of Liquid Densities As already discussed, the volumetric flow rate could be estimated accurately from a knowledge of the speed of the metering pump displacement and the cross-sectional area of the pump cylinder. For the calculation of mass flow rate, however, it is necessary to know the density of the liquid inside the pump cylinder. In a previous investigation with ethane,34 liquid densities were estimated from the available data which were believed to be accurate. For C2F6, however, density data

0 L a w () 0) l: Q I Ul TEMPERATURE, OF Figure IV-4. Range of calorimetric determinations on C F6. 2 b

-86 in the sub-cooled region were not available in the literature. Therefore, a new technique had to be developed in order to determine the necessary liquid densities experimentally. The technique involves a simple principle which can be described below: Consider a cylinder with a piston containing a liquid at temperature TO and pressure PO (see Figure IV-5). Suppose a portion of the liquid is discharged into an empty tank by opening a throttling valve connected to the cylinder. Then, the valve is closed and the position of the piston is adjusted until the pressure inside the cylinder is restored to Po. Suppose that the temperature of the liquid is maintained at To throughout the procedure. Liquid at TO, Pg Throttling Valve Cylinder Piston Figure IV-5. Diagram illustrating the measurement of liquid density Tank

-87 Then, the density of the liquid, p(TO, PO), is determined from the knowledge of volume displacement by the piston and the mass of the liquid inside the tank as P (T0o PO) = where m = mass of the liquid collected in the tank AV = volume displacement by the piston. In the actual measurement of the density, one metering pump is used as a cylinder with piston in Figure IV-5. Since the pump has a scale which reads the piston position to ~0.0025 mm, the volume displacement can be estimated to ~0.005 cc.(total volume displacement is about 100 cc). The temperature of the liquid inside the cylinder can be maintained constant as the pump bath serves to keep the pump cylinder at the desired temperature. A sufficiently long period of time (between one and two hours) is allowed after the bath starts to control at the temperature so the liquid inside the cylinder reaches a steady temperature very close to, if not at, the bath temperature. In the present measurement, the bath temperature is maintained at 0~F, well below the saturation temperature for the lowest isobaric run (247 psia). The liquid temperature is assumed to be the same as the bath temperature as measured by the thermocouple immersed in the bath fluid. Figure IV-6 illustrates schematically the actual arrangement of the equipment used for this work. One of the sample bombs used in the calibration for the flow meter in the previous recycle system was used as the tank collecting the fluid from the cylinder. As shown in the figure, part of the line connecting the cylinder (P-1A) and the throttling valve (VA) had to be exposed to room temperature since it was practically impossible to immerse the sampling tank into the pump bath. However, the external line, and hence the holdup of the fluid exposed to the ambient air was reduced as small as possible (total volume of the fluid exposed to the air was less than 10 cc). As a consequence, the rest of the recycle system was disconnected during this density calibration.

-88 Pump Bath PI ) V/ P1 O V} Heise Pressure Gage Saml High Pressure Tai Gage High Pressure Toggle Valve 3.5" Schedule 80 Aluminum Tubing (4.0 O.D x 12" Long \Weight= 6 lb. / 1/4" LPT Hole, Plugged VB pling nk / Figure IV-6. Arrangement for the liquid density measurement.

-89 The bellows (F-11 of Figure IV-1) had to be disconnected from the line since it could provide a variable volume during the measurement. As the result the pressure of the fluid in the system could not be determined by the dead weight gage. Instead, the Heise gage (P1) was connected formeasurements of the fluid pressure. The pressure could be read with the Heise gage within ~1 psi accuracy, which would affect errors somewhere between 0.004 and 0.01% on the measured densities depending on the pressure. Since these errors were tolerable for the present work, using the Heise gage for the pressure readings was considered justifiable. In the present measurement the liquid was discharged while the pump piston was moving down continuously. In the meantime the opening of the throttle valve (VA in Figure IV-6) was manually adjusted so that the fluid pressure, as monitored by the Heise gage (P1), stayed constant at the initial pressure, P0. After filling, the toggle valve (VB) is closed; the pump is stopped. Finally, the position of the piston is adjusted until the pressure settles to the initial pressure, P0. Usually about an hour is allowed between pump shut-off and the final settling-down to make sure the fluid inside the cylinder reaches an equilibrium condition. The fluid accumulated inside the tank was determined by directly weighing the tank before and after the calibration procedure. In a typical measurement, about 120 grams of the fluid are collected (resolution of the balance used for the measurements is 0.001 g). The whole procedure is repeated for various pressures to obtain a series of density data at 0~F. Those data, together with the saturation density in the literature, are plotted against pressure, as shown in Figure IV-7. The densities are fitted to an equation as Y = A + BX + CX2 + DX3 (IV-l) where Y = density of C2F6, g/cc X = pressure, psia

1.40 E o L5 &L35 >z 30 0J 1.25 I I i II /o I 0 I o Data by this Work * Saturation Density Data from DuPont I I I I I 1 I I I I 200 400 600 800 1000 1200 1400 1600 1800 2000 PRESSURE (psia) Figure IV-7. Plot of liquid densities for C F at O0F. Figure IV-7- 1 at O.26

-91 The constants in Equation (IV-1) together with the density data are listed in Table A-6 of Appendix A. The equation fits the data within 0.05%. It is important to realize that the same equipment (the metering pump) and the same condition were used in the density measurements and the actual experiments. Thus, the technique used here establishes a means for the absolute flow calibration. Although the density data represented by Equation (IV-1) should be precise, for the specific purpose of this investigation it is not imperative that the data also be accurate. Results Cp and Cp(T) Maxima Cp values are determined from isobaric measurements of enthalpy using the method described in Section II. The values so determined are listed in Table IV-2. A typical isobar (490 psia) in the supercritical region is illustrated in Figure IV-8. The isobars, designed to determine Cp(T) maxima at 437 and 442 psia, are shown in Figures IV-9 and IV-10, respectively. The value of Cp(T) maximum for 437 psia is indeterminate because the pressure is very close to, if not at, the critical pressure (refer to Figure IV-28). At 442 psia the value of Cp(T) maximum is obtained at 68.0~F as 11.64 Btu/lb-~F (cf. Cp~ at the corresponding temperature is 0.18 Btu/lb-~F). The other Cp(T) vs T plots are presented in Figures IV-11, IV-12, IV-13, IV-14, IV-15, IV-16 and IV-17. All of the Cp(T) maxima obtained in the present work are listed in Table IV-3. The basic measurements are listed in Table C-5 of Appendix C.

TABLE IV-2 ISOBARIC HEAT CAPACITIES of C2F6 Pressure = 247. psia Pressure = 432. psia Pressure = 490. psia Pressure = 598. psia Pressure = 700. psia Temperature C Temperature C Temperature C Temperature CD Temperature C (~F ) ( Btu/lb- ~F ) (~F) ( Btu/lb - ~F ) (O~F) ( (Btu/b - ~F) (~F) ( Btu lb- ~F) (~F) (Btu /lb-~F) 0. 0.2960 O. 0.2950 64. 0.3697 70. 0.4310 70. 0.3744 10. o.3080 10. 0.3060 70. 0.7095 80. 0.5732 80. 0.4177 20. 0.3290 20. 0.53150 72. 0.9093 86. 0.7378 90. 0.4869 25. 0.3515 30. 0.3260 74. 1.6350 89.6 0.8365 96. 0.5436 28. 0.3103 40. 0.3480 74.8 2.2920 92. 0.7815 100. 0.5761 34. 0.2779 50. 0.4050 75.1 2.3930 96. 0.6789 101.4 0.5800 40. 0.2658 60. 0.5405 75.4 2.2960 100. 0.5812 104. 0.5640 60. 0.2414 653. 0.7945 76. 2.0320 106. 0.4729 108. 0.5522 80. 0.2320 65. 1.2140 77. 1.6050 112. 0.3980 114. 0.4900 100. 0.2295 66. 1.4660 78. 1.2160 120. 0.5342 120. 0.4558 120. 0.2291 68. 0.9787 80. 0.8744 140. 0.2295 70. 0.7600 85. 0.5412 160. 0.2300 74. 0.5190 9. 0. 3997 180. 0.2303 80. 0.3900 100. 0.3547 200. 0.2307 90. 0.3230 110. 0.3148 220. 0.2311 100. 0.3000 120. 0.2779 250. 0.2324 120. 0.2694 140. 0.2550 16o. 0.2500 180. 0.2488 Pressure = 839. psia Pressure = 1049. psia Pressure = 1398. psia Pressure = 1969. psia Temperature Cp Temperature Cp Temperature C Temperature Cp (~F) _ (Btu/lb-OF)_ (~F)_ (Btu/lb-~F) (~F) (Btu/lb-~F) (~F) (Btu/lb-OF) 70. 0.3364 120. O. 772 120. 0.3282 0. O.2780 80. 0.3569 130. 0.3839 130. 0.3323 20. 0.2800 90. 0.3818 134. 0.3868 140. 0.3365 40. 0.2826 100. 0.4137 136. 0.3880 150. 0.3405 60. 0.2858 110. O.4457 138. 0.3868 160. 0.3427 80. 0.2893 114. 0.4586 144. 0.3815 162. 0.3428 100. 0.2929 117. 0.4666 150. 0.3758 164. 0.3427 120. 0.2965 120. 0.4511 160. O.3654 170. 0.3413 140. 0.3009 170. 0.3551 176. 0.3386 160. 0.5050 176. 0.3490 180. 0.3088 200. 0.3112 205. 0.3115 210. 0.5112 230. 0.3090 250.. 3060

-93 ISOBRRIC MERN HERT C2F6 490. CAPRCITT PSIR C2 a, I 0 r-4 0 0 CD Ck ~ * I 0 2a bb. 75. 90. TEMPERATURE iOS. (OF) Lo20 Figure IV-8. Isobaric heat capacity for C2F6 at 490 psia.

ISOBFIC HN ERN HET CAPRCITY C2F6 442. PSIR ~ ~ ~ ( ~ ~ ~ ~ W. Z 60. 68.. TEMPERRTURE tlF) Figure IV-10. Isobaric heat capacity for C F6 at 442 psia. 2L 6 60. 62. 64. 66. 68. 70. 72. 71. TEMPERRTURE (~F) Figure IV-9. Isobaric heat capacity for C2F6 at 437 psia.

-95 ISOBARIC MERN HERT CRPRCITY C2F6 247. PSIR I s3 IO0 co -10. 26. 80. 95. 130. 165. 200. 235. 10. 25. 60. 95. 130. 165. 200. 235. TEMPERATURE (OF) Figure IV-11. Isobaric heat capacity for C2F6 at 247 psia. ISOBRRIC MERN HERT CAPACITY C2F6 432. PSIR u) -r o C.% -- o 0 m O Urj tm Cl 2i ISOBRRIC MERN HEAT CRPRCITY ~ C2F6 700. PSIR -10. 25. 60. 95. 130. TEMPERRTURE (~F) 165. 80. 7S. 90. 10S. TEMPERRTURE (~F) FgrIV1 Isobaric heat capacity forC26a43psa Figure IV-15. Isobaric heat capacity for C2F.at (X0) psia.

ISOBRRTC MEAN HEAT CAPACITY C2F6 839. PSIR o a ISOBRRIC MERN HEAT CAPACITY C2F6 1398. PSIR CD 0 CM co Ln 0 o ca J ), C') bo. 70. 80. 90. 100. 9110. 120. 130. TEMPERRTURE (~F) Figure IV-14. Isobaric heat capacity for C2F6 at 839 psia. 110. 120. 130. 140. 150. 160. 10. 180. 190. TEMPERRTURE ([F) Figure IV-16. Isobaric heat capacity for C2F6 at 15398 psia. I to I ISOBRRIC MERN HERT CAPACITY C2F6 10119. PSIR ISOBARIC MEAN HEAT CAPACITY C2F6 1969. PSI o I. a 0 IaO " CA plaigzPbso - - 4. — -. I a 6 — -—. 2 —!54- -, II -1 I O C3, 110t. 120. 130. 140. ISO. 10. 170. 180. 190. TEMPERRTURE (~F Figure.IV-15. Isobaric heat capacity for C2F6 at 1049 psia. -20. 20. 60. 100. 10. 180. 220. TEMPERATURE (OF) Figure IV-17. Isobaric heat capacity for C2F at 1969 psia. 26 260.

-97 TABLE IV-3 Cp(T) Maxima Data for C2F6 Pressure TM C (psia) (OF) (Btu/ F) (Btu/1b-~F) 437 67.10 ~0.1 >25.0 442 68.0 ~0.1 11.64 ~0.4 490 75.1 ~0.1 2.343~0.01 598 89.6 ~0.2 0.8365 ~0.002 700 101.4 +0.3 0.5800 ~0.001 839 117.0 +0.5 0.4666 ~0.001 1049 136.0 ~1.0 0.388 ~0.007 1398 162.0 +1.5 0.3428 ~0.0007 1969 205.0 +2.0 0.3115 ~0.0005 Isothermal Data 0 values for all of the experimental isotherms were determined using the methods described in Section II. These are presented in Table IV-5. 0(P) maxima data are presented in Table IV-4. Plots made for the isotherms at 0, 67.6, 122, 176 and 247~F are shown in Figures IV-18, IV-19, IV-20, IV-21 and IV-22, respectively. An inversion point (0~F at 865 psia) is observed in Figure IV-18. The basic data are listed in Table C-6 of Appendix C. TABLE IV-4 0(P) Maxima Data for C2F6 Temp. Pressure -0 x 100 (~F) (psia) (Btu/lb-psid) 122 645 ~20 4.352 ~0.044 176 770 ~40 1.990 ~0.010 247 840 ~40 1.250 +0.006

TABLE IV-5 ISOTHERMAL THROTTLING COEFFICIENTS OF C2F6 Temperature = O.~F Temperature = 67.6~F Temperature = 122.~F Temperature = 176.~F Temperature = 247.~F Pressure - ~ x 100 Pressure - $ x 100 Pressure - $ x 100 Pressure - 4 x 100 Pressure - O x 100 (psia) (Btu/~F-psid) (psia) (Btu/~F-psid) (psia) (Btu/~F-psid) (psia) (Btu/~F-psid) (psia) (Btu/~F-psid) 200. 0.1190 0. 2.6800 0. 1.9600 0. 1.2500.0. o.6950 300..0930 200. 3.2250 200. 2.1360 200. 1.4780 200. 0.8277 400. 0.0532 500. 3.9400 400. 2.4900 400..1.7110 400. 0.9900 600. 0.0250 360. 5.2450 500. 350150 600. 1.9090 600. 1.1410 800. 0.00.. 400...9600 600. 4.0300 700. 1.9710 700. 1.2120 865. 0.0000 460. 5.5410 630. 4.2730 750. 1.9890 800. 1.2480 1000. -0.0100 500. 2.5980 645. 4.3520 770. 1.9900 840. 1.2500 1200. -0.0168 600. 1.1340 660. 4.3220 800. 1.9800 900. 1.2400 1400. -0.0340 700. 0.5989 700. 4.0990 900. 1.8900 1000. 1.1880 1600. -0.0436 800. 0.5224 800. 3.1200 1000. 1.7100 1200. 1.0270 1800. -0.0520 1000. 0.1683 900. 1.9700 1200. 1.2560 1400. 0.8620 2000. -0.0616 1200. 0.1500 1000. 1.2680 1400. 0.8540 1600. 0.7040 1400. 0.1100 1200. 0.6866 1600. 0.6000 1800. 0.5670 1600. 0.0900 1400. 0.3993 1800. 0.4500 2000. o.4430 1800. 0.0700 1600. 0.2507 2000. 0.3221 2000. 0. 630 1800. 0.1709 2000. 0.1150 I MO I

-99 THROTTLING COEFFICIENT 500. 750. 1000.. 5. 1500. 1750. PRESSURE (PSIR) Figure IV-18. Isothermal throttling coefficient for argon at O~F. <o orc1 (n ol r10 I _?~ 250. 500. 750. 1000. 1250, 1500. 1750, PRESSURE (PSIR) Figure IV-19. Isothermal throttling coefficient for argon at 67.5~F.

-100 1000. 1250. PRESSURE (PSIR) Figure IV-20. Isothermal throttling coefficient for argon at 122~F. ISOTHERMAL THROTTLING COEFFICIENT C2F6 176.~F Figure IV-21. Isothermal throttling coefficient for argon at 176~F. ISOTHERMAL THROTTLING COEFFICIENT C2F6 247.OF o a0 0 a C C I (n a. I \ f i. CD pe I.I 9 1: I I.. 1. 2 II R I- ---'0 250. 500. 750. 1000. 1250. PRESSURE (PSIA) 1500. 1750. 2000. Figure IV-22. Isothermal throttling coefficient for argon raL 24t".

-101 Enthalpy Changes on Vaporization A typical plot of enthalpy change vs temperature across the two phase boundary is shown in Figure IV-23. The enthalpy change on vaporization is determined from the enthalpy difference between the upper and lower break points. The enthalpy traverse at 432 psia is also presented here in Figure IV-24 which shows the latent heat of 7.7 Btu/lb. Basic data for those plots appear in Table C-7 of Appendix C. The saturation temperatures and latent heats determined from the present measurements are summarized in Table IV-6 together with literature values for comparison. Thermodynamic Consistency Checks The consistency checks between isobaric and isothermal measurements of C2F6 are presented in Figure IV-25. The average and maximum inconsistencies are 0.03% and 0.10% respectively. The accuracy of the isobaric and isothermal data is estimated at 0.05% and 0.10%, respectively. Enthalpy in the Critical Region As discussed earlier in this section, a series of isobaric enthalpy determinations have been made in the critical region (see the enclosed square in Figure IV-4). These runs were planned primarily for the sake of determining an accurate value for the critical pressure, when it became apparent that the true critical pressure is higher than 432 psia (the value obtained from the literaturel). It is, however, unprecedented that the critical constants are to be determined from the enthalpy measurements in the critical region. Also unprecedented are the present measurements of enthalpy change in vaporization at pressures only a few psi below the critical point. Even for the fluids which have been subjected to extensive calorimetric investigations, such as H20 and C02, enthalpies are seldom measured in the critical neighborhood. (For H20, the enthalpy values at 220 Kg/cm2 (P = 225 Kg/cm2) are the only ones ever determined in the closest range of the critical pressure.) Obviously the measurements

TABEL IV -6 COMPARISON OF SIAT'PTIIOCI ATIA FOR7 C2F6 Saturation TeLaera nre ( ~) Latent Heat (Btu/lb) Pressure PresseThis This (psia) Du Pont Du Pont _Work Work 247. 25.30 ~ 0.02 25.27 29.40 ~ 0.05 29.10 376. 553.5 ~ 0.02 55. 15.26 ~ 0.05 16. 2 418. 64.35 ~ 0.02 64.61 10.20 ~ 0.05 9.60 427. 65.52 ~ 0.02 66.55 8.84 ~ 0.05 2.95 452. 65.96 ~ 0.02 67.50 7.70 ~ 0.05 1.00 4355.5 66.30 ~ 0.02 -— 6.70 ~ 0.0 --- 456. 66.70 ~ 0.02 --- 4.50 0.05 ---

ISOBRRIC ENTHRLPT TRRVERSE C2F6 247. PSIR ISOBRRIC ENTHRLPT TRRVERSE C2F6 432. PSIR T 8 8 a, I I8 ~* II II.II I 1 7 R. = 1 0 - u o m Co C) O CV II 0) C c~ 11 02 -J.1 I o CO I ~ I 3 8 in ~.00.!.00 10.00 20.00 30.00'0.00 TEMPERRTURE ~F 50.00 TEMPERRTURE OF across the two phase Figure IV-23. Isobaric enthalpy traverse boundary for C2F6 at 247 psia. Figure IV-24. Isobaric enthalpy traverse across the two phase boundary for C2F6 at 432 psia.

-104 19.03 15.92 16.34 22.21 (+0.01) (+0.02) - O C, 0 _8 i^-6 I t (+0.01) -0.01 H -0.026% 1 18.25 (-0o.3) 1598 - _:t C rK 0. C c^ (+0.00) -0.02 ~ -0.044% - 20.14 o o c8 I cz1 1049. (-0.02) _z C) u% I l -0.01 -o.o l!o 21.75 J) 0 oJ0. C 6 u 700 - n vH P4 a)?VI w i^ Pd) P-1 U) id 0 (+0.02) o -0.053 o -o.o056% y 26.00 (+o.00) C) +0.00 C ~ ~'o I 29.41 (+0.01) o -1 ~ -0.02 C C -0.050o 3, 51. 55 c0 2AH. = -0.05 -1 598 H CO! o 0 0 C) o _ - -. H. H -06-1 /"C - +0.05 +0.079o 0 CC 1, 490 _.' CM 5(1,.53 ) 0 (+0.00) 0. 00 o. 0oo \C i. N I I I.C) C) o! O 432 o2 247 20). 2 153.73 (+ 0.00) / o.oo / I 40. 4o (+o.oo) (-o.oi) C) i 0.00 0.00%.-6. I I I, +0.01 C +0.0503o. I 1 2.4).1. hL ( (+o.oo) I I o I_ (+0.00) o 6 o. oo O. OOa/ r (+0.00) O 0.00 9 0.00 n. 74 (-0.02) o ) o. 04 O.10% Co!n 10.25 (+0.00) 0 67.6 (+0.00) 1T22 Temperature (~F) (+0.02) 176 247 Figure IV-25. Thermodynamic consistency present calorimetric data for C2F6. checks for the

-105 of enthalpy in the critical region alone can be a significant contribution in the knowledge of thermodynamics for C2F6 - as well as other substances. As illustrated in Figure IV-4, seven isobaric runs were made in the critical region, which consist of about one hundred measured points along those isobars. Since each run yields a set of isobaric enthalpy differences as determined from its inlet temperature and pressure, it is necessary to establish a reference which serves to relate every set of measured enthalpy differences to the enthalpy values from a common basis. For the common basis of C2F6 enthalpies, H = 0 at 0~F and 0 psia, is chosen arbitrarily but conveniently since the enthalpy on any experimental isobar or isotherm can be easily calculated from the point through the enthalpy network in Figure IV-25. In order to establish the reference for the enthalpies in the critical region, enthalpy values at the location of Cp(T) maxima and values of average saturation enthalpy (average of the saturated liquid and vapor enthalpies at a given pressure) are estimated from the common basis and those are plotted versus pressure, as shown in Figure IV-26. According to Powers,45 this plot would form a smooth curve which could serve to provide reference enthalpies for the isobaric runs in the critical region, and consequently enthalpies for all the data points of the runs. Determination of the enthalpy values for those points then makes it possible to construct the saturation boundary in H-T diagram, as illustrated in Figure IV-27, and thus to determine the critical pressure as 437 ~0.5 psia (cf. 432 psia in the literature ) by inspection of the boundary. Table IV-7 presents the values of enthalpy near the critical point. In order to determine the critical temperature the saturation data in the critical region are plotted on logP- logT coordinates, as shown in Figure IV-28. The saturation line is fitted as a straight line to the data pointsbased on the general observation46 that the vapor pressure is linear with the saturation temperature on a log-log scale near the critical point. From this plot and the critical pressure determined earlier, the critical temperature is determined as 526.8 ~0.1~R (cf. 527.17~R in the literature l) as illustrated in Figure IV-28. Plotted in Figure IV-28 are loci of Cp(T) and 0(P) maxima, determined P

r oLL 66 < ) — ^.3 1000- o Enthalpy at Cp(T) maximum /66 * Average saturation enthalpy (Basis: U =0 for ideal < 64'e gas at OF). CL 0. UC f::: I 62(n EN 500( 58 376 psio 54 -20 -15 -10 -5 0 -25 -20 -15 -10 -5 ENTHALPY (Btu/lb) ENTHALPY Btu/Ib Figure IV-26. Plot of enthalpies at Cp(T) maxima and average enthalpies Figure IV-27. Plot of enthalpies for the critical region. at saturation points as function of pressure (C F6)- at saturation points as function of pressure (C2F6) I CJ) I

TABLE IV-7 ENTHALPY OF C2F6 NEAR THE CRITICAL POINT Pressure = 376 psia Pressure = 418. psia Pressure = 427. psia Pressure = 432. psia Temperature H Temperature H Temperature H Temperature H (~F) (Btu/lb) (~F) (Btu/lb) (~F) (Btu/lb) (~F) (Btu/lb) 53.55 -25.311 62.13 -22.841 64.48 -20.858 64.15 -22.222 54.25 -24.747 63.41 -21.194 65.18 -19.608 65.32 -20.060 55.10 -23.892 64.23 -20.030 65.40 -19.162 65.60 19.214 55.32 -23.514 64.30 -19.881 65.51 -18.701 65.65 -19.211 55.36 -22.980 64.36 -18.734 65.52 -17.736 65.77 -18.765 55.36 -21.500 64.36 -18.272 65.57 -11.383 65.91 -18.305 55.41 -17.535 64.38 -15.474 65.60 -10.717 65.96 -17.540 55.47 -14.942 64.47 -12.856 65.63 -10.037 65.96 -16.317 55.50 -14.258 64.44 -10.946 65.98 - 9.344 65.97 -14.102 55.44 -12.846 64.42 -10.279 66.41 - 8.635 66.00 -12.274 55.52 - 8.615 64.54 - 9.599 66.90 - 7.911 66.05 -11.005 55.69 - 8.015 64.75 - 8.905 66.24 -10.047 56.05 - 7.546 65.07 - 8.196 66.74 - 9.001 56.35 - 7.055 65.73 - 7.470 67.33 - 7.530 56.45 - 7.055 Note: H = 0 for ideal gas at 0.~F I I1 I

TABLE IV-7 (Concluded) Pressure 433.5 psia Pressure 435. psia Pressure = 437. psia Pressure = 442. psia Terr-perature H Temperature H Temperature H Temperature H \ -) (Btu/lb)(~F) (Btu/lb) (~F) (Btu/lb) (O(~F) (Btu/lb) > 79 -.08 66.27 66.29 66.28 66.J _6.50 56.30 66.35 66.46 66.59 66.73 66.96 6.576 7.022 7.483 7.957 8.447 8.951 10.003 11.115 12.281 13.509 14.794 15.125 15.459 15.797 16.137 16.830 65.90 66.15 66.29 66.39 66.51 66.62 66.70 66.70 66.72 66.72 66.71 66.78 67.0e 67.23 67.50 -19.533 - 18.627 -18.152 -17.663 -17.159 -16.640 -16.109 -15.000 -15.829 -12.285 -11.643 -11.316 -10.651 - 9.972 - 9.280 65.67 66.21 66.83 67.08 67.19 67.27 67.53 68.40 68.85 -20.464 -19.216 -17.835 -16.324 -14.106 -12.287 -10.338 - 7.852 - 6.800 65.43 66.62 67.46 67.86 68.06 68.34 68.76 69.96 71.41 -22.537 -21.290 -19. 10 -18.599 -16.182 -13.730 -11.758 - 9.617 - 8.150 o CO! Note: H = 0 for ideal gas at 0.~F

-1092000 o Location of Cp maxima (aCp/aT)pO 0 1800 A Location of 4 maxima (a6/aP)T = 0 1600- ~ Saturation Data 1400a 1200o - y -. i (800-. 6000'0430-> 400 60 6 420Figure IV-28. Plot of the saturation line near the critical point, Cp(T) maxima and.(P) maxima for C2F6. Cp(T) maxima and <>(P) maxima for C2F6-.

-110 in the present investigation. The line of Cp(T) maxima, as discussed in Section II, demonstrates a smooth extension of the saturation line into the supercritical region. It is interesting to observe that the line of Cp(T) maxima is curved slightly downward at higher pressures. An aC value of 7.19 is obtained from the slope of the line at the critical point. The 0(P) maxima are found to lie along the curve which separates further from the line of Cp(T) maxima as the pressure increases. Table IV-8 lists the critical constants both from this work and the literature for comparison. TABLE IV-8 Critical Constants for C2F6 TC(~R) PC (psia) aC du Pont* 527.17 432 7.05** This Work 526.8 ~0.1 437 +0.5 7.19 * Reference 11. ** Value determined from the normal boiling point data using the method suggested by Riedel'6 Enthalpy Table and Diagram Enthalpies determined in the present investigation are presented as a diagram illustrated in Figure IV-30. Table IV-9 presents the saturation enthalpies. The enthalpy values of the measured isobars are presented at regular intervals of temperature, including those for the measured isotherms, in Table IV-10. The reference chosen for the enthalpy table is H = 0 for the ideal gas at 0~F. The zero enthalpies are calcuo 54 lated from Cp in the literature.5 Comparison With Previous Experimental Data Comparison of the present saturation data with those from du Pont Co. are presented in Table IV-6. Significant discrepancies shown in latent heats in the critical region are a consequence of differences in values of critical constants as shown in Table IV-5. There are,

-111 Figure IV-29. H-P-T Diagram for C2F6

TABLE IV-9 TABULATED VALUES OF SATURATION ENTHALPY FOR CF 2 6 Enthalpy (Btu/lb) Pressure Temperature Saturated Latent' ~(psia) __ (0_F)- i Liqguid Vapor Heat 247. 25.30 -35.61* - 6.21 29.40 376. 55.35 -23.61 - 8.35 15.26 418. 64.35 -19.77 - 9.57 10.20 427 65.52 -18.83 - 9.99 8.84 432. 65.96 -18.09 -10.39 7.70 433.5 66.30 -17.54 -10.84 6.70 436. 66.70 -16.38 -11.88 4.50 *H = 0 for ideal gas at O.~F I --!

TABLE IV- 10 TABULATED VALUES OF ENTHALPY FOR C F6 Temperature Pressure (psia) (~F) 0 247 432 490 598 700 839 1049 1398 1969 20 4ro 60 67.6 8oo 120 122 140 160 176 18o 200 220 240 247 0.00 3.42 6.86 10.37 11.75 14.01 17.64 21.56 21.98 25.40 29.25 32.72 33.30 37.40 41.6o 45.88 47.57 -44.19 -38.oo -44.31 -38.21 -31.66 - 2.51 2.60 4.30 7.22 11.83 16.43 16.87 21.00 25.60 29.27 30.00 34.66 39.32 43.99 45.65 - 0.31 6.29 11.97 12.52 17.22 22.26 26.24 27.08 32.12 37.16 42.20 43.95 -44.34 -38.51 -31.97 -23.96 -20.42 - 5.35 4.o8 10.36 10.93 15.81 21.07 25.20 26.09 31.27 36.39 41.48 43.28 -44.37 -38.71 -32.52 -25. 26 -22.24 -16. 40 - 2.29 6.47 7.18 12.80 18.69 23.20 24.21 29.72 35.07 40.26 42.12 -44.39 -38.76 -32.72 -25.86 -23.09 -18.21 - 8.37 2.01 2.91 9.51 16.19 21.22 22.31 28.15 33.71 39.00 40.92 -44. 40 -38.78 -32.79 -26.22 -23.65 -19.36 -11.69 - 2.79 - 1.90 5.61 12.99 18.48 19.67 25.91 31.74 37.19 39.20 -44.38 -38.78 -32.84 -26.50 -24.07 -20.16 -13.84 - 6.29 - 5.45 1.46 8.96 14.67 15.99 22.58 28.73 34.48 36.69 -44.30 -38.74 -32.86 -26. 80 -24.52 -20.79 -14.77 - 8.44 - 7.81 - 1.82 4.98 10.44 11.73 18.35 24.73 30.74 33.12 -44.03 -38.53 -32.87 -27.16 -24.99 -21.39 -15.57 - 9.64 - 9.05 - 3.66 2.41 7.30 8.52 14.72 20.94 26.98 29.48 I I - -- - ------ Note: H = 0 for ideal gas at O~F. Unit for H is Btu/lb.

-114however, good agreement between the two sources for the saturation data at 247 psia.

V - GENERALIZED CORRELATION FOR Cp(T) MAXIMA p This section is devoted to correlating experimental Cp(T) maxima data now available both from the literature and the present calorimetric investigations. Cp(T) maxima, as noted in an earlier section of this M thesis, is characterized by the temperature of the peak, TM, and the magnitude, Cp, for a given pressure and therefore, the correlation efforts are conveniently divided into two parts: 1. A correlation for locations of the peak (the correlation between the pressure, pM and TM). 2. A correlation for magnitudes of the peak [the correlation between PMand (C - Cp )]. In the second part of the correlation, the objective is chosen as M o M (Cp - Cp~), where Cp is zero pressure heat capacity, instead of Cp with the following reasons: Most of the existing Cp correlations are expressed in terms of (Cp - Cp~); (Cp - Cp~) is more directly related to the other thermodynamic functions than Cp. As discussed in Section II, this work was attempted within the principle of the corresponding states. A further discussion will follow the rest of this section. Data for the Correlation The sources of Cp(T) maxima data, as reviewed in Section II, are summarized in Table V-1. It is to be noted that the most extensive data are available from H20. Included in the table are data for C6Hg and C 6H12 which were determined from the enthalpy data of Lenoir, et al. using the method employed in previous sections. Their enthalpy measurements were not made carefully in the peak region and consequently the Cp maxima obtained were crude compared to the other data. Nevertheless, data were added to the present work because it was desirable to add the cyclic hydrocarbons into the scope of the present correlation. The data used in this work were presented in terms of reduced values in Table V-2. The critical constants used in the data reduction are listed in Table V-3.

TABLE V-1 SOURCES OF Cp(T) MAXIMA AND Cp~ DATA Molecular No. of Source Substance Source Weight* Data of Cp~ methane 16.13 6 Jones (25) Rossini (50) ethane 30.07 9 Furtado (18), Miyazaki (34) Rossini (50) propane 44.05 3 Yesavage (61) Rossini (50) argon 39-95 6 This work Cp~ = 5/2 R nitrogen 28.01 1 Mage (35) Hilsenrath (24) water 18.02 14 Sirota (51,52) Rossini (50) carbon dioxide 44.01 6 Rivikin (47) Rossini (50) hexafluoroethane 138.01 8 This work Texas A&M Univ. (54) benzene 78.06 2 Lenoir (29) Rossini (50) cyclohexane 84.16 1 Lenoir (29) Rossini (50) *Based on the materials used in the sources. I

-117 TABLE V-2 DATA USED IN THE PRESENT CORRELATION Substance P (psia) CH4 680 800 1000 1200 1500 2000 CH 750 800 820 900 1000 1250 1500 1750 2000 C H 700 1000 1200 N2 2000 Ar 800 950 1143 1371 1714 2000 H20 3271 3414 5556 3911 4267 4978 5689 6400 7112 8554 99-56 11576 12801 1-4223 CO 0 1'280 1450 1707 214 5 2857 5556 C F6 442 2 6 * 490 598 700 539 1049 1598 1969 C H 800 6 1000 C6H12 8t00 Pr TM( R) TMr 1.012 344.2 1.003 1.191 3554.4 1.033 1.488 369.2 1.076 1.786 380.7 1.109 2.231 394.2 1.149 2.976 414.7 1.208 1.059 554.9 1.010 1.130 560.4 1.024 1.158 563.4 1.025 1.271 572.0 1.041 1.412 580.9 1.057 1.765 602.7 1.096 2.118 620.9 1.150 2.471 634.2 1.154 2.824 655.7 1.200 1.134 678.7 1.020 1.620 716.7 1.077 1.944 740.7 1.117 4.073 287.7 1.269 1.134 277.1 1.022 1.547 285.7 1.054 1.620 294.7 1.087 1.944 505.7 1.120 2.450 315.7 1.165 2.855 325.7 1.201 1.019 1168.1 1.003 1.064 1174.6 1.008 1.108 1181.1 1.014 1.219 1196.9 1.027 1.550 1211.9 1.040 1.551 1259.4 1.064 1.773 1264.6 1.085 1.995 1287.1 1.105 2.216 1507.6 1.122 2.660 1543.1 1.153 5.103 1375.1 1.180 5.545 1399.4 1.201 3.990 1416.9 1.216 4.45533 142.4 1.229 1.195 )L.) 1. 026 1.554 70. 9 1.045 1.593 58.9 1.070 2.002 605.) 1.106 2.667 632.9 1.145 5.319 660.9 1.171 1.011 527.6 1.002 1.121 534.8 1.015 1.368 549.5 1.043 1.602 561.1 1.065 1.920 576.7 1.095 2.400 595.7 1.151 3.199 621.7 1.180 4.506 660.7 1.266 1.120 1028.7 1.017 1.400 1065.7 1.051 1.350 1048.7 1.055 R C p Source R 450.6 Jones (25) 53.12 Jones (25) 19.37 Jones (25) 12.50 Jones (25) 8.48 Jones (25) 5.70 Jones (25) 229.6 Miyazaki (34) 105.5 Miyazaki (54) 82.78 Miyazaki (54) 46.33 Miyazaki (34) 27.69 Furtado (18) 14.97 Furtado (18) 11.26 Furtado (18) 8.90 Furtado (18) 7.10 Furtado (18) 106.8 Yesavage (61) 21.32 Yesavage (61) 14.55 Yesavage (61) 4.47 Mage (35) 79.06 This work 30.21 This work 16.30 This work 10.81 This work 7.44 This work 6.03 This work 1111.0 Sirota (51,52) 331.0 Sirota (51,52) 186.8 Sirota (51,52) 88.07 Sirota (51,52) 52.77 Sirota (51,52) 54.54 Sirota (51,52) 24.91 Sirota (51,52) 19.82 Sirota (51,52) 16.58 Sirota (51,52) 12.81 Sirota (51,52) 10.58 Sirota (51,52) 9.15 Sirota (51,52) 8.19 Sirota (51,52) 7.414 Sirota (51,52) 75.44 Rivikin (47) 59.02 Rivikin (47) 22.53 Rivikin (47) 15.76 Rivikin (47) 8.95 Rivikin (47) b.98 Rivikin (47) 796.0 This work 150.0 This work 44.46 This work 27.16 This work 19.03 This work 13.27 This work 9.78 This work 6.98 This work 130.00 Lenoir (29) 335.9 Lenoir (29) 57.27 Lenoir (29)

-118 TABLE V-3 CRITICAL CONSTANTS FOR THE SUBSTANCES USED IN THIS WORK Critical Critical Substance Temperature Pressureac (~R). (psia) methane 343.2 672.0 5.86 ethane 549.7 708.2 6.28 propane 665.7 617.4 6.54 argon 271.1* 705.6* 5.76 nitrogen 226.7 491.0 5.98 water 1165.1 3208.6 7.39 carbon dioxide 547.6 1071.3 6.71** hexafluoroethane 526.8*** 437 5*** 7.19*** benzene 1011.8 714.4 6.83 cyclohexane 995.8 588.0 6.85 *Grigor and Steele 21) **Vukalovich and Altunin(55 ***This work Otherwise, data from Reid and Sherwood48)

-119 Location of Cp(T) Maxima Figure V-1 demonstrates a plot of the reduced temperature, M M M/ TM = TM/Tc, vs reduced pressure, = P P/PC, which includes the values presented in Table V-2. All data points do not fall on a single curve with this particular choice of the coordinates as the points of different gases, as characterized by values of aC, diverge from each other as illustrated by a set of curves for different values of aC (6, 6.5 and 7.0). This divergence shows that a two parameter corresponding states principle does not hold satisfactorily for the location of Cp(T) maxima and therefore an extension to at least a three parameter corresponding states principle seems to be necessary. In this work, using aC as a third parameter, the following equation is proposed as a correlation for loci of Cp(T) maxima: M 1 M In Pr= C [A(1 - M) + B In Tr ] (V-1) r where A = 0.3414 B = 0.6586 A and B are determined by the least square fit with equal weight on each data point. In fact, Equation (V-1) is a linear combination of the two previous equations [Equations (11-29) and (11-30)] suggested by Sirota, et al.(51) and Powers,45 respectively. Figure V-2 demonstrates the correlation of the data on new coordinates, X-Y, where X = In P, Y = aC [0.3414 (1 - 1/T ) + 0.6586 In Tr]. The data points were observed to fall closely on a straight line representing Equation (V-1). Magnitude of (CpM - Cp~) Figure V-3 shows a plot of (CpM - Cp~)/R vs PM on a log-log scale. The data of the different gases diverge from each other because of the need for a three parameter, rather than a two parameter CSP. It seems that this divergence is somehow related to aC since the substances with higher aC values show higher (CpM - Cp~)/R values than those with lower aC values when compared at the same level of Pr. Thus, ac is introduced

-120 U,. N 01'L 1.00 1.00 1.05 1.10 1.15 1.20 Tr = T/Tc 1.25 Figure V-1. Plot of Cp(T) maxima locations in Pr-Tr coordinates.

1.5 1.0 InPr=ac{A(ll/Tr)+ Bi 0.5 C 0.5 ~~0.~0.5 ac{A( 1.0 1.5 - I/Tr) + Bn Tr} Figure.V-2. Plot showing the correlation for the location of Cp(T) maxima.

-122 C~< 4*- 4 * C6H6 6.83 o C H.2 6.85 2 L 0. I 2 - ac 6.5 ac 6.0 0.5 1.0 1.5 In Pr Figure V-3. Plot for the Cp(T) maxima on In Pr - In cPCpOR coordinates.

-123 as a third parameter in this part of the correlation. The correlational effort is focused on the selection of a proper ordinate which will make the data points fall on a single curve. As the first step [(uC/(y + a)] was taken, where y = In[(CpM - Cp~)/R] and a is an arbitrary constant. The particular choice of the ordinate is intended to make the correlation zero at the origin, which is more convenient than infinity in correlating the data analytically. aC in the numerator is designed to reduce the discrepancy between the plots of different gases. With a = 1.2 the data plotted in the new coordinates is shown in Figure V-4. Compared to Figure V-3, the new plot shows better correlation of data points especially in the region of high Pr. In the intermediate region for Pr' the data between different gases still are not gathered closely to each other. To compensate for this discrepancy, the ordinate is modified again by introducing a factor f as TC Y + 1.2 (1 + f) (V-2) (7 - aC) where f = 9(1 + 3X18) The mapping of the data on the final coordinates is presented in Figure V-4. The points are observed to be correlated closely into a single curve (average absolute deviation of the points to the curve is 1.5%) which can be represented as -D/g(X) = ae + bX + CX2 + dX3 (V-3) where a, b, c, and d are constants determined by the least square method as below: a = 0.9106 b = 1.9045 c =-1.2774 d = 0.4239

-124 y L "W"3"8,,-' 112 v ac ac ".0 1.5 M 0 a Y =ac{ n(. p P)+1.2} X =In Pr 0.5 I I I l II I 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 X Figure V-4. Plot showing a correlation for the magnitude of Cp(T) maxima on intermediate coordinate. 2.5 a = 0.9106 -D/bxcx b = 1.0045 Y=e +bx+cx2+dx3 2.0- c =-1.2774 \ d = 0.4239 \ CH4 D 1.0x104 A Cp Y A^-^ ~~ O C3H8 X Figure V-5. Plot showing the final correlation for the magnitude of Cp(T) maxima.

-125 -D/X The factor, e, in the equation is added so that g(0) = 0. D is chosen -4 as 10, an arbitrary small number, which makes the first term essentially the same as a, even for X corresponding to the data nearest to the critical point. The final correlation, therefore, can be expressed as M 0 rCp - Cp a C 7 - aC In (cPM- PO =T 1 + l8 -1.2 (V-4) R 1X 1 +3.8 L 9(1+3X') where X = In P g(X) = a function given by Equation (V-3) Discussion of Results In order to evaluate the performance of Equation (V-l) values of TM were calculated for given pressures and compared with experimental values. They are presented in Table V-4. The average absolute deviation, in terms of temperature difference, is 2~R and in terms of % deviation is 0.3. It is to be noted from the table that in most cases the deviations were within the range of errors associated with experimental TM values. Those error ranges were estimated from the original experimental Cp data from which the maxima were determined. Usually larger errors were observed in the determination of TM's at higher reduced pressures where the Cp(T) curves showed broad maxima. Included in Table V-4 are the values of T calculated using Equations (II-29) and (11-30). The mean and standard deviations for each set of calculated values from the experimental ones are presented in Table V-5 for comparison. This comparison confirms that Equation (V-l) correlates the data better than the other equations.

-126 TABLE V-4 COMPARISON OF THE DATA WITH VALUES DETERMIED FROM THE CORRELATION TM TM ** TM **** /TsCp —C\ /C cal(l) cal(2) cal(3) \ R exp \ R cal Si Pressure ubstance (a) CH4 680 800 1000 1200 1500 2000 C2H6 1000 1250 1500 1750 2000 750 800 820 900 C3H8 700 1000 1200 NH 2000 2 Ar 800 1143 1371 1714 2000 950 H20 3271 3414 3556 3911 4267 4978 5689 6400 7112 8534 9956 11378 12801 14223 Co2 1280 1430 1707 2145 2857 3556 C2FP 442 490 598 700 839 1049 1398 1969 C/HM. 800 C6H6 800 6 1000 C6HI2 800 TM (OR) exp 344.2 ~ 0.5 343.9 (-0.3)* 343.9 (-0.3)* 343.9 (-0.)* 450.6 22.5 467.3 (16.7)* 354.4 0.7 353.6 (-0.8) 353.7 (-0.7) 353.6 (-0.8) 53.12 1.59 56.99 (3.87) 369.2 1.5 367.3 5 -1.9) 368.2 (-1.0) 367.6 (-1.6) 19.37 0.19 19.43 (0.0T) 380.7 2 1.5 378.9 ( —8) 380.9 (0.2) 379.5 (-1.2) 12.50 ~ 0.09 12.47 (-.0o3) 394.2 ~ 1.5 393.6 (-0.6) 3957 (-1.5) 394.9 (0.7) 8.48 ~ 0.04 8.56 (0.08) 414.7 3.0 413.4 (o.7) 42.17 (9.0) 415.9 (3.2) 5.70 0.03 5.75 (0.05) 580.9 ~ 0.5 580.7 (-0.2) 381.7 (.8) 581.1 (.2) 229.6 ~ 4.6 239.6 (10.0) 602.7 ~ 0.5 601.8 (-1.0) 604.4 (1.7) 602.6 (-0.1) 105.5 i.6 107.1 (1.6) 620.9 ~ 1.0 619.5 (-1.4) 624.3 (3.4) 621.0 (0.1) 82.78 ~ 0.83 84.84 (2.06) 634.2 ~ 1.0 634.9 (0.7) 642.2 (8.0) 637.2 (3.0) 46.33 0.37 44.22 (-2.11) 655.7 ~ 2.0 648.5 (-7.2) 658.6 (2.9) 651.6 (-4.2) 27.69 ~ 0.14 27.56 (-0.13) 554.9 0.4 554.7 (-o0. ) 5548 (-.1) 554.8 (-0.1) 14.97 ~ 0.07 15.34 (0.37) 560.4 t 0.5 560.5 (.1) 560.6 (.2) 560.5 (o.1 11.26 ~ o.0 11.18 (-0.08) 563.4 ~0.5 562.7 (-0.7) 62.8 (-.6) 62.8 (-0.6) 8.90. 8.87 (-0.03 572.0 0.8 571.1 (-0.9) 571.5 (-o.5) 571.2 (-0.8) 7.10 0.03 7.37 (0.27) 678.7 ~1.3 678.6 (-0.1) 678.7 (0.0) 678.7 (0.0) 106.8 ~ 2.1 112.6 (5.8) 716.7 3.0 716.6 (-0.1) 718.7 (2.0) 717.3 (0.7) 21.32 * 0.11 20.49 (-0.83) 740.7 5.0 736.9 (-3.8) 741.0 (0.3) 738.3 (-2.5) 14.53 0.07 14.36 (-0.17) 287.7 ~8.0, 286.7 (-1.0) 296.3 (8.6) 289.4 (1.7) 4.47 ~ 0.02 4.49 (0.02) 277.1 ~ 0.2 277.1 (0.0) 277.2 (0.1) 277.1 (0.0) 79.06 ~ o.32 83.09 (4.03) 294.7 ~ 0.2 294.8 (0.1) 295.9 (1.2) 295.1 (0.4) 30.21 ~ 0.09 28.83 (138) 303.7 ~ 0.5 304.3 (0.6) 306.5 (2.8) 305.0 (1.3) 16.30 o0.06 14.73 (-1-57) 315.7 ~ 0.8 316.3 (0.6) 320.5 (4.8) 317.6 (1.9) 10.81 ~ 0.03 10.20 (-0.61) 325.7 ~ 1.0 324.9 (-0.8) 331.0 (5.3) 326.7 (1.0) 7.44 ~ 0.02 7.21 (-0.23) 285.7 + 0.2 285.5 (-0.2) 285.9 (0.2) 285.6' (-o.1). 6.03 ~ 0.02 5.85 (-0.18) 1168.1'~ 0.1 1168.2 (0-.1) 1168.2 (0.1) 1168.3 (0.2) 1111.0 ~ 44.4 992.2 (-11.8) 1174.6 ~ 0.4 1174.9 (0.3) 1175.0 (0.4) 1175.0 (0.4) 331.0 ~ 6.6 300.0 (-31.0) 1181.1 ~ 0.5 1181.5 (o.4) 1181.6 (0.5) 1181.6 (0.5) 186.8 ~ 0.9 176.7 (-10.1) 1196.9 ~ 1.0 1196.8 (-0.1) 1197.2 (0.3) 1196.9 (0.0) 88.07 ~ 0.44 78.12 (-9.95) 1211.9 1.4 1211.0 (-0.9) 1211.9 (0.o) 1211.4 (-0.5) 52.77 ~ 0.16 49.68 (-3.09) 1239.4 + 1.8 1236.5 (-2.9) 1238.8 (-0.6) 1237.2 (-2.2) 34.34 ~ 0.03 30.67 (-3.67) 1264.6 ~ 2.5 1259.0 (-5.6) 1263.0 (-1.6) 1260.4 (-4.2) 24.91 ~ 0.02 23.41 (-1.50) 1287.1 ~ 2.0 1279.3 (-7.8) 1285.2 (-1.9) 1281.3 (-5.8) 19.82 ~ 0.02 19.31 (-0.51) 1307.6 ~ 2.7 1297.6 (-10.0) 1305.8 (-1.8) 1300.3 (-7.3) 16.58 + 0.02 16.48 (-0.10) 1343.1 ~ 3.0 1330.0 (-13.1) 1342.9 (-0.2) 1334.1 (-9.0) 12.81 ~ 0.01 12.65 (-0.16) 1375.1 ~ 3.5 1358.i (-17.0) 1376.0 (-0.9) 1363.6 (-11.6) 10.58 ~ 0.01 10.27 (-0.31) 1399.4 ~ 35 1382.8 (-16.6) 1406.0 (6.58) 1389.9 (-9.5) 9.15 ~ 0.01 8.81 (-0.34) 1416.9 ~5.0 1405.1 (-11.84) 1433.6 (16.7) 1413.5 (-3.4) 8.19 ~ 0.01 7.95 (-0.24) 1432.4 ~ 4.0 1425.2 (-7.2) 1459.1 (26.8) 1435.2 (2.8) 7.44 ~ 0.01 7.55 (0.11) 561.5 ~ 0.2 562.3 (0.8) 562.5 (1.0) 562.4 (0.9) 73.44 ~ 2.93 75.72 (2-28) 570.9 ~ 0.2 571.6 (0.7) 572.2 (1.3) 571.8 (0.9) 39.62 ~ 1.19 40.37 (0.75) 585.9 ~ 0.4 586.9 (1.0) 588.4 (2.5) 587.4 (1.5) 22.53 ~ 0.45 22.76 (0.23).605.5 ~0.5 607.3 (1.8) 610.8 (5.3) 608.4 (2.9) 135.76 ~ 0.21 14.68 (0.92) 632.9 ~ 2.0 633.7 (0.9) 641.3 (8.4) 636.1 (3.2) 8.95 ~ 0.09 9.55 (0.60) 660.9 ~ 2.0 654.8 (-6.1) 666.8 (5.87) 658.4 (-2.5) 6.98 ~ 0.07 7.22 (0.24) 527.6 ~ 0.1 527.5 (-0.1) 527.6 (0.0) 527.6 (0.0) 796.0 ~ 15.9 804.9 (8.9) 534.8 ~ o.1 535.2 (0.4) 535.2 (0.4) 535.2 (0.4) 150.0 ~ 0.8 151.5 (1.5) 549.3 ~ 0.2 550.3 (1.0) 550.9 (1.6) 550.6 (1.) 44.46 ~ o0.09 41.99 (-2.47) 561.1 ~ 0.3 562.4 (1.3) 563.6 (2.5) 562.8 (1.7) 27.16 * 0.05 26.75 (-0.41) 576.7 ~0.5 576.8 (0.1) 579.4 (2.7) 577.7 (1.0) 19.03 (-0.04 19.02 (-1) 595.7 ~ 1.0 595.0 (-0.7) 599.8 (4.1) 596.5 (0.8) 13.27 ~ 0.03 13.54 (0.27) 621.7 ~ 1.5 619.2 (-2.5) 628.4 (6.7) 622.0 (0.5) 9.78 ~ 0.02 9.14 (-0.64) 660.7 ~2.0 649.4 (-1L3) 666.2 (5.5) 654.3 (-6.4) 6.98 ~ 0.01 6.97 (-0.01) 1028.7 ~ 5.0 1028.7 (0.0) 1028.8 (0.1) 1028.8 (0.1) 130.0 ~ 19.5 139.29 (9.29) 1063.7 ~ 8.0 o1062.8 (-0.9) 1064.2 (0.5) 1063.4 (-0.3) 33.39 ~ 1.67 34.64 (1.25) 1048.7 ~15.0 1041.5 (-7.2) 1042.6 (-6.1) 1042.0 (-6.7) 37.27 ~ 1.86 38.93 (1.66) ~~~~~~~~~~~~~~~~~~~~~~3.9 (1.66 *Number in parentheses represents (calc. value -.exp. value). **Calculations from In PMr= ac In TMr. ***Calculations from. In PMr = ac. ****Calculations from In PMr= OC {.3414 -( ) + 0.6586 nTMr}. _.pr=a 031 1 1.68 n -

-127 TABLE V-5 M M Mean and Standard Deviations of (TMp - TM ) exp calc Present Correlation Eq. II-29 Eq. II-30 Mean Deviation (OR) -0.5 -2.2 +3.0 Standard Deviation (OR) 3.0 5.0 5.5 To examine the performance of Equation (V-4) (CpM - Cp~)/R values were calculated from the equation for given pressures and compared with the experimental ones (Table V-4). The errors associated with the experimental values, as presented in the table, have been estimated from the original data for Cp(T) plots from which the maxima was determined. Generally, larger errors were observed in the determination of Cp values at the pressures close to the critical values where the Cp(T) curves exhibit steep maxima. This was in contrast to the case of TM, in which TM was less susceptible to error in this region since the peak locations, on the other hand, are more clearly defined at the sharp peaks than at the smooth ones shown in the higher pressure region. Consequently, higher deviations of the calculated values from the experimental ones were observed in the region near the critical point. The mean and standard deviations of the calculated values from the experimental ones were 1.5% and 5.0% respectively. The relatively high standard deviation probably resulted from the uncertainty of the data especially in the critical region, not from the lack of the fittability of the present correlation. Considering the present correlation includes substances which have widely different aC values, and notably a polar substance as H20, it is felt that the results were satisfactory.

VI - SUMMARY AND CONCLUSIONS 1. Calorimetric data for argon were obtained from the isobaric, isothermal and isenthalpic measurements using the recycle flow system 19 originally designed by Faulkner.9 The measurements covered the liquid, two-phase, and gaseous regions at temperatures from -240~F to 220~F and at pressures from 286 to 2000 psia. Particular emphasis was placed on the measurements of Cp and Cp(T) maxima in the supercritical region. These data were interpreted to yield Cp, 0 and V and further processed to yield enthalpy values. Enthalpy diagrams and tables were prepared. Thermodynamic consistency checks showed that the data were self-consistent to ~0.09%. The accuracy of the isobaric and isothermal data was believed to be 0.2% and 0.4% respectively. 2. Calorimetric data for Freon-116 (C2F6) were obtained from the experimental measurements of isobaric and isothermal changes on enthalpy 34 using the new recycle flow system designed by Miyazaki.4 The measurements covered the liquid, two-phase, and gaseous regions at temperatures from 0~F to 247~F and at pressures between 247 and 1969 psia. Particular emphasis was placed on the measurements of isobaric latent heats of vaporization near the critical point to determine the critical pressure and temperature and Cp and Cp(T) maxima in the supercritical region. Thermodynamic consistency checks showed that the data were self-consistent to ~0.03%. The accuracy of the isobaric and isothermal data was believed to be 0.05% and 0.1%, respectively. 3. From the Cp(T) maxima data obtained from this research together with the ones available from the literature a generalized correlation for the Cp(T) maxima was developed within the framework of the corresponding P states principle. The correlation was divided into the two parts: (1) the correlation for the location of the maxima and (2) the correlation for the magnitude of the maxima. The correlation was found to predict the locations and magnitudes of maxima within ~2~F and ~5% errors, respectively. -128

VII - RECOMMENDATIONS FOR FUTURE WORK 1. As soon as the calorimetric investigation was finished, the old recycle system of the thermal properties of Fluids Laboratory had ceased to operate. At the time of preparing this thesis, it had been dismantled to clear the site for another research activity. There are, however, many fine instruments which can still be used in the new system as replacements wherever and whenever needed. Among them are KEPCO D.C. power supplies, bath controllers (used for the calorimeter and heat exchanger baths) and the pressure transducers. There are many miscellaneous items which should be useful in the future. Therefore, all of these should be reserved. 2. Some suggestions as to the improvements of the new recycleflow system are in order: (a) Mass leaks were frequently observed through the gland packing of the metering pump cylinders when the pump cylinders were cooled down at the start-up of the system. Those leaks, which were caused by insufficient temperature compensation of the packings, were arrested by tightening the bolts of the packing rods. However, once the measurements were finished and the pump bath was allowed to warm up (as was the case with the present work) the cylinders could be subjected to more than normal strain due to the thermal expansion. This could be harmful to the precision pumps in the long run. Therefore, some measure should be taken to maintain the pump bath at a constant temperature on a 24 hour basis. This could possibly be done by installing a refrigeration unit which could be operated at relatively low costs. (b) It would be desirable to have a valve on the line before the calorimeter so the calorimeter could be isolated from the pump bath when it is necessary to repair or replace some parts of the calorimeter. (c) Replacing the Heise gage on the helium line with the one which could read the pressure of at least 2000 psig is recommended. The present gage reads only to 1000 psig. -129

-1303. The present mechanism of lifting and lowering the pump bath should be improved. Installation of a motorized gear or a hydraulic lifter would be desirable if possible. 4. Prediction of location and magnitude of Cp(T) maxima, which has been accomplished through the correlation of the data could be of value in establishing a new generalized correlation of Cp data in the maxima region. It is recommended that an effort be extended to correlate the existing Cp data which have been obtained from calorimetric measurements.

APPENDIX A CALIBRATION DATA -131

-132 TABLE A-1 CALIBRATION CONSTANTS FOR PLATINUM RESISTANCE THERMOMETER a = 3.9261045 x 10-3 8 = 1.4916703 = 0.1101088 Ro = 25.5548 where 1 Rt a R 0 t t 1+ 6 11 — 1 Bp 100 100 100 -11004_3 t = temperature, ~C Rt = resistance of the thermometer at t~C Ro = resistance of the thermometer at 0~C

-133 TABLE A-2 CALIBRATION DATA FOR THERMOPILES Temperature 6 Junctions Temperature 15 Junctions, (0~C)_) TP-A TP-B ("c) TP-C -196. -33338 -33327 -182.85 - 79856 -183. -31996 -31986 -110. - 54995 -100. -20342 -20332 0. 0 - 80. -16781 -16779 50. 30800 - 60. -12956 -12955 100. 64665 - 40. - 8880 - 8876 148.89 100316 - 20.- 4555 - 4554 0. 0 0 20. 4775 4776 40. 9762 9762 60. 14950 14945 80. 20328 20322 100. 25878 25875 120. 31607 31602 140. 37494 37491 160. 43543 43536 Note: Reference junctions at 0.~C. EMF is in VtV. Calibrations are fitted to the equation E = At + Bt2 + Ct + Dt where E = EMF, TV t = temperature, ~C The constants are A B TP-A TP-B TP-C 233.34 233.29 583.08 0.27630 0.27643 0.69165 C x 103 -0.22327 -0.22306 -0.57190 D x 107 0.71210 0.68403 1.27582

TABLE A-3 PRESSURE TRANSDUCER (HIGH) CALIBRATIONS X YEXP YCAL EXP YCAL P YCAL,ig) g) (Vv) nv)(psig () ()(v) 1987.4 2387.94 2588.45 1986.1 2387.48 2386.88 1983.8 2583.72 2384.12 1789.7 2150.66 2150.91 1789.0 2149.77 2150.07 1786.9 2147.83 2147.55 1590.7 1911.49 1911.82 1590.9 1911.54 1912.06 1587.4 1908.47 1907.86 1390.0 1670.41 1670.67 1392.6 1673.31 1673.80 1386.0 1665.99 1665.87 1190.7 1431.43 1431.21 1251.1 1503.52 1503.82 1184.7 1423.64 142&.00 988.8 1188.17 1188.62 1081.2 1299.37 1299.70 988.7 1188.46 1188.50 789.3 948.57 948.93 904.1 1087.12 1086.92 784.4 942.89 943.03 595.6 716.40 716.21 719.6 865.56 865.26 588.9 708.19 708.17 417.9 502.55 502.74 560.4 674.01 673.90 405.3 487.51 487.60 I lI YCAL = A + BX + CX2 + DX3 A = 0.7360 C = 2.830 x 10-7 B = 1.2012 D = -6.810 x 1011 = 0.02% YEXP - YCAL YEXP average

TABLE A-4 PRESSURE TRANSDUCER (LOW) CALIBRATIONS X YEXP YCAL X Xp YCAL X EXP YCAL (psig) (Lv) (<Iv) (psig) (>V) (|jv) Ipsig). (,Uv). (Lv) 1988.0 2421.04 2421.14 1986.7 2420.28 2419.57 1982.9 2414.71 2415.08 1790.5 2185.46 2185.44 1789.3 2183.67 2184.03 1786.5 2180.73 2180.70 1593.6 1949.49 1949.86 1592.7 1948.14 1948.86 1587.5 1942.67 1942.64 1389.4 1705.11 1705.25 1392.8 1708.51 1709.26 1385.5 1700.99 1700.58 1191.6 1467.62 1467.86 1250.9 1538.52 1539.08 1183.8 1458.35 1458.50 989.5 1224.47 1225.18 1082.1 1336.06 1336.37 988.3 1223.36 1223.76 789.5 984.77 985.10 906.1 1125.01 1125.08 782.9 977.09 977.14 595.7 751.99 752.36 719.8 901.83 901.34 589.2 744.59 744.62 418.0 539.41 539.24 557.9 706.89 707.05 404.3 523.11 522.89 CAL = A + BX + CX2 + DX3 A = 39.004 B = 1.1942 C = 7.236 x 10-6 D = -2.6122 x 10-9 YEXP YCAL 0.....E..' v 0.025% EXP average

TABLE A-5 FLOW METER CALIBRATIONS X YCAL X Y YCAL YCAL 0.2259 0.11039 0.11008 0.3279 0.11156 0.11169 0.1737 0.10952 0.10927 0.2269 0.11008 0.11009 0.3292 0.11223 0.11171 0.1830 0.10904 0.10941 0.4332 0.11318 0.11340 0.5580 0.11547 0.11547 0.2983 0.11108 0.11122 0.4341- 0.11317 0.11342 0.5582 0.11533 0.11547 0.3011 0.11108 0.11126 0.6272 0.11673 0.11662 0.7450 0.11876 0.11860 1.0197 0.12329 0.12319 0.6281 0.11667 0.11664 0.7446 0.11898 0.11860 1.0219 0.12500 0.12525 0.7226 0.11835 0,11823 0.9323 0.12174 0.12175 1.2336 0.12678 0.12664 0.7573 0.11857 0.11881 0.9368 0.12183 0.12182 1.2344 0.12656 0.12665 0.8588 0.12045 0.12052 1.1367 0.12499 0.12510 1.4494 0.12993 0.12990 - CA) I x = (F/ ) x 103 Y = (pAP)/(FI): (lb/min)(ipoise): (lb/ft3)( in. H20)/(lb/min)/(4poise) YCAL = A + BX + CX2 + DX3 A = 0.10670 B = 14.2716 C = 3466.40 D = -1.56576 x 106 Y - YCAL Y average = 0.14%

-137 TABLE A-6 DENSITY DATA OF C2F6 AT 0.~F X Y YCAL (psia) (g/cc) ( g/cc) 165.9 1.25905 1.25931 492.8 1.32165 1.32056 676.3 1.34120 1.34178 932.3 1.36010 1.36105 1243.3 1.37779 1.37671 1506.3 1.39091 1.39127 1980.3 1.42060 1.41991 CAL = A + BX + CX2 + DX3 A = 1.21322 B = 3.13492 x C = -22.5504 x 10-8 D = 63.6379 x 10-12 Y - YCAL Y average = o.o05

APPENDIX B EXPERIMENTAL DATA -138

-139 TABLE B-l BASIC ISOBARIC DATA FOR ARGON Inlet Run Press. N (pia) Inlet Temp. (~F) Outlet Temp. (~F) Power Flow Corr. AHp (~) (Btu/min)(lb/min) (Btu/lb) (Btu/lb)(Bt/l ~~~~~~~~~BuI-F 10.02 10.03 1). 04 10.05 10.06 10,07 22.02 22.03 22.04 22.05 22.06 22.07 22.08 22.09 22.10 22.11 38.01 38.02 38.03 38.04 38.05 39.01 39.02 39.03 39.04 39.05 39.06 44.02 44.03 44.04 46.01 46.02 46.03 23.01 23.02 23.03 23.04 28-8. 8 289. 3 289. 1 289.5 288.7 28 8.5 286.0 286.0 285.5 28 6 * 3 285.6 286.0 286.2 285.9 285.5 285.3 285.5 285.3 285.3 285.7 285.7 285.6 285.5 285.3 285.5 285.9 285.5 285.5 285.7 285. 1 457.2 457.3 457.3 456.9 -5Q.34 -4.65 -50.32 30.23 -50.35 73.26 -50.46 100.46 -50.43 110. 16 -50.51 119.93 -240.00 -230.06 -24n.00 -226.73 -240.00 -229 24L -240.00 -227.51 -240,.0 -226.75 -240.00 -240. 00 -240.00 -240. 00 -240.00 -200.29 -200.29 -200. 30 -200.30 -200.29 -100.53 -100.48 -100.49 -100.46 -100.49 -100.55 70.26 70. 26 70.28 99.95 99.75 99.71 -240.09 -240. 08 -240.08 -240. 09 -2 26.75 -226,72 -225.14 -223. 91. -220.71 -189.87 -169.48 -146. 36 -121 14 -93.61 -80.23 -50.42 -20.76 9.37 33.78 50. 58 99.50 125.68 1.49.46 170.73 190.13 218.28 -229.98 -215.03 -210.65 -209.52 1.45 n.23485 -.o06 6. 189 0.1355 2.530 0.23414 -0,005 0.,799 0.1341. 3.843 0.23372 -0.004 16.438 0.133n 4.660 0.23336 -0.004 19.965 0.1323 4,945 0,23278 -0.003 21.241 0.1323 5.240 0.23275 -o.003 22.512 0. 1321 n 852 0.25411 n0. 3.351 0.3371 1.690 0.25285 -0.0 6.684 0.5037 0.922 O 253O -0.0 3.637 0.3380 1.088 O.25408 -0.0 4.282 0.3428 1.262 0.25275 -O., 4.994 0.3769 7.475 0.15028 -0.001 49.739 3.7539 7.129 0.1n5003 -0.175 47,341 3.56 48 7.q28 0.15060 -0.016 52.630 3.5417 7.982 0.15071 -0.016 2.948 3.2907 8.105 0.15070 -0.019 53.766 2.7873 0.426 0,21998 -0.007 1.931 0.1853 1.198 0.21970 -O.00, 5.447 0.1768 1.988 0.21.919 -0.006 9.062 0.1680 2.816 0.21922 -0.005 12.841 0.1622 3.692 0.2'1904 -0.005 16.850 0.1579 n.560 0.19502 -0.004 2.867 0.1412 1. 368 0.19584 -0.004 6.980 0.1394 2.155 0.19568 -0.004 11.007 0.1380 2.942. 19562 -0.003 15.037 0.1369 3.573 0.19548 -0.003 18.274 0.1361 4.009 0.19567 -0.003 20.484 0.1355 0.931 0.24443 -0.004 3.804 0.1301 1.761 0.24490 -0.004 7.186 0.1297 2.510 0.24490 -0.004 10.244 0.1294 2.018 0.22139 -0.003 9.114 0.1288 2.576 0.22159 -0.003 11.624 0.1286 3.369 0.22111 -0.003 15.233 0.1285 0.614 0.18831 -0.0 3.263 0.3228 1.676 0.18843 -0.0 8.896 0.3551 2.045 0.18845 -0.001 10.851 0.3687 2.147 0.18828 -0.001. 11402 0.3730 2.261 0.18855 -0.003 11.987 0.3778 2.348 0.18831 -0.001 12.468 0.3871 2.487 0,18860 -0.001 13.188 0.4106 6.954 O. 18969 -0.003 36.659 1.1445 8.192 0.18790 -0.004 43.594 1.3606 9.006 0.17849 -0.390 50.069 1,4408 8. 879 0) 17837 -0.386 49.390 1.4805 7.184 0. 14409 -0.013 49.847 1.4461 6.922 0.14391 -0.012 48.088 1.5013 7.277 0.14390 -0.014,50.558 1.4142 7.432 0.14404 -0.013 51.583 1.3226 23.05 457.3 -240.08 -208.35 23.06 457.1 -240.08 -207.87 23.07 457.3 -240.11 -207.99 23.08 457.5 -240.00 -207.97 23.09 457.3 -240.00 -207.96 24.01 457.3 -240.00 -205.25 24.02 457.5 -240.00 -206.64 25.01 457.4 -240.00 -205.53 25.02 456.9 -240.00 -207.97 25.03 47,.0 -240.00 -204.25 25.05 457.2 -240.00 -201.00

-140 TABLE B-1 (Continued) Inlet Run o Press. (psia) Inlet Temp. (~F) Outlet Power Flow Corr. AHp (/ — p T(em (Bt/mn) (lb/min) (Btu/lb) (Btu/lb) (B (OF) kBtu/1b-*F) 29 01 455. 9 -1.49.84 29.0 454.9 -149.86 29.03 457. 5 -149.89 29.04 457 7 -14q.8 29.05 457.1 -149.86 26.01 571.6 -240.00 26.02 571.3 -239.96 26.03 572.2 -239.93 26.04 571.7 -239.82 26.05 571.3 -239 89 26' 06 571.4 -240.01 27.01 571.6.-240o00 27.02 571,4 -240,00 27.03 571.4 -240.00 27.04 571.3 -240.00 27.05 571.5 -240.00 27.06 571.1 -240.00 30.01 571.3 -149.97 30.02 570.9 -149.92 30.03 572.1 -149.94 30.04 571,5 -149 89 30.05 571.5 -149.90 21.01 706.2 -239.90 21.02 707.2 -239,89 21.03 707,6 -239,89 21.04 707.4 -239.90 21.05 708.5 -239.95 21.06 709.0 -239.86 21.07 709.0 -239.87 21.08 704.8 -239.84 21.09 707.0 -239,92 21.10 708.2 -239.9? 31.01 706.9 -149.90 31.02 706.6 -149.89 31.03 706.7 -149.90 31.04 706.9 -149.89 31.05 706.9 -149.85 41.01 706.5 -200.02 41.02 706.3 -200.03 41.03 706.3 -199.96 41,08 706,0 -199,89 41.09 706.0 -199.99 41.10 706.0 -199.96 18.01 799.4 -240.52 18.02 799.3 -240.51 18.03`801.2 -240.49 19,051 797.9 -239.79 19,02 798 3 -239.74 -140. 31 -- 14.05 -89. 82 -63.46 -52.75 -229, 91 -209. 97 -201. 49 -200. 19 -198.87 -198.23 -196.56 -197.97 -'197.99 -195.74 -194. 10 -196.01 -140. 23 -112.83 -89.92 -64. 22 -53.89 -229.87 -207.46 -188.83 -188. 57 -1 95,70 -1. 87.1 9 -185.86 -177.87 -159.60 -139.67 -139.32 -113.22 -89.58 -63.76 -49. 73 -194.95 -193. 11 -190.63 -179.63 -175.15 -164.70 -230.48 -210.32 -185.20 -179.91 -174.46 0. 361] 0.20817 -0.01.3 1.276 0.20781 -0.01? 2-132 0.2149c -0.011 2.982 0.21487 -0.008 3.321 0.21482 -0.006 0,620 0.1.9449 -0.0 2.060 0.19433 -0,001 2.901 0.19467 -0.001 3.054 0.1 9444 -0.002 3.242 0.19425 -0.003 3.511 0.19442 -0.002 8.101 0.17461 -0o034 7,909 0.17478 -0,005 7.731 0.17474 -0.005 8.216 0.17463 -0,031 8.385 0.17463 -0.025 8.167 0.17460 -0.038 0.426 0.21258 -0.010 1.50? 0.21234 -0.009 2.331 0.21283 -0.008. 3,192 0,21292 -0.007 3.709 0.22416 -0,006 0.676 0.21529 -0.0 2.416 0.21547 -0.0 5.380 0.21530 -0.024 5.718 0.21482 -0.043 3.706 0.21564 -0.002 8.951 0.21576 -0.132 9.181 0.21550 -0,045 1.0.433 0,21029 -0.019 11.898 0.21497 -0.012 1.3.099 0 21551 -0.010 0.580 0.22379 -0.010 1.796 0.22433 -0.010 2.782 0.22427 -0.009 3.756 0.22412 -0.007 4.233 0.2241.6 -0.006 0.657 0.21923 -0.001 0.971 0.21954 -0.001 1.379 0.21.994 -0.002 7.250 0.22003 -0.009 7.679 0.21790 -0.010 8,598 0.21951 -0.008 0.683 0.22229 -0.001 2.235 0.22193 -0.0 5.654 0.22211 -0.003 8.380 0.21338 -0.007 9.606 0.21335 -0.003 1. 719 (0.1 80()4 6.130 0.1712 9.910 016h50 13.870 0.1605 1 5.453 n. 1591 3.188 0.31.60 1.n.601 0.3535 14.902 0.3877 15.707 0.3963 16.689 0.4068 18.055 0.4321 46.358 1.0672 45.244 1.0765 44.236 1.0530 47.014 1.0622 47.991 1.0456 46,738 1.0625 1.993 0.2047 7.063 0.1904 10.946 0.1824 14.986 0.1749 16.542 0.1723 3.138 0.3129 11.213 0.3458 24.963 0.4889 26.574 0.5177 17.184 0.3883 41.354 0.7852 42.558 0.7880 49.593 0.8003 55.334 0.6889 60.770 0.6062 2.580 0.2438 7.995 0.2180 12,394 0.2055 16.750 0.) 945 18.878 0.1885 2.996 0.5910 4.421 0.6388 6.268 0.6718 32.940 1.6259 35.229 1.*4182 39.159 1.1106 3.071 0.3059 10,069 0,3335 25.454 0.4604 39.267 0.6558 45.021 0o6897

-141 TABLE B-1 (Continued) Inlet Inlet Run Run Press. Temp. No. (psia) (~F) Outlet power Flow Corr. AHp ( Te(F (Btu/min)(lb/min) (Btu/lb) (Btu/lb) (Btu/lbbF) 19.03 800.3 -239.76 -177.08 19.04 797.9 -239.74 -168.93 19.05 798.9 -239.74-171.87 20.01 798.0 -239.69 -156.97 20.02 800. O -239,70 -142.29 32.01 799.1 -149.76 -138.99 32.02 799.6 -149.78 -113.83 32.03 799.5 -149.74 -90.25 32.04 799.5 -149.72 -64. 4 32.05 799.5 -149.74 -48.76 4?.01 800.2 -209.97 -199.91 42.02 800.9 -209.94 -189.79 42.03 800.0 -209.97 -187.11 42.04 800.1 -209.94 -184.95 42.05 799.5 -209.93 -183.93 42.06 800.2 -209.94 -182.99 42.07 799.7 -209.94 -181.80 42.08 800.2 -209.94 -180.91 42.09 800.2 -209.91 -178.98 42.10 799.8 -209.91 -174.75 42.11 800.0 -209.91 -169.55 42.12 799.6 -209.91 -159.27 42.13 800.4 -209.91 -149.44 40.01 950.9 -180.61 -178.71 40.02 950.3 -180.46 -176.48 40.03 951.0 -180.46 -174.47 40.04 951.1 -180.48 -172.34 40.05 950.1 -180.45 -170.44 40, 06 950.5 -180.44 -168.32 40.07 950.5 -180.45 -166.33 9.01 1142.7 -50.49 -40.79 9.02 1141.7 -50.48 -5.25 9.03 1141.1 -50.51 30.14 9.04 1143.2 -50.49 73.16 9.05 1142.7 -50.46 100.65 9.06 1142.4 -50.48 109.95 9.07 1142.3 -50.46 120.15 15.01 1141.1 -240.18 -23N.64 15 02 1143.0 -240 28 -209.79 15.03 1143.8 -240.25 -180.03 15.04 1143.2 -240.25 -164.55 16.01 1143.5 -240.35 -230.18 16.02 1141.8 -240.34 -209.94 17.01 1141.2 -240.35 -180.12 17.02 1142.7 -240.35 -164.94 17.03 1141.3 -240.41 -160.02 17.04 1143.5 -240.35 -154.83 17.05 1141.4 -240.41 -149.78 9.152 0.21.375 -0.004 42.810 0.6830 10.336 0.21338 -0.001 48.437 0.6840 1 1 1 I 0.000 0.21357 -0.001 46.821 0.657 0.19987 -0.002 53.316 1.577 0.20058 -0.001 57.719 0.685 0.22815 -0.007 2.995 2.016 0. 2 835,-0.006 8, 824 3.078 0.22820 -0.006 13.484 4.093 0.22824 -0.004 17.931 4.662 0.22801 -0.003 20.445 0.98 1 0.22956 -0,0 4.275 2.329 0.23079 -0.001 10.091 2,875 0.23052 -0.001 12.469 3.494 0.23050 -0.006 15.153 3.958 0.23035 -0.009 17.175 4.h12 0.23062 -0.011 19.989 5.708 0.23034 -0.029 24.751 6.292 0.23065 -0.030 27.251 7.063 0.23062 -0.015 30.610 7.999 0.22956 -0.014 34.831 8.807 0.23069 -0.010 38.168 9.829 0.22629 -0.009 43.425.0.537 0.23074 -0.008 45.657 0.431 0.22977 -0.002 1.874 1.001 0.22962 -0.003 4.358 1.673 0.22972 -0.003 7.279 2.421 0.22665 -0.011 10.670 3.006 0.22769 -0.010 13.193 3.569 0.22795 -0.011 15.647 4.023 0.22869 -0.010 17.582 0.415 0.23180 -0.002 1.789 1.847 0.23185 -0.001 7.965 3.164 0.23182 -0.001 13.646 4.688 0.23201 -0.001 20.203 5.624 0.23216 -0.001 24.223 5.932 0.23169 -0.001 25.601 6.271 0.23182 -0.001 27.050 0.621 0.22085 0.0 2.810 2.112 0.22123 0.0 9.547 4.896 0.22114 -0.001 22.141 7.446 0.22105 -0.002 33.683 0.628 0.21018 0.0 2.990 1.976 0.20955 0.0 9.429 4.842 0.21925 -0.001 22.082 7.298 0.21959 -0.003 33.232 8.232 0.21882 -0.008 37.614 9.111 0.21908 -0.007 41.578 9.828 0.21855 -0.007 44.961 0.6899 0.6445 0. 5925 0.2781 0.2454 0.2267 0.2095 0.2025 0.4249 0,5008 0.5454 0.6064 0.6606 0.7417 0, 8796 0.9387 0.9897 0.9906 0.9457 0.8575 0.7550 0.9865 1 0949 1.2151 1. 3108 1.3179 1 2910 1.2452 0 1844 0 1761 0.1692 0.1634 0.1603 0.1596 0.1585 0.2945 0.3131 0.3677 0,4450 0.2940 0,.3102 0.3666 0,4407 0.4679 0.4862 0.4961

-142 TABLE B-1 (Continued) Inlet Run Press. N (psia) Inlet Temp. (~F) Outlet Power Flow Corr. AHp (T)p Temp. (Btu/min)(lb/min) (Btu/lb) (Btu/lb) (Btu/lb-F) (OF) Bt.1*F 17.06 1142.2 -240.37 37.01 1143.9 -180.20 37.02 1144.1 -180.13 37.03 1144.1 -180.13 37.04 1144,1 -180.15 37.05 1144.3 -180.17 37.06 1144.4 -180.17 37.07 1143.7 -180.16 37,08 1144.1 -180.13 33.01 1143.9 -149.75 33.02 1143.1 -149.74 33.03 1143.9 -149.70 33.04 1143.7 -149.71 33.05 1143.3 -149,74 43.01 1144.4 70.04 43.02 1143.4 70.00 43.03 1143.2 70, 03 43.04 1143.8 70.03 43.05 1143.6 69.77 13.01 1370.4 -240.28 13.02 1369.2 -240.27 13.03 1374.3 -240.25 13.04 1371,4 -240.23 13.05 1371.8 -240.24 13.06 1370.3-240.18 13.07 1370.2 -240.23 13.08 1371.1 -240.31 14.01 1371.2 -240.23 14.02 1372.2 -240.22 14.03 1372.1 -240.38 14.04 1371.0 -240.22 14.05 1372.0 -240.24 36.01 1372.3 -170.17 36.02 1372.7 -170.25 36.03 1372.5 -170.21 36.04 1372.3 -170.23 36.05 1371.9 -170.21 36.06 1372.1 -170.19 36.07 1372.9 -170.21 36.08 1372.9 -170.18 36.09 1372.3 -170.23 36.10 1372.7 -170.13 36.11 1373.0 -170.10 36.12 1372.4 -170.14 36.i3 1372.3 -170.11 36.14 1372.4 -170.11 12.01 1716,3 -240.38 12.02 1717.9 -240.36 I II I -140.50 -174.76 -169.65 -166.68 -165.57 -163.07 -159.78 -154.56 -149.97 -139.09 -113.52 -88.99 -63.69 -41.34 79,77 99.92 125. 12 150.04 169.47 -230.30 -211 00 -180.20 -158.98 -157.05 -155.03 -152.76 -148. 51 -144.70 -140. 50 -137.48 -134.87 -129.23 -164.67 -160.46 -158,73 -1 56.11 -153 81 -15 239 -150.72 -145 33 -141. 10 -130.11 -110.42 -89.90 -64. 02 -55.64 -231.39 -210.84 10.824 0.21871 0.701 0.21174 1.484 0.21098 2.025 0.21136 2.246 0.21193 2.735 0.21159 3.345 0.21134 4.191 0.21154 4.811 0.21133 1.108 0.21120 Z.911 0.21158 4.186 0.21172 5.5308 0.21172 6.185 0.21154 0.346 0.23792 1.055 0.23883 1.926 0.23874 2.776 0.23959 3.432 0.23898 6.658 0.22818 2.020 0.22812 4.633 0.22856 7.190 0.22810 7.493 0.22842 7.776 0.22781 8.128 0.22809 8.715 0.2271.9 8.766 0.21.558 9.288 0.21644 9.624 0.21598 9.866 0.21483 10,413 0.21517 0.661 0.21435 1.222 0.21483 1.452 0.21495 1.829 0.21579 2.167 0.21721 2.36h6 0.21765 2,608 0,21789 3.317 0.21812 3.831 0.21791 4.99.4 0.21770 6.559 0.21721 7.837 0.21741 9.126 0.21708 9.526 0.21685 0.520 0.20742 1.789 0.20775 -0. 005 49,486 0.4955 0.0 3.313 0.6091 0.0 7.032 0.6709 0.0 9.579 0.7122,0.0 10.598' 07269 0.0 12.925 0.7558 0.0 15.829 0.7763 -0.002 19.810 0.7738 -0.002 22.764 0.7548 -0.004 5.243 0.4918 -0.003 13.754 0.3797 -0.003 19.767 0.3256 -0.003 25.070 0.2914 -0.002 29.238 0.2697 -0.001 1.453 0.1493 -0.001 4.415 0.1476 -0.001 8.065 0.1464 -0.001 11.585 0.1448 -0,001 14.360 0.1440 0.0 2.883 0.2889 0.0 8.854 0.3025 -0.0 20.269 0.3375 -0.002 31.520 0.3879 -0.001 32.804 0.3943 -0.001 34.135 0,4009 -0.002 35.635 0.4074 -0.002 38.356 0.4178 -0.004 40.656 0.4256 -0.005 42.907 0.4303 -0.004 44.556 0.4330 -0.005 45.920 0.4359 -0.003 48.390 0,4359 -0.001 3.084 0.5607 -0.002 5.688 0.5810 -0.002 6.753 0.5883 -0.002 8.472 0.6000 -0,002 9.973 0.6081 -0.003 10.867 0.6105 -0.004 11.964 0.6138 -0.004 15.205 0,6119 -0,005 17.576 0.6034 -0.004 22.938 0.5732 -0.003 30.193 0.5059 -0.003 36.042 0.4492 -0.003 42.036 0.3962 -0.003 43.924 0.3837 0.004 2.510 0.2792 0.001 8.615 0.2918

-143 TABLE B-1 (Concluded) Inlet Inlet Run Press. Temp. No (psia) (~F) utlet ower Flow Corr. AHp (X) Temp. (Btu/nin)(lb/min) (Btu/lb) (Btu/lb)(Btu/lb-F) (~F) Bul-E 12.03 1717.1 12.04 171h6. 12.05 1716.9 34.01 1715.2 34.02 1715.0 34.03 17,14.4 34.04 1716.0 34.05 1715.8 34.06 1714,8 34.07 1715.4 34.08 1714.6 34.09 1715.2 34.10 1714.8 8.01 1999.0 8. 02 1999.5 8.03 1999.6.,04 2003.1 8.05 2002.1 8.06 2001.? 8.07 2000.3 11.01 2001.2 11.02 2001.0 11.03 2002.0 11.04 2000.8 11.07 1998.8 35,01 2001,0 35.02 2000.6 35.03 2001.2 -240. 37 -240.35 -240. 45 -1 59. 52 -159. 57 -1 59. 50 -159.50 -1 59.52 -1 59.52 -159 55 -159.49 -1 59 * 52 -159.51 -50.52 -50.49 -50.49 -50.43 -50 45 -50,42 -50.42 -240.12 -240.11 -240. 09 -240.06 -240. 04 -140.09 -140. 07 -140.09 -.79 3 -150 20 -144. 17 -1. 54 22 -148. 08 -144. 30 -139. 60 -134 77 -123.78 -109.20.-65 —.05 -5_- 42' -4n.67 -_p5 4- 5 5 29 93 72.71 99.52 109,74 120.43 -230.42 -210.19 -180, 13 -148.96 -134.52 -134.36 -129.51 -125.63 -114.75 -89. 11 -65.02 -44. 86h 80.22 100,79 126.32 150.41 171.26 3.958 0.2Q759 -0.009 19.057 0.3148 6.61.2 0.20p821 -0.055'31.700 0.3516 7. 21. 0.20793 -Q0.054 34.620 0.3596 0485 0.19930 -0.n001 2.434 0.4592 1.077 0.1991.2 -0.001 5.410 0.4708 1.448 0.19993 -0.00. 7.243 0.4765 1.907 0.20004 -0.001 9532 0,4790 2.368 0.20000 -0.001 11,839 0.4783 3.377 0, 19972 -0,001 1 6.906 0,4730 4,5 3 0.19940 -0,002 22.749 0.4518 5.832. 1996? -0.002 29.211 0.4169 7.149 0.20027 -0.002 35.693 0.3778 7.678 0.19947 -0.002 38.489 0.3628.541 0.23090 -0.0, 2.341 0.2376 2.341 0 23628 -0.0 9.908 0.2205 3.95h6 023672 -0.0 16.710 0.2078 5.791 0. 2391 -0.0 24.170 0.1963 6.835 0.23924 -0.0 28.571 0.1905 7.229 0.23917 -0.0 30.224 0.1887 7.631 0.23904 -0.0 31.925 30.1869 0.620 0.23315 0.002 2.660 0.2743 1.982 0.23289 -0.0 8.510 0.2844 4.200 0.23295 -0.007 18.024 0.3006 6.852 0.23263 -0.014 29.439 0,3231 8.247 0.23234 -0.032 35.465 0.3361 0.515 0.21347 -0.0 2.413 0.4212 0.955 0.'21372 -0.001 4.467 0.4230 1.305 0.21390 -0.001 6*101 0.4219 2.250 0.21410 -0.001 10.508 0.4150 4.209 0.21426 -0.001 19.642 0.3855 5.667 0.213h4 -0.001 26.527 0.3537 6.737 0.21340 -0.001 31.569 0.3316 0.384 0,22960 -.0O 1.670 0,1677 1.181 0.23504 -0.0 5.023 0.1648 2.166 0.23838 -0.0 9.088 0.1623 3.095 0.24184 -0.0 12798 0.1598 3.874 0.24202 -0.0 16.007 0.1585 35.04 35.05 35.06 35.07 45.01 45.02 45.03 45.04 45.05 2001,4 -140,07 2000,4 -140.06 2000.6 -140.02 2000.0 -140.07 1999.4 70,26 2001.2 70.31 1999.3 70.31 1998.3 70.31 1999.4 70.25

-144 TABLE B-2 BASIC ISOTHERMAL DATA FOR ARGON Run No. Inlet Inlet Temp. Press. (~F) (psia) Press. Power Flow Corr. AHT Drop \(Bu/min) (lb/min) (Btu/lb) (Btu/lb) (-o A~ (Btu/lb-psid) k P ~U. 49.02 -208.88 49,03 -208.92 49.04 -208.89 49.05 -208.89 49.06 -208.89 49.07 -208.89 50.01 -191.21 50.03 -191.19 50.05 -191.17 50.07 -191.20 50.09 -191. 17 50,11 -191.20 50.12 -191.17 50.13 -191.18 50.15 -191.17 50,16 -191.21 51.01 -168.24 51,03 -168,23 51,05 -168.20 51.07 -168,31 51.08 -168.25 51.09 -168.22 51.10 -168.20 51.11 -168.26 51.12 -168.25 51,13 -168.22 511.14 -168.23 51.15 -168.16 51'.16 — 168.25 /.!01 -58.02 47.02 -58.02 47.03 -57.99 47.04 -57.99 47.05 -57.98 47.06 -57.99 47,07 -58.03 47 08 -57.99 47.09 -57.99 52,01 166.95 52.02 166,92 52.03 166.94 52,04 166.88 52.05 166.47 52.06 166.65 52,.07 1.6.662 52.08 166.85 52.0'9 166.82 1801.3 1601.8 1400.4 1199.1 1003.1 798.8 1996.4 1795.7 1597.5 1397.6 1196.1 1014.2 936.1 845.1 635.4 439.9 1995.5 1796.8 1 598.4 1397.7 1298.3 1200,6 1098.0 999 5 898.2 797.1 697.0 596.9 401.2 2001.4 18'03. 7 1604.7 1404.0 1204.7 1002.8 803.3 609.6 432.0 1998.7 1801.4 1604.7, 1411.8 1207.5 1008.0 798.5 601.8 430.5 200.73 201.49 198.29 211,74 221.13 223.78 97.80 103.87 109.12 115. 50 100.50 84.79 96.19 96.40 234.24 175.36 87.98 99.46 99.68 105.37 11 3.03 114 54 122.84 128.60 128 02 126.39 139 92 241.81 232.47 254.93 229.39 208.26 231.76 227.74 223,91 265.96 195.33 242,87 209.69 192.31 201.41 213.90 233. 31 245.52 260.09 280. 38 199.34 0.008 0.16165 -0.012 0.017 0.16257 -0.014 0.031 0.16393 -0.030 0.050 O. 16760 -0.035 0.065 0.17069 P.020 0.105 0.17813 0.023 0.018 0.32183 0.006 0.037 0.32591 0.010 0.071 0.33469 -0.009 0.102 0.34174 0.015 0.127 0.31504 0.010 0.164 0.28259 0.020 0.274 0.29929 0.007 0.415 0.29431 0.033 2.542 0.22383 0.004 0.706 0,13922 0,003 0.075 0.28547 0.018 0.-129 0.30158 0.016 0.184 0.29408 0.027 0'.346 0.29411 0.063 0.622 0.29643 0.040 0.919 0.286,31 0.020 1.873 0.27176 0.021 2.025 0.24225 0.046 1.349 0.20971 0.027 0,891 0.18174 0.0 0.736 0.16791 0.005 1.120 0.18390 0.003 0.624 0.12993 -0. 010 0,285 0.11459 0.018 0.235 0.10116 0.002 0.196 0.09055 0.008 0,214 0.08681 0.002 0,194 0,07941 -0.002 0.16.7 0.07045 0.005 0,181 0.06623 0.009 0.096 0.04929 0.006 0,100 0.04215 0,008 0,147 0.21644 0.002 0,124 0,19611 0.005 0.130 0.18855 0.001 0,136 0,18090.0,004 0.147 0.17262' -0.003 0,145 0,15889 0.003 0.141 0.14105 -0.003 0,133 0.12112 0,004 0.068' 0.08566 0.007 0.036 -0.00018 0.089 -0.00044 O. 162 -0.00'82 0.263 -0.00124 0.402 -0.00182 0.615 -0.00275 0.061 -0,00062 0,124 -0.00119 6.204 -0.00187 0.312 -0'.00270 0.414 -0.00412 0.601 -0.00709 0.923 -0.00960 1.443 -0.01497 11.361 -0.04850 5.073 -0.02893 0.280 -0.00318 0.442 -0.00444 0.654 -0.00656 1.240 -0.01177 2.139 -0,01892 3.229 -0.02819 6.911 -0.05626 8.404 -0.06535 6.461 -0.05'047 4.901 -0,.03878 -4.386 -0.03135 6.096 -0.02521 4.791 -0.02061 2.509 -0.00984 2.324 -0.01013 2.170 -0,01042 2.468 -0.01065 2.439 -0,01071 2.369 -0.01058 2.747 -0.01033 1.963 -0,01005 2.392 -0.00985 0,681 -0,00325 0,638 -0,00332 0.691 -0.00343 0.755 -0.00353 0,847 -0.00363 0.916 -0,003G73 0.994 -0.0.0382 1.102'-0.00393 0.801 -0.00402

-145 TABLE B-3 BASIC ISOBARIC DATA FOR C F6 2F6 Inlet Run Press. No. ( (psia) Inlet Temp. (~F) Outlet a(a)H\ Tlpe Power Flow Corr. AH T (Fe (Btu/min) (lb/min) (Btu/lb) (Btu/b) (OF) (t/b11F 1. 01 1.0? 1 * O 3 1.03 1.04 1.05 1. 06 2.01 2.02 2.03 2.04 2.05 2,06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 13.01 13.02 14.01 14.02 14.03 23.01 23.02 23.03 28.01 4;01 4.02 4.03 4.04 16.01 16.02 16.03 27.01 27.02 27.03 27.04 27.05 27.06 27.07 27.08 29.01 29.02 29.03 12.01 12.02 248.6 248.6 248.6 248.6 248 6 248.6 248.8 248.7 248.7 248.8 248.8 248.8 248.8 248.8 248.8 248.8 248.8 248.8 248. 8 247.2 247 1 246.7 246.6 246.7 247. 2 247.2 247.3 247.0 432. 1 432.1 432. 1 432.2 431.0 431.0 430.9 431.9 432.0 432.1 432.2 432.3 432.2 432.5 432.4 431.7 431.8 431.8 489.7 489.9 0. 04 0.04 0. 04 0.04 0.04 0.04 24.98 24.98 24.98 24.98 24. 98 24.98 24. 98 24.98 24.98 24.98 24.98 24.98 24.98 67.65 67.65 122.16 122. 16 122.16 176.26 176.26 176.26 55.88 -0. 02 -0.02 -0. 02 -0.02 1222. 11 122.11 122.11 55.94 55.94 55,94 55.94 55.94 55.94 55.94 55.94 68.00 68. O0 68.00 67. 65 67.65 13.73 21.05 25.29 2<.13 26. 24 26.25 27.06 26.39 26.75 27.08 27. 09 27.09 27. 11 27.11 27. 10 27.09 33. 87 41.32 49.20 86.24 120.87 135.21 159.79 173.11 190.95 234.30 247.73 68.08 10.22 25.35 41.62 47.68 133.22 154.94 176.72 59.28 62.94 6,.51 65.87 67.23 65.85 72.16 87.11 70.11 82.48 119.88 71.33 72.84 0.017 0.00399 0.026 0.00399 0.032 0.00399 0.036 0. 040 0.047 0.003 0.002 0. 002 0.004 0. 007 0.009 0.016 0.041 0.091 0. 108 0.127 0. 13 0. 143 0.174 0.491 0.120 0. 348 0.00399. 00 399 0.00399 0. 00399 0.003.99 0.00399 0, 00399 0.00399 0.00399 0.00399 0. 00399 0.00399 0. n00399 0.00399 0.00399 0. ) ( 39 93 0.03991 0. 03991 0,.03991 O. 0399 1 -0. 00.1 -0 001. -0.001 0.002 0 010 0.014 -0.001 -0.001 -0,001 -0.001 -0.002 -0.002 -0.005 0.016 0.049 0.021 0.004 0.002 0.008 -0.018 -0.042 -0.015 -0. 042 -0.039 -0.030 -0.001 0.471 0.03991. 136 0.03991 0.534 0.03991 4.169 0 3046 6.524 0.3106 7,972 0.3157 8.982 0.3442 10.053 0.3837 11.770 0.4489 0.754 0.3618 0.482 0.34Ut 0.611 0.3461 1.086 0.5183 1.697 0.8030 2.180 1.0372 3.990 1.8752 10.326 4.8561 22,81310.7362 27. 14912,, 708 31.857 3.5845 33.844 2.0722 35.887 1.4819 4.334 0.233,12.263 0.2304 3.000 0.229' H.668 0.2303 11.752 0.2306 3.379 0.2300 13.377 0.2305 16.510 0.2310 2.928 0.2400 3.069 0.2997 7.814 0.3080 13.229 0.3177 15.498 0 3249 20929 0.2636 8.453 0.2575 13.885 0.2543 1.669 0.4996 3.934 0.5620.6.635 0.6933 11.691 1.1773 1.8.257 1.6171 9.461 0.9546 22.095 1.3622 28.065 0.9004 1.782 0.8446 7.877 0.5440 19.223 0.3705 2.4'86 0,6756 3.911 0.7535 0.658 0.03991 0.022 0.117 0.03991 -0.007 0.126 0.04095 0.001 0.320 0.04095 -0.006 0.542 0.04095 -0.001 0.635 0.04095 -0.001 0.121 0.04095 -0.021 0.347 0.04095 -0.017 0.569 0.04095 -0.017 0.067 0.04095 0.030 0.161 0.04095 0.008 0.269 0.04095 0.078 0.469 0.04095 0.246 0.739 0.04095 0.208 0.383 0.04095 0.120 0.898 0.04095 0.156 1.146 0.04095 0.086 0,070 0.04095 0.071 0.320 0 04095 0.052 0.785 0.04095 0.051 0.103 0.04121 -0.008 0.162 0.04121 -0.010

-146 TABLE B-3 (Continued) Inlet Run Press. No. (psia) 12.03 12.04 12.05 12.06 12 07 I 2 O9 12,09 12. 10 30.02 30.03 30j04 30. 05 30.06 30.07 30.08 10.01 10.02 10.03 10,04 10. 05 10,.06 10 07 10.08 10.09 10. 10 9.01 9.02 9,(04 9,05 9.07 17.01 17.02 17.n3 17.04 17.05 17.06 19. n 01 19.02 19.03 19.04 19.0q 19.06 6.0 2 489.9 490.0 489.9 489.9 4R9.9 489.9 489.9 598.2 598,2 598.4 598.4 598.5 598, 5 598.5 699.7 699.7 699.8 699.7 699.7 699.6 699.* 699.7 699.7 h99.8 839.0 839.1 839.1 2 39.1 839 1 839.1 839. 1 839.2 1048.6 n48.6 1048.6 1048.6 1048.7 1048.7 1398.4 1 398.3 ]1398.q 139a.4 1 39a. 4 1 3q8.t 1. 968F.7 1.967.7 Inlet Temp. (~F) 67.65 67.65 67.65 67.65 67.65 67.65 67.65 68. 00 68,0o 68.00 68. 00 68.00 68. 00 68,00 67,65 67.65 67, 65 67.65 67. 6 5 67.6 67. 65 67.65 67. 65 67. 5 67.57 67. 57 67.57 67,.57 67.57 67, 57 67.57 67. 57 122. 09 122.09 122.09 122.09 i22.09 ].22.11 1 22211. 122. 11 1 2 2.1 1 122. 11 16(.1 1 0.,02 74. 20 75.78 77.91 77.1? 79. 74 87.74 110,83 121.11 77.77 83.43 85. 59 88.44 91.36 96.76 106. 48 120.49 75. 30 83.97 91. 16 96. 54 101. 03 98.80 97. 69. 04. 63 111. 2 121.54 75,91 105.55 1 0O 5. 5 5 100.60 113. 06. 110.02 116. 27 1. 2 ].35 123. 94 128.04 132.67 149.91 175. 19 138.1.) 132.?2 145.00 149. 69 165.34 1 7 5.7 6 1 ]A7.76 41.. 53 0.239 0.04121 0.383 0.04121 0.529 0. 4121 0.484 0.04121 0.608 0.04121 0.814 0.04121 1.152 0.04121 1.278 0.04121 0,188 0.04163 0.325 0.04163 0.386 0.04163 0.473 (0.04163 0.573 0.04163 0.730 0.04163 0.953 0.04163 1.182 0.04163 0.122 0.04195 0.274 0.04196 0.415 0.04195 0.534 0.04195 0.639 0.04195 o'. 587 O.04195 0.560 0.04195 n.7'26 0.04195 0,876 0.04195 1.081 0.04195 0. 119 0.04195 0.364 0.04195 0.599 0.04195 0.511 0.04195 0.737 0,04195 0.681 0.04195 0.802 0.04195 0.897 0.04195 0.030 0.042,69 0.097 0.04269 0. 173 0.04269 0.455 0.04269 0.846 0.04269 0.067 0.04269 (. 145 0.04322 0.330 0.04322 0. 399 0. 4322 n.630 0.04322 0.783 0.04322 0.113 0.04322 O0 133 0.04501 0.524 0.04501 Outlet Power Flow Corr. H ^) (Temp (Btu/min) (lb/min) (ButuAb) (Btb) tF) (OF).-(t~ -F -0.012 -0,01 2 -0.006 -0.o009 -0. 007 0.004.007 0.007 0).013 0.030 0.041 0.062 0,073 0,140 0. 095 0.078 -0.002 -0.002 -0,001 -0. 002 -O. OO4 -0.001 -0.002 -0.0 -0. O01 -0.001 -0. 001 -0.002 -0.002 -0. 002 -0.001 -0. 002 0.01602 -0.002 0.0024 0.019 O.on) 0,.002 0. 002 5.790 0,.8839'9.281 1.1416 12.838 1.2512 11.736 1.2393 14.747 1.2197 19.753 0.9832 27. 966 0.6476 31.010 0.5801 4,530 0.4636 7.845 0.5084 9.315 0,5296 11.434 0,5594 13.831 0.5921 17.686 0.6149 22.984 0,5973 28.467 0.5423 2.911 0.3806 6.534 0.4003 9.884 0.4204 12.725 0.4404 15.228 0.4562 13.996 0.4493 13.341 0.4441 17.313 0.4682 20. 883 0,4786 25.773 0.4783 2.833 0,.3396 8.668 O'. 3570 14,283 0.3761 12,184 0.3689 17.578 0.3864 16.231 0.3823 19.112 0.3924 2.1.376 0.3975 0,.702 0.3792 2.265 0.3807,4.042 0.3821 10.668 0.3835 19.831 0.3735 1.581 0.3876 3,357 0.3311 7.638 0.3337 9.227 0.3346 14.583 0.3373 18.128 0.3379 2.615 0.3418 0.001 2.949 0,2785f -0.001 11.631 0.2802

-147 TABLE B-3 (Concluded) Run No. Inlet Inlet Press. Temp. (psia) (~F) Outlete /AH Olet Power Flow Corr. AHp (A~ T(em (Btu/min) (lb/min) (Btu/lb) (Bttu/b)(u F) (~F) (3tu/b-OF) 6.03 1968.8 0.02 7.01 1968.7 67.61 7.02 1969.0 67.61 7.03 1969.2 67.61?0.01 1968.9 122.93 20.02 1968.9 122.93 20.03 1968.9 122.93 21.01 1969.5 176.20 21.02 1969.5 176.20 21.'03 1969.5 176.20 21.04 1969.6 176.20 21.05 1969.5 176.20 68.95 77.30 92.20 122.01 134.74 163.61 175. 60 181.02 188.52 213.76 230. 37 248.93 0.875 0.045 1 0.126 0.04501 0.320 0.04501 0.715 0.04501 0.159 0.04501 0.552 0.04501 0.718 0.04501 0.067 0.04501 0.171 0.04501 0.524 0.04501 0.756 0.04501 1.013 0.04501 -0.002 19.445 0.2821 0.001 2.791 0.2880 0.0 7.114 0.2893 0.0 15.879 0.2919 -00 3.24 0.2984 O.0 12.265 0.3015 0.001 15.954 0.3029 0.0 1.491 0.3094 0.001 3.808 0.3091 0.004 11.647 0.3101 0.009 16.809 0.3103 0.009 22.517 0.3096

-148 TABLE B-4 BASIC ISOTHERMAL DATA FOR C2F6 2 6 Inlet Run Temp. No. (~F) 3.01 B.02 3 ()2 5.01 5.0? 5.03 5.04 11.01 11.02 11.03 11.04 11. 0'5 8.01 8.02 8.03 8.04 15.01 15.02 15.03 15.04 1 5.05 18.01 18.02 18.03 18.04 18.05 22,01 22.02 22.03 22..04 22.05 22.06 22.07 22.08 24.01 24.02 24.03 24.04 24.05 24.06 24.07 -0.07 -0. o -0.03 -0.03 -0.02 -0.02 67.60 67.62 67.60 67.60 67.58 67.56 67.57 67.57 67.54 122.05 122.06 122.06 122.06 122.06 122.06 122.07 122.05 122.06 122.06 176.15 176.16 176.16 176.16 176.17 176.17 176.16 176.14 246.78 246.77 246.65 246.66 246.71 246.65 246.73 Inlet Press. (psia) 247.3 432. 1 720.3 992. 7 1460.9 1968.7 699. 0 533. 5 404. 3 367. 5 384.5 1969.1 1496.3 990.7 839. 1 430.8 613. 1 765.8 918.4 1015.3 1213.6 139 8.? 1613. 1 1814.0 1969.0 1928.9 1613.3 1420. 5 1219.9 1013.3 813.9 516.1 364,7 473.5 713.6 913.1 1013.2 1413.2 1873.2 1721.2 Press.,\ Dro Power Flow Corr. AHT ()T (psid) (B/min)(lb/min) (Btitlb) (Btu/lb)(B tp (Bdtu/lb-Psid) 22.6,8 2?. (4 8 23.24 2. 72 24. 62 29.20 29,07 94.22 123.67 109,58 28.07 27.72 27.71 27.81. 130.52 67.48 44.29 35.99 33.76 31.66 31.11 31.07 31.04 31.01 25.15 26. 20 27.56 30. 06 35.63 46.58 80.46 150. 09 123.85 73. 13 55.44 49.64 36.48 30.96 32.05 0. 00] 0.0 0. 0. 0 0.0 0.008 0.023 0. 208 0.2 04 0.0 n. n001 0.002 0. 003 0.128 0. 107 0.071 0.032 0.019 0.009 0.005 0. 03 0.002 0.002 0.004 O. 006 0.009 0.014 0.022 0.033 0.050 0.081 0.043 0.031 0.025 0.021 0.012 0.006 0.008 0. 03990 0. () 40 5 0. 04201 0.042 9 0. 04334 0.04501 ~0.04195 (.O 1 9 5 ().04139 0.04081 0.04062 0. 0407 1 0.04S0? 0. 04341 0.042 59 0. 04230 0.04094 0.04169 0.04213 0. 04246 0.04263 0. 04293 0.04322 0. 04374 0.04438 0.04508 0.03792 0.03696 0.03661 0. 03634 0.03607 0.03575 0.03497 0.03436 0.03481 0.03553 0.03592 0. 03607 0.03660 0. 03722 0.03770 o(. 0 0).0 0.0 0.007 -0.003 0. 008 -(). 006 0.018 0.0 0.0 0.011 -0.013 -0.019 -0.033 -0.004 0.008 0.011 0,008 -0.003 0. 003 -0.007 -0.003 -0.006 -0.010 -0.003 -0.003 -0.005 0.006 -0.002 -0.002 0.001 0.002 -0,005 0.004 -0.002 0.023 -0.00100 O.0-11 -0.00049 0.003 -0.00014 -0.002 0.00009 -0.009. 00036 -0.015 ()0.00059 0.186 -0.00658 0.552 -0.01900 4.996 -0.05303 5.130 -0.04148 5.016 -0.04578 0.018 -0.00066 0.028 -0,00102 0.050 -0.00179 0.078 -0.00279 3.132 -0.02400 2.564 -0.03800 1.655 -0.03736 0.709 -0.01970 0.431 -0.01276. 0.219 -0.00692 0.131 -0.00420 0.072 -0.00232 0.053 -0.00171 0.038 -0.00123 0.094 -0.00372 0.157 -0.00599 0.233 -'0.00846 0.374 -0.01244 0.609 -0.01710 0.924 -0.01983 1.438 -0.01787 2.377 -0.01584 1.235 -0.00997 0. 874, -0.01195 0.689 -0.01243 0.596 -0.01200 0.316 -0.00867 0.164 -0.00530 0.203 -0.00633

APPENDIX C CORRECTED BASIC DATA -149

-150 TABLE C-l Cp VALUES FOR ARGON PRESSTU INLET TEMP. OUTLET T EP. (PIlA) (~F) (0r) (BTUA/B-OF) 286. -200.29 -200.30 -200.30 -200.29 -100.53 -100.48 -100.49 -100.46 -100.49 -100.55 -50. 34 -50.32 -50. 35 -50.46 -50.43 -50.51 70, 26 70.26 70.28 99.95 99 75 99.71 -223.91 -208.70 -220.10 -189 87 -189.87 -146.36 -121.14 -1 89,87 -146.36 -121. 14 -93.61 -80.23 -50.42 -20.76 9.37 33.78 50.5 -4.65 30.23 73.26 100.46 110.16 119.93 99.50 125.68 149.46 170.73 190.13 218.28 -220.71 -192.39 -208.70 -146.36 -169.48 -121.14 -93.61 0. 1853 0.1680 0. 1622 0.1579 0.1412 0. 1394 O.1380 0.1369 0.1361 0.1355 0.1355 0.1341 0.1330 0.1323 0.1323 0. 1321 0.1301 0. 1297. 1294 0.1288 0.1286 0 1285 0.2556 0. 1952 0.2278 0.1640 0 1706 0,1498 0. 1407

-151 TABLE C-1 (Continued) PRESSURE INLET TEMP. OUTlET TEMP. (op) cp (BTU/LB-~F> (PSUt) ( a) 457 -240.09 -240.08 -240. 08 -240. 09 -240.08 -149.84 -149.86 -149.89 -149 85 -149.86 -229.98 -229.98 -229.98 -215.03 -215.03 -215.03 -210.65 -210.65 -210.05 -209.52 -208.35 -206.64 -205.53 -204.25 -205.49 -201. 00 -192.47 -192.47 -174. 61 -1.74.61 -140. 31 -89.e -63.46 -229.98 -215.03 -210.65 -209 52 -208.35 -140.31 -114.05 -89 82 -63.46 -52.75 -215.03 -209. 52 -207.87 -210.65 -209.52 -208. 35 -209.52 -208.35 -207.87 -207.87 -207.87 -204.25 -201.00 -192.47 -201.00 -174.61 -174.61 -155.47 -155.47 -1 39.72 -114.05 -63.46 -52.75 0.322 8 0. 3551 0.3687 0, 3730 0.3778 0, 1804 0. 1712 0.1650 0.1605 0,1591 0.3767 0.-3976 0.4172 0,4463 0.4543 0.4627 0.4970 0. 5300 0. 5888 0. 6600 1.0438 0.4887 0.3830 0. 3052 0.3873 0.2477 0.2384 0.2213 0.2054 0.1919 0.1679 0. 1502 0.1476

-152 TABLE C-1 (Continued) PRESSURE (PSIA) INLET TEMP. (o~) OUTLET TEMP. (OF) Op (BTU/LB-OF) 571. -240, 00 -239.96 -239.93 -239. 2 -239*89 -240.01 -149.97 -149 92 -149.94 -149.89 -149.90 -229.91 -229 91 -229.91 -2 29.9 1 -209.97 -209,97 -209.97 -201.49 -201.49 -200.49 -200.19 -200. 19 -198 87 -196.56 -196.56 -196, 56 -196.56 -196. 56 -196.01 -195. 74 -195.74 -194.10 -194.410 -184. 35 -184.35 -163, 56 -112.83 -112.83 -89.92 -64. 22 -229,. 91 -209.97 -201.49 -200. 9 -19 8.87 -19.23 -140.23 -112.83 -89 92 -64.22 -53.89 -209.97 -200.19 -198.87 -198.23 -201.49 -200.19 -198.87 -200.19 -198.87 -198.23 -198.87 -198.23 -198.23 -195.74 -194.10 -184.35 -163.56 -140.22 -194.10 -194.10 -184.35 -184.35 -163.56 -163.56 -140.22 -140.22 -89.92 -64.22 -64.22 -53.89 0 3160 0 3535 0, 3&77 0.3963 0. 4068 0.4321 0.2047 0.1904 0.1824 0.1749 0,1723 0.3723 0.4249 0.4367 0 4740 0.5146 0. 5323 0.5523 0.6277 0.6744 0.9905 0.7008 1.2179 2,2844 0, 8000 0. 6638 0.4822 0. 3574 0.2978 0.6560 0,5957 0.4593 0.4364 0 3327 0.2841 0.2467 0,2134 0.1690 0O1630 0.1578 0,1506

-153 TABLE C-1 (Continued) PRESSURE (PSIA) INLET TEMP. (o0) OUTLET TEMP. (oF) Cp( (BTU/LB-OF) 706. -239.90 -239.89 -239.89 -239.90 -239.95 -149.90 -1.49.9 -149*,9 -149.89 -149.85 -194.95 -63.76 -18.83 -188.57 -1R8.96 -229.87 -207.46 -195.70 -194.95 -193.11 -190.63 -177.87 -187.86 -186.97 -185.05 -179.63 -175.15 -89.58 -229.87 -207.46 -188.83 - 88. 57 -195.70 - 139.32 -113.22 -89.58 -6 3.76 -190.63 -49.73 -1.88. 57 -185,86 -186.97 -207.46 -195. 70 -188.83 -193.11 -188.96 -1.88.96 -159.60 -186.97 -185 05 -179 63 -175.15 -164.70 -63.76 0.3129 0. 3458 0.4889 0.5177 0.3883 0.2438 0.2180 0.2055 0.1945 0 1885 0.7655 0.1608 4.6732 5. 9693 8.2814 0,3618 0.4976 1.1776 0.7364 1.2783 2.0078 0.3129 2.6573 1.4229 0.7659 0.4971 0.3778 0,1677

-154 TABLE C-1 (Continued) PRESSURE (PSIA) INLET TiEP. (oF) OUTLET TDIP. (oF) Cp (BTU/LB-oF) 800. 950. -240.52 -240.51 -240.49 -239.79 -239. 74 -239.76 -239.74 -239.74 -239.69 -239.70 -149.76 -149.78 -149.74 -149.72 -149.74 -209.97 -209.94 -209.94 -209.91 -209.91 -209.91 -209.91 -230.48 -179.91 -177.08 -17 1. 87 -17,.11 -184.95 -183.93 -182.99 -181.80 -180.91 -178.98 -90.25 -64.14 -180.61 -180.46 -180,46 -180.48 -180.45 -180.44 -180.45 -178.71 -176.48 -174.47 -172.34 -170.44 -168.32 -230.48 -210.32 -185.20 -179.91 -174.46 -177.08 -168.93 -171. 87 -156. 97 -142. 29 -138.99 -113* 83 -90.25 -64.14 -48.76 -199.91 -18 1 80 -180.91 -178.98 -174.75 -169.55 -149,e 44 -210.32 -177 08 -174.46 -156.97 -184.95 -183.93 -182.99 -181.80 -180.91 -178. 98 -174.75 -64, 14 -48.76 -178 71 -176.48 -174.47 -172.34 -170.44 -168.32 -166.33 -176.48 -174,47 -172. 34 -170.44 -168.32 -166. 33 0.3059 0. 3335 0.4604 0.6558 0.6897 0.6830 0.6840 O0 6899 0.6445 0. 5925 0.2781 0.2454 0.2267 0.2095 0.2025 0.4249 0.8796 0.9387 0.9897 0. 9906 0.9457 0 7550 0.3474 1.233.9 0.8954 0.4561 1.2477 1.9853 2.9904 3. 9319 2.9034 1.7627 1.0319 0. 1769 0.16.57 0.9865 1 -0949 1.2151 1.3108 1,.3179 1.2910 1.2452 1.1731 1.4408 1.5864 1.3584 1.1632 0,9668

-155 TABLE C-1 (Continued) PRESSURE (PSIA) 1143. INLET TEMP. -2?4..18 -?40.28 -240.25 -240.25 -240.35 -240. 35 -?4035 -240.41 -240. *35 -240. 4]. -240.37 -180.20 -1]0. 13 -180. 13 -]n8,15 -180. 17 -180. 17 -180. 16 -18n.13 -149.75 -149.74 -149.70 -149.71 -149.74 -50.49 -50.48 -50.51 -50.49 -50.46 -50.48 -50.46 70.04 70.00 70.03 70.0,3 69.77 -230.18 -209.94 -160.02 -154.83 -174.76 -169.65 -165.57 -163.07 -159.78 -139. 09 -113.52 -88.99 -63.69 -5. 25 30 14 150.04 OUTLET TVMP. -230.64 -209.79 -180.03 -1 64.55 -230 1 8 -180.12 -164.94 -160. 02 -154.83 -1.49 78 -1.40.50 -174.76 -169.65 -166.68 -165.57 -163.07 -159.78 -154.56 -149.97 -139.09 -113.52 -88.99 -63.69 -41.34 -40.79 -5.25 30.14 73.16 100.65 109.95 120.15 79.77 99.92 125.12 150.04 169.47 -209.94 -180.12 -149.78 -149.78 -169.65 -166.68 -163.07 -159.78 -149.97 -113.52 -88.99 -63.69 -41.34 30,14 73.16 169.47 Cp (BTU/LB-~F) 0.2945 0.3131 0.3677 0.4450 0.2940 0. 3666 0.4407 0.4679 0.4862 0.4961 0.4955 0. 6091 0. 6709 0.7122 0.7269 0. 7558 0.7763 0.7738 0.7548 0.4918 0.3797 0.3256 0.2914 0.2697 0.1844 0.1761 0.1692 0, 1634 0.1603 0 1 596 0, 1585 0. 1493 0.1476 0. 1464 0.1448 0.1440 0,3179 0.4242 0.7175 0, 6661 0.7348 0.8576 0.9268. 8833 0.7090 0.3332 0,2450 0. 2096 0.1861 0. 1604 0.1523 0,1409

-156 TABLE C-1 (Continued) PRESSURE(PSIl) 1371. INLET TEMP. (OF) -240.28 -240.27 -240.25 -240.23 -240.24 -240.18 -240.23 -240.31 -240.23 -240.22 -240.38 -240.22 -240.24 -170.17 -170.25 -170.21 -170.23 -170.21 -170.19 -170.21 -170.23 -170.13 -170.10 -170.14 -170.11 -170.11 -230. 30 -211.00 -180.20 -144.70 -140.50 -164.67 -160.46 -158.73 -156 11 -152,39 -150.72 -141.10 -145 33 -130.11 - 110. 42 -64.02 OUTLET TEMP. (oF) -230.30 -211.*00 -180.20 -158 98 -157.05 -155.03 -152.76 -148.51 -144.70 -140.50 -137.48 -134.87 -129.23 -164.67 -160.46 -158.73 -156.11 -153.81 -152.39 -150.72 -145.33 -141.10 -130.11 -110.42 -89.90 -64.02 -55.64 -211.00 -180.20 -158.98 -137.48 -134.87 -160.46 -156.11 -156.11 -153.81 -150.72 -141.10 -130.11 -110.42 -110.42 -89. 90 -55.64 Cp (BTU/LB-OF) 0. 2889 0. 3025 0.3375 0.3879 0..3943 0.4009 0.4074 0.4178 0. 4256 0.4303 0.4330 0.4359 0.4359 0. 5607 0.5810 0.5883 0.6000 O. 6081 O0.6105 0. 6138 0.6119 0. 6034 0. 5732 O.5059 0.4492 0 3962 0.3837 0.3096 0.3673 0. 5355 0. 5445 0.4996 0.6050 0. 6464 0.6542 0. 6580 0.6333 0.6064 0.4805 0.4277 0. 3672 0.2840 0.2233

-157 TABLE C-1 (Continued) PRESSURE INLET TEMP. OUTLET TEMP. (PSIA) 1714. (OF) -240.38 -240. 36 -240. 37 -240.35 -240.45 -159.52 -159.57 -159.50 -159.50 -159. 52 -159.52 -159 55 -159.49 -1 59 52 -159.51 -231. 39 -210.84 -179. 83 -154.22 -148.08 -144. 30 -139 60 -134.77 -123.78 -109.20 -89.42 -65*05 (OF) -231.39 -210. 84 -179.83 -150.20 -144.17 -154.22 -148.08 -144. 30 -139.60 -134.77 -123.78 -109.20 -89.42 -65.05 -53.42 -210.84 -179.83 -150.20 -148.08 -144.30 -139.60 -134.77 -109.20 -109.20 -89.42 -65.05 -53.42 CP (BTU/LB_~F) 0.2792 0.2918 0.3148 0.3516 0.3596 0.4592 0.4708 0.4765 0.4790 0.4783 0,4730 0.4518 0.4169 0.3778 0.3628 0.2973 0.3364 0.4268 0.4805 0.4926 0.4902 0.4754 0,4261 0.3998 0.3281 0.2654 0.2408

-158 TABLE C-1 (Conclulded) PRESSURE (PSIA) INLET TEMP* (OF) OUTLET TIEP. (OF) Cp (BTU/LB-OF) 2000. -240.12 -240. 11 -240.09 -240.06 -240.04 -140.09 -140.07 -140.09 -140.07 -140.06 -140.02 -140.07 -50.52 -50.49 -50.49 -50.43 -50.45 -50.42 -50.42 70.26 70.31 70.31 70.31 70.-25 -230.42 -210. 19 -180.13 -148.96 -144.71 -125.63 -114.75 -89.11 -65.02 -40.67 -5.55 150, 41 -230.42 -210.19 -180.13 -148.96 -1 4. 52 -134.36 -129.51 -125.63 -114.75 -89.11 -65.02 -44.86 -40.67 -5.55 29.93 72.71 99.52 109.74 120.43 80. 22 100.79 126.32 150.41 1.71.26 -210.19 -180.13 -148.96 -134.52 -139.33 -114.75 -65.02 -65.02 -44.86 -5 55 29.93 171.26 0.2743 O: 2844 0. 3006 0. 3231 0. 3361 0.4212 0.4230 0.4219 0.4150 0.3855 0.3537 0. 3316 0. 2376 0.2205 0.2078 0.1963 0.1905 0 1887 0.1869 0.1677 0.1648 0.1623 0.1598 0.1585 0.2884 0.3156 0. 3651 0.4143 0.4128 0.4085 0.3210 0.2877 0.2432 0.2156 0 1917 O 1533

-159 TABLE C-2 i VALUES FOR ARGON TEDPI&AT RE (0F) INILX PRESS. (PSIA) PRESS. DROP (PSID) I ( / (OaFpSID) -240. 419.7 574, 8 918.5 1095.6 1265.5 1407.0 1605.3 1803.4 2000.5 164.5 188.8 186.7 179.1 17-1.5 149.5 185.0 194. 2 174.9 0. 000'28 -0 00018 -0.00088 -0.00114 -0.00139 -0.00162 -0.00188 -0..00212 -0. 00240 TABLE C-3 ~ VALUES FOR ARGON TEMPEPATURE INLET PRESS, (oF) (PSIA) PRESS. DROP (PSID) (BTU/B-PSID) 1801.3 798.8 1003 1 1199 1 1400.4 1601.8 -191.2 439.9 635.4 845.1 936.1 1014.2 1196.1 1397.6 1597.5 1795.7 1996.4 200. 7 223.8 221.1 211.7 198.3 201.5 175. 4 234.2 96 4 96.2 84.8 100.5 115.5 109.1 103.9 97.8 -0. 00018 -0.00275 -0.00182 -0.00124 0.0 -0. 00044 -0.02893 -0.048,50 -0.01497 -0.00960 -0.00709 -0.00412 -0.00270 -0.00187 -0.00119 -0.00062

-160 TABLE C-3 (Concluded) TPERAIURE INI.sT PRoSS, (oF) (PSIA) PRESS.S DROP (PSID) (BTU/LB-PSID) -168.3 -58. 167. 401.2 596.9 697.0 797.1 898.2 999.5 1098.0 1200.6 1298.3 1397.7 1598.4 1796.8 1995.5 432.0 609. 6 803.3 1002.8 1.204.7 1404. 0 1604.7 1803.7 430.5 601.8 798.5 1008.0 1207.5 1411.8 1604.7 1801.4 1998.7 232. 5 241.8 139. 9 126.4 128.0 128.a 122. 8 114.5 113.0 105.4 99, 7 99.5 88.0 242,9 195.3 266 0 223.9 227.7 231.8 208.3 229.4 199.3 280. 4 260.1 245. 5 233.3 21.3. 9 201.4 192.3 209.7 -0O02061. -0.02521 -0.03135 -0.03878 -0.05047 -0.06535 -0.05626 -0.02819 -0.01892 -0.01177 -0.00656 -0. 00444 -0.00318 -0.0098 5 -0.01005 -0.01033 -0.01058 -0.01071 -0.01065 -0.01042 -0.01013 -0. 00402 -0. 00393 -0.00382 -0.00373 -0.00363 -0.00353 -0.00343 -0.00332 -0.00325

-161 TABLE C-4 ENTHALPY TRAVERSE DATA FOR ARGON Pressure = 286. psia Pressure = 457. psia Pressure = 571. psia Temperature A H* Temperature AH* Temperature AH* (~F) (Btu/lb) (~F) (Btu/lb) (~F) (Btu/lb) -230.06 3.353 -215.03 8.870 -201.49 14.999 -229.24 3.640 -210.65 10.825 -200.19 15.841 -227.51 4.286 -209.52 11.373 -198.87 16.766 -226.75 4.994 -208.35 11.961 -198. 0 17.450 -226.73 6.684 -207.99 13.178 -198.23 18.228 -226.75 27.994 -207.97 14.462 -198.04 21.491 -226.72 47.341 -207.97 36.659 -198.01 27.905 -226.75 49.739 -207.96 43.594 -197.97 35.362 -225.14 52.630 -207.97 47.889 -197.97 40.598 -223.91 52.498 -206.64 49.390 -197.99 44.236 -220.71 53.766 -205.53 49.910 -197.97 45.243 -205.25 50.069 -196.56 46.358 -204.25 50.558 -196.01 46.738 -201.00 51.583 -195.74 47.014 -194.10 47.991 *AH= O at -240.~F

-162 TABLE C-5 Cp VALUES FOR C2F6 26D PRESSURE INLET TEMP. (PSIA) (Op) 247. 432. 0. 04 0.04 0.04 67,65 67.65 122. 16 122.16 122.16 176.26 176.26 176.26 55.88 13.73 21.05 25.29 26.39 28.01 33.87 41.32 86.24 135.21 159.79 190.95 234 30 -0.02 -0.02 -0.02 -0.02 122 11 122.11 122 ].1 55.94 55.94 55.94 68.00 68. 00 68.00 10. 22 25. 35 41.62 55 94 59.28 62.94 67.23 72.16 70 11 82 48 133. 22 1 54-94 OUTLET TMP. 13.73 21.05 25.29 86.24 120.87 135.21 159.79 173.11, 190.95 234.30 247.73 68.08 21.05 25.29 26.39 26.75 33.87 41.32 49.20 120.87 159.79 173.11 234.30 247.73 10.22 25 35 41 62 47.68 133.22 154.94 176.72 59.28 62.94 65.51 70.11 82.48 119.88 25.35 41.62 47.68 59.28 62.94 65.51 72.16 87.11 82.48 119.88 154.94 176.72 Cp (BTU/LB-oF) 0. 3046 0.3106 0.3157 0.2331 0.2304 0.2299 0.2303'.2306 0.2300 0,2305 0.2310 0,2400 0. 3220 0, 3390 0.3499 0. 3550 0.2913 0.2697 0.2573 0.2290 0.2305 0.2300 0.2310 0.2320 0.2997 0.3080 0.3177 0,3249 0.2636 0,2575 0.2543 0.4996 0.5620 0. 6933 0.8446 0. 5440 0.3705 0.3128 0.3340 0.3708 0.4996 0,6170 1.0530 Q,7999 0.4250 0.4925 0.3021 0 2543 0.2494

-163 TABLE C-5 (Continued) PRESSURE INLET TEMP. OUTLET TEMP.Cp (PSIA) (OF) (OF) (BTU/LB-OF) 437. 55.96 61.80 O04999 55.96 65.17 0.5782 55.95 66.21 0.6404 55.96 66.83. 0.7317 55.97 67.08 0.8518 55.95 67.19 1.0400 55.96 67.27 1.1931 55.97 67.53 1.3367 56.00 68.40 1.4470 56.11 69.58 1.4099 61.80 65.17 0.7148 65.17 66.21 1.1918 66.21 66.83 2.2229 66.83 67.08 5.7079 67.08 67.19 20O4450 67.19 67.27 22.0190 67.27 67.53 7.5757 67.53 68.40 2.8704 68.40 69 58 O.8859 442. 55.95 61.85 0.4953 55.96 65.43 0* 5620 55.96 66.62 0.6163 55*96 67.46 0.6908 55.96 67o86 0.7951 55.96 68.06 0.9653 55.96 68.34 1.1418 55.96 68.76 1.2591 55.96 69.96 1.3032 55.96 71.41 1.2768 61.85 65.43 0.6719 65.43 66.62 1.0472 66.62 67.46 1.6306 67.46 67.86 3.8156 67.86 68.06 10.9965 68.06 68.34 8.8466 68.34 68.76 4.6887 68.76 69.96 1.7800 69.96 71.41 1.0226

-164 TABLE C-5 (Continued) PRESSURE (PSIA) 490. 598 INLET TEMP. (OF) 67.65 67.65 67.65 67.65 67.65 67.65 67.65 67.65 67.65 67.65 71.33 72.84 74.20 75.78 77*12 77.91 79.74 87.74 110.83 68 00 68.00 68.00 68 00 68.00 68,00 68.00 68.00 77.77 83.43 85.59 88.44 91., 36 96,76 106.48 OUTLET TEMP. (oF) 71.33 72.84 74.20 75.78 77.91 77.12 79.74 87.74 110.83 121.11 72,84 74.20 75.78 77.12 77.91 79.74 87.74 110.83 121.11 77 * 77 83.43 85. 59 88,44 91.36 96076 10'6.48 120.49 83.43 85,59 88,44 91*36 96.76 106,48 120.49 Cp (BTU/LB-oF) 0. 6756 0.7535 0. 8839 1.1416 1.2512 1.2393 1.2197 0.9832 0o,6476 0.5801 0. 9435 1.3818 2 2103 1 8345 1.3938 1 0449 0.6250 0O 3576.0 2935 0.4636 0, 5084 0.5296 0* 5594 0.592 1 0 6149 0. 5973 0* 5423 0.5860 0.6816 0 7426 0 8208 0. 7068 0* 5496 0.3883

-165 TABLE C-5 (Continued) PRESSURE (PSIA) 700. 839. INLET TEMP. (oF) 67.65 67.65 67.65 67.65 67.65 67.65 67.65 67.65 67*65 75.30 83.97 91.16 96.54 980..80 101.03 97.69 104.63 111.28 67.57 67.57 67.57 67.57 67.57 67. 57 67.57 67.57 75.91 91.85 100.60 105.55 110.02 113.06 116.27 OUTLET TEMP. (OF) 75.30 83.97 91.16 96.54 101.03 98.80 97.69 104.63 111*28 121.54 83.97 91.16 96, 54 97.69 101.03 104.63 98 80 111.28 121.54 75.91 91.85 105.55 100.60 113.06 110.02 116,27 121,35 91.85 100.60 105.55 110.02 113.06 116,27 121.35 Cp (BTU/LB-OF) 0. 3806 0.4003. 0.4204. 0.4404 0. 4562. 0.4493 0.4441 0.4682 0 4786 0.4783 0.41 6 04684 0 524t 0.5538 0. 575t1 O 5725 0. 5627 0.5314 O* 47.77 0.3396 0, 3570 003761 0.3689 0.3864 0,3823 0).3924 0,3975 0.3661 0.4011 0 4237. 0.4387 0.4505 0.4603 0.4581

-166 TABLE C-5 (Concluded) PRESSURE (PSIA) 1049. 1398. 1i969* IiZET TEMP. (OF) 122.09 122.09 1 22 0O9 122.09 122.09 134.02 123.94 128.04 132.67 149 91 122.11 122. 11 122 11 122.11 160.11 132.25 145.00 149.69 165.34 0.02 0.02 0402 67.6; 67.61 67.61 122.93 122.93 122.93 176.20 176.20 176.20 17.6.20 176.20 10.61 416 53 77.30 92.20 134.74 163.61 181. 02 188.52 213.76 230.37. OUTLET TE1P. (OF) 123.94 128.04 132.67 149.91 175.19 138.10 128.04 132.67 149 91 175.19 132.25 145.00 149.69 165.34 175.76 167.76 145.00 149.69 165.34 175.76 10 61 41.53 68.95 77.30 92.20 122.01 134 74 163.61 175.60 181.02 188.52 213,76 230.37 248.93 41.53 68.95 92.20 122.01 163.61 175.60 188.52 2'13.76 230.37 248.93 Cp (BTU/LB-OF) 0. 3792 0.3807 0.3821 0.3835 0.3735 0' 3876 0.3817 0.3836 0. 3843 0.3625 0.3311 0 3337 0 3346 0.3373 0. 3379 0.3418 0.3358 0.3394 0 3421 0.3412 -. 2785 0.2802 0 2821 0.2880 0.2893 0.2919 0.2984 0. 3015 0, 3029 0.. 3094 0, 3091 -0.3101 0 3103 0.3096 0, 2808 0.2850 0,2902 0.2941 0,3025 0.3070 06 3093:0.3107 0, 3105 0-3080

-167 TABLE C-6 VALUES FOR C 2 2 6 TEMPERATURE (oF) 0. INLET PRESS. (PSIA) 247 3 432. 1 720 3 992.7 1460,9 1968.7 PRESS. DROP (PSID) 22.7 23.2 23.7 24.3 25. 1 25.9 (BTU/LB-PSID) -0 00100 -0(. 00049 *-0.00014 0.00009 0.00036 0-00059 68. 384.5 367.5 404. 3 533.5 699.0 A39.1 990. 7 1496.3 1969.1 122. 430.8 613.1 765.8 918.4 1015.3 1213.6 1398,2 1613.1 1814.0 1 QAQ, 0 109.6 123.7 94. 2 29.1 28. 2 27. 27.7 27.7 28. 1 130.5 67. 5 44.3 36.0 33.8 31.7 31.1 31.1 31.0 31 0 150.1 80. 5 46.6 35.6 30.1 27.6 26.2 2'5. 1 123.8 73.1 55.4 49, 6 36.5 31.0 32.0 -0.04578 -0. 04148. -0.05303 -0.01900 -0.00658 -0. 00279 -0. 0179 -0.00102 -0.00066 -0.02400 -0.03800 -0.03736 -0,01970 -0.01276 -0.00692 -0.00420 -0.00232 -0.00171 -0.00123 -0.01584 -0,01787 -0.01983 -0.01710 -0.01244 -0.00846 -0.00599 -0.00372 -0.00997 -0.01195 -0.01243 -0.01200 -0 00867 -0,00530 -0.00633 176. 364.7 516. 1 813.9 1013.3 1219.9 1420, 5 1613.3 1928.9 247. 473.5 713,6 913.1 10.13,2 1413.2 1873,2 1721.2

-168 TABLE C-7 ENTHALPY TRAVERSE DATA FOR C2F6 Pressure = 247. psia Pressure = 432. psia Temperature AH* Temperature AH** (~F) (Btu/lb) (~F) (Btu/lb) 11.93 4.169 59.36 1.644 19.25 6.524 61.77 2.924 23.49 7.972 63.01 3.865 25.26 8.620 64.15 4.568 25.29 9.563 65.32 5.730 25.30 11.856 65.60 6.576 25.31 18.192 65.65 6.579 25.31 30.679 65.77 7.075 25.32 35.015 65.91 7.485 26.5o 38.202 65.96 8.450 32.07 39.723 65.96 9.473 39.52 41.710 65.97 11.688 47.40 43.753 66.oo 13.516 66.05 14.785 66.24 15.743 66.74 16.787 67.33 18.260 67.70 18.268 *AH =0. at 0.~F **AH =0. at 55.97'F

REFERENCES 1. Angus, S., Armstrong, B., "International Thermodynamic Tables of the Fluid State, Argon, 1971", Butterworths, London, 1971. 2. Bird, R. B. et al., Transport Phenomena, John Wiley & Sons, Inc., 1960. 3. Bhirud, V. L., Powers, J. E., "Thermodynamic Properties of a 5 mole Percent propane in Methane Mixture," University of Michigan, August, 1969. 4. Bird, R. B., Brock, J. R., A.I. Ch. E. J., 5, 436 (1959). 5. Carl, R. F., Pitzer, K. S., Ind. Eng. Chem., 50(2), 265 (1958). 6. Carnahan, B. et al., "Applied Numerical Methods," John Wiley & Sons, Inc., 1969. 7. Clusius, K., Z. Phys. Chem., B31, 459 (1936). 8. Clusius, K., Frank, A., Z. Phys. Chem., B42, 395 (1939). 9. Carney, R. A., et al., J. Mole. Spec., 7_, 209 (1961). 10. Din, F., "Thermodynamic Functions of Gases," 2, Butterworths Scientific Publications, London, 1956. 11. E. I. du Pont de Nemours, "Thermodynamic Properties of'Freon-116' Refrigerant," Wilmington, Dela. (1968). 12. Dymond, J. H., Smith, E. B., "A Compilation of Second and Third Virial Coefficients," Univ. Oxford (1964). 13. Douslin, D. R. et al., J. Chem. Thermodyn., 1(3), 305 (1969). 14. Edmister, W. C., Petroleum Refiner, 27, 113, 314, 609 (1948). 15. Eucken, A., Verh. Deut. Phys. Ges., 18, 4 (1916). 16. Eucken, A., Hauck, F., Z. Phys. Chem., 134, 161 (1928). 17. Eubank, P. T., Smith, J. M., A.I.Ch.E.J., 8, 117 (1962). 18. Furtado, A. W., Ph.D. Thesis, Univ. of Mich., 1973. 19. Faulkner, R. C., Ph.D. Thesis, Univ. of Mich., 1959. 20. Flynn, G. P. et al., J. Chem. Phys, 51, 3860 (1969). 21. Grigor, A. F., Steele, W. A., J. Phys. Chem. Liq., 1, 129 (1968). -169

-170 22. Gosman, A. L. et al., "Thermodynamic Properties of Argon from the Triple Point to 300K at Pressures to 1000 Atmospheres," NSRDS-NBS27, 1969. 23. Hall, L. A. et al., "A Bibliography of Thermophysical Properties of Argon from 0 to 300~K," NBS Technical Note 217, June, 1964. 24. Hilsenrath, J. et al., "Table of Thermal Properties of Gases," NBS Circ. No. 564 (1955T. 25. Jones, Jr., M. L., Ph.D. Thesis, Univ. of Mich, 1961. 26. Kaganir, M. G., J. Ph. Ch. (Russian), 32, 1958. 27. Leong, K. S., "List of Experimental Specific Heat Determinations of A.M. Sirota," Technical Report No. 19, Univ. of Glasgow, 1966. 28. Leong, K. S., "List of Experimental Determinations of the Specific Enthalpy, Specific Heat and Joule-Thomson Coefficients of Steam," Technical Report No. 20, Univ. of Glasgow, 1966. 29. Lenoir, J. M. et al., A Paper Presented at 34th Midyear Meeting of A.P.I., Chicago, Ill., 1969. 30. Leland, T. W., Chappelear, P.S., Ind. Eng. Chem., 60 (7), 85 (1968). 31. Lee, A. L. et al., A.I.Ch.E.J., 10 (5), 694 (1964). 32. Lydersen, A. L. et al., Eng. Expt. Stat. Rept., 4, The Univ. of Wiscons i n, Oct., 1955. 33. Lard, E. W., Horn, R. C., Anal. Chem., 32 (7), 878 (1960). 34. Miyazaki, T., Ph.D. Thesis, Univ. of Mich. 1973. 35. Mage, D. T., Ph.D. Thesis, Univ. of Mich. 1964. 36. Manker, E. A., Ph.D. Thesis, Univ. of Mich. 1964. 37. Mather, A. E., Ph.D. Thesis, Univ. of Mich. 1967. 38. Michels, A. et al., Physica, 24, 769 (1958). 39. Michels, A. et al., Physica, 15, 689 (1949). 40. Montgomery, J. B., Devries, T., J. Am. Chem. Soc., 64, 2372 (1942). 41. Pace, E. L., Aston, J. G., J. Am. Chem. Soc., 70, 566 (1948). 42. Powers, J. E., Proceedings Natural Gas Processors Association 48th Convention, 1969. 43. Pitzer, K. S., et al., J. Am. Chem. Soc., 77, 3433 (1955).

-171 44. Pope, G. A., Ph.D. Thesis, Rice Univ., 1971. 45. Powers, J. E., Private Communications, 1971-1973. 46. Riedel, L., Chem-Ing. Tech., 26, 83 (1954). 47. Rivikin, S. L., Gukov, V. M., Teploenergetika, 15 (10), 72 (1968). 48. Reid, R. C., Sherwood, T. K., "The Properties of Gases and Liquids," McGraw-Hill, Inc., 2nd ed., 1968. 49. Roebuck, J. R., Osterberg, H., Phys. Rev., 46 (2), 785 (1934). 50. Rossini, F. D. et al., "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," Carnegie Press, Pittsburgh, Pa., 1953. 51. Sirota, A. M. et al., Teploenergetika, 1960 (7). 52. Sirota, A. M., Shrago, Z. Kh., Teploenergetika, 15 (3), 1968. 53. Sherwood, T. K., J. Chem. Eng. Data, 7, 47 (1962). 54. "Selected Values of Properties of Chemical Compounds," Thermodynamic Research Center Data Project, Texas A & M Univ., Dec., 1967. 55. Vukalovich, M. P., Altunin, V. V., "Thermophysical Properties of Carbon Dioxide," Collets Ltd., London & Wellingborough, 1968. 56. Vasserman, A. A., Rabinovich, V. A., "Thermophysical Properties of Liquid Air and Its Components," Israel Program for Scientific Translations, Jerusalem, 1970. 57. Vasserman, A. A. et al., "Thermophysical Properties of Air Components," Israel Program for Scientific Translations, Jerusalem, 1971. 58. Underwriters Laboratories Report. 59. Weiss, A. H., Joffee, J., Ind. Eng. Chem., 49, 120 (1957). 60. Walker, P. A., Ph.D. Thesis, Univ. of London, 1956. 61. Yesavage, V. F., Ph.D. Thesis, Univ. of Mich. 1968.

UNIVERSITY OF MICHIGAN 3 9015 03023 7765