THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THERMAL CONDUCTIVITY OF POTASSIUM VAPOR Dale E. Briggs A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Chemical and Metallurgical Engineering 1968 February, 1968 IP-809

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ACKNOWLEDGEMENT The author gratefully acknowledges the assistance of members of his Doctoral Thesis Committee. Special thanks are due Professor E. E. Hucke for his special help and encouragement throughout the course of the research. This study received generous financial support from the Michigan Memorial Phoenix Project of The University of Michigan and the U.S. Atomic Energy Commission. Finally, the work of Mrs. Alvalea May in preparing the manuscript and the Industry Program of the College of Engineering for printing the manuscript is greatly appreciated. ii

ABSTRACT The purpose of this investigation was to design, construct and operate a high temperature cell for measuring the thermal conductivity of potassium vapor within the temperature range of 900-1400~F. A thorough review of all the techniques used to measure thermal conductivity of gases and vapors was made with particular attention to those methods suitable for high temperatures and corrosive vapors. A parallel plate cell with guard heated top plate was selected. Heat generated in the 2,01 inch diameter top plate by the top plate heater was transferred across a 0.0182 inch vapor space to the bottom plate. Molybdenum was selected for the cell material because of its corrosion resistance to potassium, low emissivity and high thermal conductivity. The thermal conductivity of nitrogen was measured with the cell to serve as a check on the cell and analysis procedure. The thermal conductivity of nitrogen thus measured for a temperature range of 900 to 12000F. was in excellent agreement (within 1 percent) with existing data. Thermal conductivity data for superheated potassium vapor were taken at temperatures of 1000, 1100 and 1200~F. and a range of pressures of 0.01 to 0.075 atmospheres. The pressure of the potassium vapor in the cell was kept below the saturation pressure by maintaining liquid potassium in a boiler connected to the thermal conductivity cell at`a temperature 100 to 4000F. below the cell iii

temperature. As predicted by theory the data show that pressure has a significant effect on the thermal conductivity. Combining theory with experimental results, the increase in thermal conductivity over that for an equivalent non-reacting system at 11000F. was found to be 7 and 42 percent, for pressures of 0.01 and 0.075 atmospheres, respectively. The increase is caused by the heat of reaction associated with shifts in the equilibrium composition with changes in temperature and pressure. Potassium exists in the vapor as a monomer, dimer and tetramer. The thermal conductivity of potassium for an equivalent non-reacting system at 11000F. was calculated to be 0.0074 Btu/hr.-ft.-~F. as compared to measured values of 0.0079, 0.0088, and 0.0105 Btu/hr.-ft-~F. at pressures of 0.01, 0.03, and 0.075 atmospheres, respectively. Kinetic theory was used as a basis for placing correlating curves through the data. The mean values of the thermal conductivity of potassium are estimated to be accurate to within + 10 percent. These results agree closely with a limited amount of data taken with a different type cell reported in the literature. iv

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii ABSTRACT iii LIST OF TABLES vii LIST OF FIGURES xiii NOMENCLATURE xv I. INTRODUCTION 1 II, LITERATURE REVIEW 3 A. Introduction 3 B. Theory of Thermal Conductivity 4 C, Thermal Conductivity of Gas Mixtures in Equilibrium 13 D, Experimental Methods 17 1. Steady State Methods 17 2,. Transient Methods 32' E. Experimental Cells for Alkali Metal Vapors 38 F. Physical Properties of Potassium 41 G. Theoretical Predictions of Thermal Conductivity of Potassium Vapor 45 III. DESCRIPTION OF EQUIPMENT 48 IV, EXPERIMENTAL PROCEDURES 64 V. EXPERIMENTAL DATA AND ANALYSIS 82 VI. DISCUSSION OF RESULTS 115 VII. CONCLUSIONS AND RECOMMENDATIONS 122

TABLE OF CONTENTS (continued) Page APPENDIX A ORIGINAL DATA 125 APPENDIX B PRELIMINARY PROCESSED DATA 157 APPENDIX C COMPUTER PROGRAM 189 APPENDIX D MISCELLANEOUS FIGURES 191 REFERENCES 194 vi

LIST OF TABLES Page Table I. Representative Sample of Original Data for Potassium Run 206955, Data Set 32 70 Table II. Summary of Operating Conditions for the Experimental Data - Data Sets 1-32 84 Table III. Summary of the Top Plate Heater Temperatures and Resistances - Data Sets 1-32 88 Table IV. Experimental Results for Apparent Thermal Conductivity Under Vacuum Conditions 90 Table V. Experimental Results for Thermal Conductivity of Nitrogen 91 Table VI. Experimental Results for Thermal Conductivity of Potassium Vapor at Various Saturation Temperatures 92 Table VII. Correction of Experimental Values of Thermal Conductivity of Potassium Vapor to Constant Boiler Temperature and Comparison to Correlating Curve 10l Table VIII. Equilibrium Vapor Composition of Potassium 106 Table IX. Summary of Force Constants for Lennard-Jones: 6-12 Potential Predicted from Experimental Results 108 Table X. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Determined from the Second Virial Coefficient 111 Table XI. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Determined from Saturated Vapor Viscosity Data 112 Table XII. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Determined from Normal Boiling Point Data 113 vii

P age Table XIII. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Which Give a Least Squared Deviation Fit with the Experimental Data 114 Table A.l. Original Data for Data Set 1 - Vacuum Runs at 9430F. 125 Table A.2. Original Data for Data Set 2 - Nitrogen Runs at 9250F. 126 Table A.3. Original Data for Data Set 3 - Vacuum Runs at 1032~F. 127 Table A.4. Original Data for Data Set 4 - Nitrogen Runs at 10270F. 128 Table A.5. Original Data for Data Set 5 - Vacuum Runs at 11170F. 129 Table A.6. Original Data for Data Set 6 - Nitrogen Runs at 11130F. 130 Table A.7. Original Data for Data Set 7 - Vacuum Runs at 12130F. 13l Table A.8. Original Data for Data Set 8 - Nitrogen Runs at 12130F. 132 Table A.9. Original Data for Data Set 9 - Vacuum Runs at 10080F. 133 Table A.10. Original Data for Data Set 10 - Vacuum Runs at 11130F. 134 Table A.11. Original Data for Data Set 11 - Vacuum Runs 135 at 12050F. Table A.12. Original Data for Data Set 12 - Vacuum Runs 136 at 13050F. Table A.13. Original Data for Data Set 13 - Potassium Runs at 10100F. 137 Table A. 14. Original Data for Data Set 14 - Potassium Runs at 1018~F. 138 viii

Page Table A.15. Original Data for Data Set 15 - Potassium Runs at 1106~0F. 139 Table A.16. Original Data for Data Set 16 - Potassium Runs at 11080F. 140 Table A.17. Original Data for Data Set 17 - Potassium Runs at 1113~F. 141 Table A.18. Original Data for Data Set 18 - Potassium Runs at 1190~F. 142 Table A.19. Original Data for Data Set 19 - Potassium Runs at 11920F. 143 Table A.20. Original Data for Data Set 20 - Potassium Runs at 12010F. 144 Table A.21. Original Data for Data Set 21 - Potassium Runs at 10040F. 145 Table A.22. Original Data for Data Set 22 - Vacuum Runs at 9980F. 146 Table A.23. Original Data for Data Set 23 - Vacuum Runs at 10000F, 147 Table A.24. Original Data for Data Set 24 - Vacuum Runs at 10020F. 148 Table A.25. Original Data for Data Set 25 - Vacuum Runs at 11910F. 149 Table A.26. Original Data for Data Set 26 - Potassium Runs at 1016~0F. 150 Table A.27. Original Data for Data Set 27 - Potassium Runs at 10160F. 151 Table A.28. Original Data for Data Set 28 - Potassium Runs at 10950F. 152 Table A.29. Original Data for Data Set 29 - Potassium Runs at 10970F. 153 ix

Page Table A.30. Original Data for Data Set 30 - Potassium Runs at 11910F. Table A.31. Original Data for Data Set 31 - Potassium Runs at 11910F. 155 Table A.32. Original Data for Data Set 32 - Potassium Runs at 10990F. 156 Table B,1. Preliminary Processed Data for Data Set 1 - Vacuum Runs at 9430F. 157 Table B.2. Preliminary Processed Data for Data Set 2 - Nitrogen Runs at 9250F. 158 Table B.3. Preliminary Processed Data for Data Set 3 - Vacuum Runs at 10320F. 159 Table B.4. Preliminary Processed- Data for Data Set 4 - Nitrogen Runs at 10270F. 160 Table B.5. Preliminary Processed Data for Data Set 5 - Vacuum Runs at 11170F. Table B.6. Preliminary Processed Data for Data Set 6 - Nitrogen Runs at 11130F. 162 Table B.7. Preliminary Processed Data for Data Set 7 - Vacuum Runs at 12130F. 163 Table B.8. Preliminary Processed Data for Data Set 8 - Vacuum Runs at 12130F. 164 Table B,9. Preliminary Processed Data for Data Set 9 - Vacuum Runs at 10080F. 165 Table B.10. Preliminary Processed Data for Data Set 10 - Vacuum Runs at 11130F. 166 Table Bl. Preliminary Processed Data for Data Set 11 - Vacuum Runs at 12050F. 167 Table B.12. Preliminary Processed Data for Data Set 12 - Vacuum Runs at 13050F. 168

Table B'.13. Preliminary Processed Data for Data Set 13 - Potassium Runs at 10100F. 169 Table B.14. Preliminary Processed Data for Data Set 14 - Potassium Runs at 10180F, 170 Table B,15. Preliminary Processed Data for Data Set 15 - Potassium Runs at 11060F. 171 Table B.16. Preliminary Processed Data for Data Set 16 - Potassium Runs at 11080F. 172 Table B.17. Preliminary Processed Data for Data Set 17 - Potassium Runs at 11130F. 173 Table B.18. Preliminary Processed Data for Data Set 18 - Potassium Runs at 1190~F. 174 Table B.19. Preliminary Processed Data for Data Set 19 - Potassium Runs at 11920F. 175 Table B.20. Preliminary Processed Data for Data Set 20 - Potassium Runs at 12010F. 176 Table B.21. Preliminary Processed Data for Data Set 21 - Potassium Runs at 10040F. 177 Table B.22. Preliminary Processed Data for Data Set 22 - Vacuum Runs at 9980F. 178 Table B.23. Preliminary Processed Data for Data Set 23 - Vacuum Runs at 10000F. 179 Table B.24. Preliminary Processed Data for Data Set 24 - Vacuum Runs at 10020F. 180 Table 13.25. Preliminary Processed Data for Data Set 25 - Vacuum Runs at 11910F. 181 Table B.26. Preliminary Processed Data for Data Set 26 - Potassium Runs at 10160F. 182 Table B.27. Preliminary Processed Data for Data Set 27 - Potassium Runs at 1016~0F. 183 xi

Page Table B.28. Preliminary Processed Data for Data Set 28 - Potassium Runs at 1095~F. 184 Table B.29, Preliminary Processed Data for Data Set 29 - Potassium Runs at 10970F. 185 Table B.30. Preliminary Processed Data for Data Set 30 - Potassium Runs at 1191~F. 186 Table B.31. Preliminary Processed Data for Data Set 31 - Potassium Runs at 1191~F. 187 Table B.32. Preliminary Processed Data for Data Set 32 - Potassium Runs at 10990F. 188 xii

LIST OF FIGURES Page Figure 1. Schematic Representation of the Thermal Conductivity Cell of Michels, Sengers and Van Der Guilk (75) 19 Figure 2. Schematic Representation of the Thermal Conductivity Cell of Vines (100) 23 Figure 3. Wheatstone Bridge Circuit for a Symmetrical Two Pair Hot Wire Thermal Conductivity Cell of Coffin and O'Neal (24) Figure 4. Experimental Thermal Conductivity Results for Potassium Vapor Measured with a Dilatometric Thermal Conductivity Cell (93) 42 Figure 5. Experimental Viscosity Results for Potassium Vapor Measured with a Falling Piston Apparatus (93) 46 Figure 6. Theoretical Thermal Conductivity of Saturated Potassium Vapor (102) 47 Figure 7. Disassembled View of the Thermal Conductivity Cell 49 Figure 8. Schematic Representation of the Thermal Conductivity Cell Showing Heaters and Thermocouples 50 Figure 9. Top View of the Thermal Conductivity Cell Showing Exact Placement of Heaters and Thermocouples 51 Figure 10. Schematic View of Thermal Conductivity Equipment 55 Figure 11. Thermal Conductivity Cell Heater and Guard Heater Wiring Circuit 57 Figure 12. Schematic Representation of the Furnace Temperature Control Circuit 61 Figure 13. Overall View of the Experimental Equipment 63 Figure 14. Typical Experimental Results for Potassium Vapor Thermal Conductivity - Data Set 32 72 Figure 15. The Apparent Thermal Conductivity Under Vacuum Conditions 96 xiii

Page Figure 16. Comparison of the Experimental Thermal Conductivity Results for Nitrogen with the Results of Rothman (84) 99 Figure 17. Experimental Thermal Conductivity Results for Potassium Vapor 101 Figure 18. Comparison of Thermal Conductivity Data for Potassium Monomer with Results of Stefanov (93) and Weatherford (102) 117 Figure D.1. Vapor Pressure of Potassium (33) 191 Figure D.2. Calibration for RCA 1946 Thermocouple Vacuum Gauge 192 Figure D.3. Lead Wire Resistance of Top Plate Heater 193 xiv

NOMENCLATURE A Heat — transfer area, sq. ft. a Cell constant in Eq. 44. a Distance from center of hot wire cell in Eq. 42, ft. B. Correction for Wheatstone bridge unbalance in Eq. 44, millivolts. c Heat capacity at constant pressure, Btu/lb.-~F. p C Heat capacity for rotation, Btu/lb. r Ct Heat capacity for translation, Btu/lb. c Heat capacity at constant volume, Btu/lb.-~F. C Heat capacity at constant volume, Btu/lb.mole-~F. d Distance between top and bottom plates in Eq. 76, ft. D Diameter, ft. D Diffusion coefficient, sq. cm./sec. or sq.ft./hr. D Thickness of top plate in Eq. 76, ft. f Eucken factor. F Radiation configuration factor. a F Factor to account for the departure of the two surfaces from complete blackness. g Temperature jump distance, ft. h Convective heat transfer coefficient, Btu/hr.-sq.ft.-~F. i Current, amperes. k Boltzman's constant. xv

-1 -3 k Equilibrium- constant, atm. or atm.. k Thermal conductivity, Btu/hr.-ft.-~F. K1 Potassium monomer K2 Potassium dimer K4 Potassium tetramer kc Actual thermal conductivity, Btu/hr.-ft.-~F. corr Thermal conductivity corrected to constant boiler temperature, Btu/hr.-ft.-~F. kf Frozen thermal conductivity, Btu/hr.-ft.-~F. k Contribution to thermal conductivity due to chemical reaction, Btu/hr.-ft.-~F. k Contribution of radiation to total thermal conductivity, kt, Btu/hr.-ft.-~F. k Thermal conductivity of reference gas, Btu/hr.-ft.-~F. ref k Total thermal conductivity including radiation, Btu/hr.ft.-OF. Length, ft. k Mean free path of molecules, cm. M Molecular weight. n Number of molecules in chemical balance. Nu Nusselt number. P Pressure, atmospheres, Pr Prandtl number. Q Heat duty, Btu/hr. xvi

QC Heat duty for conduction, Btu/hr. Qrad Heat duty for radiation, Btu/hr. rad Qt Total heat duty, Btu/hr. r Molecular separation distance in Eq. 12, A~. r1 Radius of hot wire, ft. r2 Radius of cell container, ft. rg Inside radius of guard plate cover in Eq. 76, ft. ru Radius of top plate in Eq. 76, ft. R Gas constant, appropriate units. T Absolute temperature, ~R. tl Inlet temperature of vapor to heat exchanger,'F. t2 Outlet temperature of vapor from heat exchanger, OF. T1 Absolute temperature of the hotter surface, ~R. T2 Absolute temperature at the colder surface, ~R. Tb Absolute temperature at normal boiling point,'K. T Absolute temperature of the molecules after collision m T Absolute temperature of the molecules before collision in Eq. 21, ~R. t Recovery temperature which flat plate assumes in high velocity flow when it exchanges heat with fluid, ~F. Ts Absolute temperature of the surface in Eq. 21, oR. xvii

t Static temperature of vapor in Eq. 48, ~F. t t Total temperature in the vapor at a sufficient distance from plate in Eq. 48,'F. t Tube wall temperature of heat exchanger, OF. w v Mean molecular speed, cm./sec. or ft./sec. Vb Molecular volume of liquid at normal boiling point, cu.cm./ g. mole W Flow: rate, lbs./hr. x Mole fraction. X Plate spacing, ft. Xt Output from Wheatstone bridge, millivolts. a Accomodation coefficient in Eq. 22. a Thermal diffusivity, k/Pcp. Y Ratio of heat capacity at constant pressure to heat capacity at constant volume. Y Ratio of heat capacity at constant pressure to heat capacity at constant volume for ideal gas. AH Heat of reaction, Btu/lb. mole. AHI Standard heat of reaction for monomer to dimer, Btu/lb. mole dimer. AH0 Standard heat of reaction for monomer to tetramer, Btu/lb. mole tetramer. At Temperature difference, 0F. xviii

Atref Temperature difference for reference gas, OF. C Lennard-Jones force constant. Radiation emissivity. G Temperature rise of vapor from initial condition in Eq. 50, ~F. Viscosity, poises or lb./ft.hr. p Density g./cu.cm. or lb./cu.ft. ra Lennard-Jones force constant, A~. Time from initial condition, hr. Potential energy of interaction between two molecules. Lennard-Jones collision integral for diffusion. Lennard-Jones- collision integral for viscosity. v W Frequency for a periodic temperature variation in Eq. 58. xix

CHAPTER I INTRODUCTION The use of alkali metals in nuclear power generation systems has been of considerable interest in recent years both in conventional nuclear power plants and in magnetohydrodynamics (MHD) power generation (86) for space craft. During this time, several experimental and design studies of Rankine cycle space power generation systems have been initiated with potassium as the working fluid. These studies include the SPUR-SNAP (79) program and the General Electric (12,36) boiling and condensing investigations. In all such investigations accurate transport property data are necessary for complete experimental and theoretical analysis. The thermal conductivity of the vapor is such a property. Heat transfer data for boiling, condensation and forced convection' of alkali metals have been taken by an increasing number of investigators since 1955 when Lyon (71) completed an extensive study of boiling of liquid metals which included sodium and a mixture of sodium and potassium. The General Electric Company (36) measured boiling heat transfer coefficients for potassium in forced convection in 1964 and Padilla (78) measured film boiling heat transfer coefficients for potassium in 1966. Theoretical film boiling heat transfer correlations have been formulated by Bromley (11), Chang (20), and Berenson (6). In order to evaluate the validity and soundness of these theoretical models in

comparison with experimental data, it is necessary to know the physical properties of the vapor and liquid. In each correlation, the thermal conductivity of the vapor is an important variable. The thermal conductivity of the vapor is important also in forced convection heat transfer and in two phase forced convection heat transfer where an alkali metal vapor is the working fluid. Experimental measurements of thermal conductivity, viscosity and heat capacity are important thermodynamic properties because of the important relationships between the three variables. An independent evaluation of the experimental data would be possible based on thermodynamic considerations. The objective of this work was to measure the thermal conductivity of potassium vapor in the range of 900 to 14000F. at pressures below the saturation pressure using a parallel plate thermal conductivity cell.

CHAPTER II LITERATURE REVIEW A. Introduction Heat conduction in gases is a diffusion process in which gases moving from a warmer position to a colder position and vice-versa exchange kinetic energy as a result of molecular collisions. Although the gas molecules may be identical, they will have different average velocities because of temperature differences. The basic law of heat conduction is Q = k At (1) s The law originated with Biot (7) but is generally called Fourier's equation and it was used as a fundamental equation in Fourier's analytic theory of heat (35). In differential form, for one dimension heat conduction, Fourier's equation is dt Q ==k A dx dx dr ~~~~~~~~~~~(2) The thermal conductivity of gases can be determined experimentally from Equation 1 by measuring the heat flux and the temperature gradient. It can be determined also from simple kinetic theory in which thermal conductivity is related to the viscosity and to the constant volume heat capacity of the vapor. Modern kinetic theory has been used to extend the theoretical efforts to include the

calculation of thermal conductivity (or viscosity) based on a mathematical model' for the intermolecular forces. Experimental measurements of the thermal conductivity of gases and vapors which associate or dissociate with changes in temperature are often considerably higher than the values of an equivalent nonreacting mixture of the species. This apparent increase in thermal conductivity is due to the heat of reaction associated with changes in the equilibrium composition with temperature as the molecules move through the temperature gradient. Potassium in its vapor state exists as a monomer, dimer and tetramer in equilibrium and would be expected to have a higher effective thermal conductivity than for a non-reacting condition. B. Theory of Thermal Conductivity Simple Kinetic Theory The theory of conduction of heat by molecular self diffusion was developed by Maxwell (73) and Boltzman (9). For monatomic molecules which possess only the kinetic (translation) energy corresponding to their velocity, the thermal conductivity was estimated to be k = 1/3 pvkcv (3) Since the simple kinetic theory of gases predicts that the viscosity of the gas for a constant velocity is 1 = 1/3 pvQ (4)

The predicted thermal conductivity of a gas from simple kinetic theory is k= V c (5) Equation 5 predicts values of thermal conductivity which are generally low. Chapman (21) made calculations in 1912 which showed that for monatomic, spherical molecules with any central forces between them, Equation 5 was low by a factor of 2.5. This value was predicted independently by Enskog (30) in 1917 for a repulsive potential energy between molecules of the form E (r) = a (a/rn (6) where a and n are constants, n being the steepness of the repuls~ive wall. Variations in n from five to infinity change the factor by less than 1 percent. Therefore, if the kinetic theory is correct, thermal conductivities for monatomic gases should be closely related by k= 2.5 p C (7) Equation 7 is most often written as k = f P cv (8) and the numerical factor f called the Eucken factor. A review of thermal conductivity data by Liley (69) showed that k varies from

2.40 to 2.60 for monatomic gases over a range of temperatures from 200-to 27000R. Eucken Factor Eucken (31) originally proposed a magnifying factor for Equation 5 to account for the fact that an average molecular velocity as used in simple kinetic theory will predict low values of thermal conductivity. Molecules with greater energy transport their energy faster than molecules with less energy because the energy level is proportional to cvT and T is proportional to the velocity squared (61). Eucken (31) further proposed that the thermal conductivity of diatomic gases could be estimated by accounting for rotation as well as translation. He split the specific heat into two components, cr and ct for translation which led to 2.5 c c k =(c + cv (9) v v for diatomic molecules with negligible energy of oscillation. Since there is no correlation between the velocity of the molecule and internal rotation, the contribution of rotation can be expressed in the form of Equation 9 rather than Equation 7 which is appropriate for the translational contribution. Equation 9 has been simplified to (see Reference 82) k = 9y-5 c 4 v (10) or

k 9-5/ c (11) 4 p The value of the Eucken factor for diatomic gases is less than 2.5. Liley (69) reported values of 1.8 to 2.3 for temperatures from 1300R to' 2100~R Several authors (40,48,54) have presented variations of the Eucken factor given in Equation 9 for polyatomic gases and vapors. The values of the thermal conductivity of diatomic molecules predicted by their equations are generally more accurate at temperatures above 1000F. For linear non-polar molecules such as nitrogen and oxygen the predicted values are within 6 percent of experimental results. This presupposes that accurate values of the viscosity and heat capacity are available. If both viscosity and heat capacity values are predicted from theory, the thermal conductivity estimates could be in error by amounts greater than 6 percent. Modern Kinetic Theory Modern kinetic theory, or as often called, the Chapman-Enskog theory, is based upon the number, time, velocity distribution of molecules in space and their interaction with each other. It is rigorous only for dilute monatomic gases. The theory does provide however tremendous insight in predicting transport properties of gases that can be considered dense. In the theory one of the more common models for describing the intermolecular interaction of non-polar molecules is the LennardJones (6-12) potential. In this model the intermolecular potential energy function is given by

+(r) = 4E [(r (/r)12) where the parameters a and E have dimensions of length and energy respectively, ~ being the depth of the potential well and a being the collision diameter for low energy collisions. The parameters a and e are constants characteristic of the chemical species of the colliding molecules. From modern kinetic theory the thermal conductivity of a pure monatomic gas is given in first approximation by (56) -4 (T/M)12 k = 1.9891 x 10 (13) v where in Equation 13 k = thermal conductivity in cal/cm sec~k M-=- molecular weight T = temperature in ~K a -= collision diameter in A~ Qv = collision integral when compared to the modern kinetic theory of viscosity of pure monatomic gases. Equation 13 leads to k 15 R (14) where p - viscosity in poises.

Since Cv is 3/2Rfor monatomic gases, Equation 14 simplifies to k 2.50 Pcv (7) which —was developed in the simple kinetic theory. Although the Chapman-Easkog kinetic theory strickly speaking, does not apply to polyatomic gas molecules because of the internal degrees of freedom, it may be applied quite successfully to such molecules when they are reasonably spherical. This is true because the viscosity and the diffusion of simple polyatomic molecules are not appreciably affected by the presence of internal degrees of freedom. Therefore, the thermal conductivity of diatomic gas molecules can be approximately from Equation 13 if multiplied by the Eucken factor. Thus for diatomic gas molecules k = 1.9891 x 10 (15) [15 +52 (15) v The Eucken factor in Equation 15 varies between 1.2 and 1.5 for a considerable range of gases (56). Estimation of the thermal conductivity of monatomic and diatomic gases from Equations 13 and 15, respectively require values for the collision diameter a and the molecular collision integral v. Values of Qv depend upon the intermolecular potential energy function. Values of Q are tabulated as a function of kT/E for the Lennard-Jones potential function where k in this instance

10 is Boltzman's constant. Therefore, the fundamental parameters necessary to estimate thermal conductivity are the collision diameter a and the depth of the potential well E. Hirschfelder, Curtiss, and Bird (56) give methods of determining the Lennard-Jones parameters from experimental viscosity data or experimental vapor pressure data. They recommend that the parameters obtained from viscosity data should be used for making transport property calculations and that parameters obtained from experimental second virial coefficients be used for calculation of thermodynamic properties. A third method for estimating the parameters was developed empirically by Wilke and Lee (104) in which the force constants are estimated by the expressions a = 1.18 Vbl /3 b (16) and = 1.21 (17) where Tb and Vb are the normal boiling point and the molecular volume at the normal boiling point, respectively. Modern kinetic theory also permits the estimation of the diffusion coefficient of a binary mixture using the constants a and e for the Lennard-Jones potential. Hirschfelder, Curtiss and Bird (56) give for the diffusion coefficient of a binary mixture in first approximation

11 0. 001858 T3/2 [(M1+M2)/MM 1/2 D12 2 P P12 SD 12 D (18) where, D = binary diffusion coefficient cm2/sec 12 a12=- arithmetic mean of o1 and a2 D = collision integral comparable to Q The procedure requires a knowledge of the force constants for both components. The collision integral QD is tabulated for the LennardJones potential as a function of kT/c12. In the case of diffusion a12 = 1/2 (a1 +a2) (19) and 12 = 61 E2 (20) Accomodation Coefficient When gas or vapor molecules collide with a solid surface they do not always come to the surface temperature before they rebound. The degree to which molecules approach the surface temperature upon collision is given by the thermal accomodation coefficient defined as T -T m o a = T -T (21) s o Where T and T are the temperatures of the molecules before and after o m collision, respectively and T is the surface temperature. The magnitude of the accomodation coefficient is a function of the molecule,

12 surface material, and temperature. A complete review of the subject is given by Vines (99). Although kinetic theory asserts that the thermal conductivity of-a perfect gas is independent of pressure, all conventional thermal conductivity cells exhibit a decrease in thermal conductivity with decreases in pressure at very low pressures. This phenomenia results from the temperature discontinuity which exists at the surface of the cell. When the pressure is such that the mean free path of the molecules is of the same order of magnitude as the distance between which temperatures are being measured, the effect becomes very pronounced. The effect of thermal accomodation upon thermal conductivity is most noticeable at pressures below 0.01 atmospheres. At pressures above 0.01 atmospheres the effect is rather small and becomes-even more so as the pressure is increased. Accomodation coefficients are generally obtained from the slope of a plot of the reciprocal of the thermal conductivity versus the reciprocal of the pressure for low pressure thermal conductivity data. Kennard (63) gives the following expression for the temperature jump distance: 2-a (2 MRT) k 2k a (yO +l)C P (22)

13 C. Thermal Conductivity of Gas Mixtures in Chemical Equilibrium Many gases such as nitrogen dioxide and hydrogen fluoride undergo association-dissociation reactions over a range of temperatures. Alkali metal vapor also exhibit this phenomenia. Such reactions are 2N02 * N204 (23) 2K + K2 + 2 (24) 4K + K 4 (25) Since the equilibrium gas compositions for Equations 23 to 25 vary with temperature, concentration gradients will always exist whenever a temperature gradient is imposed between two surfaces. Diffusion of the molecules from an equilibrium condition to a different temperature region results in a further shift in the concentration to satisfy the equilibrium conditions at the new temperature. Changes in composition will result in a release or absorption of energy. In a gas such as potassium vapor which absorbs heat by dissociating as the gas temperature is increased, heat is transferred to the reacting molecules as the molecules dissociate in the high temperature region. The molecules then diffuse toward the low temperature region since there is a lower concentration of dissociated molecules at the lower temperature. In the low temperature region the gas molecules reassociate releasing the heat absorbed

14 from the high temperature dissociation. This phenomenon was first recognized by Nernst (77) who attributed the exceptionally high thermal conductivity of nitrogen dioxide to this effect, In mixtures of gases in chemical equilibrium the effective thermal conductivity (conductivity determined by physical measurement) may be considerably higher than for the "frozen" thermal conductivity of non-reacting mixtures. The "frozen" thermal conductivity is the conductivity one would expect to exist if no chemical reactions took place. The "frozen" thermal conductivity may be predicted from theory to the extent that theory applies to each specie and to the mixture. The effective thermal conductivity is given by kc kf + kr (26) For the N - N204 equilibrium at 1250F., the effective thermal conductivity (24) has been found to be 10 times greater than the "frozen" thermal conductivity, that is, k -c= 10 kf (27) Several investigators have considered the effective thermal conductivity of gases undergoing simple dissociations. Dirac (28) and Hirschfelder (56) both developed the theory for systems of

15 reacting gases with finite chemical reaction rates. Hirschfelder concluded that the assumption of local chemical equilibrium is good when the activation-energy for reaction in one direction is small. In a later work, Hirschfelder (57) developed also the theory for heat transfer in chemically reacting gases in which local equilibrium is assumed, i.e., very high chemical reaction rates. For such conditions the theory is based upon the total heat flux vector which includes the effect of the bulk transport of energy due to the diffusion of molecules. Meixner (74), Hasse (52), and Prigogine (101) and his associates considered problems of heat transfer in a chemically reacting mixture from the standpoint of thermodynamics of irreversible processes. Their method leads to the same relationship as is obtained from assuming the local composition is in equilibrium with the local temperature. For single reactions of the dissociation type A + nB, all the methods result in expressions which are equivalent to p AH2 XA xB k =D 2 r AB RTT T xB) (28) RT D P SH A XB 2 (28) Butler and Brokaw (14) extended the work of Hirschfelder to include gas mixtures involving any number of reactants, inert diluents and chemical equilibria. For three reacting components such as exist in the potassium vapor, the results of Butler and Brokaw reduce to

16 0 AH2 AH4 AH2 A11 A12 1 AH4 A21 A22 k =. r RT2 A11 A12 A21 A22 (29) where for the reactions K2 1 (30) and K4* K1 (31) A RT 4 RT 4 RT ( Xl+2x21 A 16 -..+ —--- --— + —---- D14P Xl D24P x2 D12P Xl x2 (32),2 RT X2 RT X2 RT (Xl+4X4) A = 2 --— + —-- + 22 D12P x4 D24P X4 D14 x 4 (33) and RT X2 8RT X4 RT RT RT A A 8 + -- + —- -(+4 + 2 12 =21= D12P Xl D14P X1 D12P D14P D24 (34)

17 D. Experimental Methods Experimental techniques for the measurement of the thermal conductivity of gases can be divided into two general categories: steady state and transient methods. Steady state thermal conductivity apparatus include such devices as parallel plates, (75) concentric cylinders (84), concentric spheres (66), hot wires (17), hot ribbon filaments (62), and porous beds (58). Thermal diffusivity (98) and Prandtl number methods (29) are used also. Dynamic probe (2) and shock wave (25) methods are common transient techniques. All the devices have certain advantages and disadvantages with regard to the measurement of the thermal conductivity of alkali metal vapors. 1. Steady State Methods Steady state methods were used first in 1840 when Andrews (4) developed a simple hot wire cell. Through'the years steady state methods have developed extensively and are preferred for reliability. Data from steady state methods are used generally as standards and transient methods evaluated by comparison. Parallel Plates The parallel plate method is the simplest method conceptually. It was first used by Christiansen (22) in 1881. The rate of heat transfer and the temperature difference between a heated plate and a parallel plate spaced at a small distance away is measured. Hercus and Laby (54) improved the technique somewhat by the use of guard rings and Michels, Sengers and Van Der Guilk (75) improved the procedure significantly by the use of an insulated

18 guard heater. The thermal conductivity cell of Michels, Sengers and Van Der Guilk was designed to minimize convection heat transfer between the two horizontal parallel plates. A schematic representation of their cell is given in Figure 1. By placing thermocouples at several points in the guard plate and top plate and by connecting the thermocouples together to detect very small differences in the average guard and top plate temperatures, they were able to balance the heat inputs to the guard and top plate heaters to prevent heat loss from the top plate except in the direction desired. They were able to obtain extremely accurate results for very small heat fluxes and temperature differences between the cell plates. Such conditions are necessary when convective heat transfer is significant, i.e., near the critical. The thermal conductivity is found from Q X k C s A At (35) At elevated temperatures the contribution of radiation to the overall heat transfer process can become significant even for small plate spacings. For such conditions the heat transferred by conduction Qc is obtained by subtracting the radiant transfer Qrad. from the total heat transferred Qt. Qc = Qt - Qrad. (36)

19 where Qrad A F F (T14-T24) (37) rad e a 1 2 Radiation effects can be measured at elevated temperatures in the absence of conduction by operating at low pressures, i.e., 1 micron of mercury absolute. At such pressures the contribution of conduction is negligible. GUARD HEATER TOP PLATE INSULATION CAP GUARD RING \ i _ LOWER PLATE TOP PLATE HEATER VAPOR GAP GLASS SPACER NOTE:. NUMBERS DENOTE LOCATION OF THERMOCOUPLES Figure 1. Schematic Representation of the Thermal Conductivity Cell of Michels, Sengers and Van Der Guilk (75)

20 The contribution of convective heat transfer can be made insignificant by the proper design and operation of a thermal conductivity cell. If the Grashof number is below 10, (60) convection within the cell becomes very small with respect to conduction and radiation. In a parallel plate apparatus, the small vertical distance between horizontal parallel plates presents the most favorable orientation for minimizing convection. Grashof numbers of 10 4 are not uncommon in such cells. The parallel plate method includes also the variable gap method (70). As the name implies, the space between plates is variable. This can be done easily with a parallel plate cell and is a definite advantage when the effect of radiation on the total heat transfer is being sought independently of very low pressure runs. By measuring the combined effects of radiation and conduction for a series of plate spacings the actual thermal conductivity of the gas is determined from the changes in the overall heat transfer coefficient with plate spacings. For constant T and At the thermal conductivity can be computed from such runs using Equation 38. At X k A Qt Qrad. (38) Measurements of the contribution of radiation for other steady state and transient devices are not as simple.

21 Concentric cylinders To obviate the difficulty of undesired and undetermined heat losses in a parallel plate apparatus, early investigators, notably Stefan (92), devised and experimented with concentric cylinder thermal conductivity cells. The concept is similar in nature to the parallel plate method in that a cylinder is placed inside a hollow cylinder forming a small uniform gap between the two cylinders across which heat is transferred by conduction. Heat input to the center cylinder is transmitted radially to the outer cylinder except for heat losses at the ends. The end area is usually a small fraction of the total surface area of the inner cylinder and thus the heat losses are minimized by the geometry of the cell. Keyes and Sandell (64) made significant improvements in the concentric cylinder method by placing a bottom on the outer or receiver cylinder at a distance from the inner or emitter cylinder equal to the radial spacing between cylinders. They placed a guard heater above the cell to prevent heat loss from the emitter by conduction at the top surface and by transfer along the electrical leads. The cell was constructed of silver with an axial heater throughout the length of the inner cylinder. Thermocouples were placed in the cylinder walls of both the inner and outer cylinders. The inner cylinder was approximately 7/8 inches in diameter with a length of 4 1/2 inches. The radial gap was 0.025 inches. Radiation effects were minimized because

22 the low emissivity of silver and convection was minimized by maintaining small temperature differences. Rothman (84) made measurements on several gases up to temperatures of 1400~F. using a cell similar in design to the cell of Keyes and Sandell (64). Vines (100) also made high temperature thermal conductive measurements of gases going to temperatures of 1650~F. The inner cylinder of his vertical concentric cylinder cell, shown in Figure 2, consisted of three sections placed on a hollow rod containing the thermocouple and heater wires. The two shorter sections on each end of the middle emitter cylinder were separated from the middle section by a 0.039 inch gap. Guard heaters located in the end sections were used to reduce heat loss from the ends. Nearly all the heat transferred from the emitter was in the radial direction across a 0.0786 inch gap to the outer cylinder. Conductivities were found from the total heat transferred from the emitter at steady state. The heat transferred by radiation and end conduction was determined from data taken with the apparatus highly evacuated and at the same temperature levels as the normal runs. Applying such corrections, the heat transferred by conduction becomes Qc =t - Qrad. (36)

LAVA SPACING PIECE GUARD HEAT STATION WITH GUARD HEATERS EMITTER EMITTER HEATER THERMOCOUPLES RECEIVER GUARD HEAT STATION WITH GUARD HEATERS HEATER LEADS Figure 2, Schematic Representation of Thermal Conductivity Cell of Vines (100)

24 where Qrad f (T, At) (393 The thermal conductivity is found then from r2 Q in r2 k = 27r9,At (40) Although most concentric cylinders cells are vertical, Lee (67) built a horizontal cell with a very small radial gap to minimize convection and radiation effects. Gilmore (38), Kramer and Comings (65) and Gilmore and Comings (39) built similar cells. Gilmore and Comings (39) made measurements on gas mixtures using a cell consisting of three horizontal concentric cylinders - the outer two were of copper with a 0.006 inch clearance between them and the inner cylinder was of a synthetic glass bonded mica. A fine platinum wire wound around the mica cylinder became the emitter heater and resistance thermometer. Guard heaters were not used in the ends but the ends were insulated. To account for end losses Gilmore and Comings obtained the necessary cell constants (bias corrections) by measuring the quantity At/Qt for gases of known thermal conductivity over the temperature range of interest. Concentric Spheres Concentric sphere thermal conductivity cells were first introduced in 1875 by Kundt and Warburg (66). Other investigators employed the technique over the next 35 years but with limited success~ Although the concept is excellent with

25 regards to heat loss from the emitter, severe difficulties are encountered in obtaining good boundary conditions of spherical symmetry. Hot Wire Hot wire thermal conductivity cells consist basically of an electrically heated fine wire, usually platinum, stretched axially within a cylindrical container containing the gas or vapor of interest. The wire serves both as an electrical heater and a resistance thermometer. Andrews (4) in 1840 made the first measurements on such cells. Kundt and Warburg (66) predicted the existance of a temperature discontinuity in such cells at low pressure in 1879. Significant improvements in hot wire cells were made by Schleirmacher (85) by using a pair of potential lead wires across the center portion of the hot wire. This reduced the error caused by axial conduction along the wire. Subsequent investigators (17, 41, 83), eliminated the end effects by using two cells identical except for the wire length. Such apparatus are termed compensated hot wire systems. By subtracting the two results for the same temperature conditions the end- effects were presumably eliminated and the heat transferred for the effective wire length determined. Gregory and Archer (44,45,46) conducted a series of experiments to determine the effects of convection in horizontal and vertical hot wire cells. Experimenting with two compensated hot wire systems in which the receiver cylinders were of different radii, they found it was possible to eliminate the effects of convection by observing the pressures in both systems at which such losses vanished, the

26 temperature conditions in the two systems being identical. Later Gregory- (47) modified the hot wire procedure to permit better analysis of the data. He maintained the electrically heated emitter wire at a constant temperature while the pressure of the gas was lowered for successive runs. By plotting 27rrAt in (r2/rl) versus 1/P a straight line was observed. The intercept is the thermal conductivity at high pressures as can be seen from Equation 40 and the slope of the line A is a measure of a quantity which is related to the temperature jump at the wire. The slope A is given by (99) A = k rlln r2) (41) The accomodation coefficient can be found from Equations 22 and 41. Much of the earliest experimental work on accomodation coefficients and temperature jumps was performed by Gregory (47) and Archer (5). Although few high temperature conductivity data have been taken with hot wire cells, Stops (94) obtained data up to 19000F. for air and carbon dioxide using a simple platinum hot wire in a fused quartz cell. Radiation effects amounted to 21 percent and end losses amounted to 8 percent at 19000F. Callear and Robb (15,16) developed a new approach in hot wire techniques to obviate the difficulty of separating the effects of the temperature jump and the reduction of thermal conductivity with

27 pressure at low pressures. They built a cell containing two identical wires. One wire was used to supply heat to the gas and the other wire, situated some distance from the first wire, was used to measure the temperature produced by the heated wire. In this way they were able to eliminate the interference from the temperature discontinuity arising at the solid gas interface of the heated wire. For a heated wire located coaxially in a hollow cylinder of radius a and a second wire located at a distance r from the heated wire k _2At (42) 27TkRt (42) Coffin and O'Neal (24) developed a new approach to hot wire thermal conductivity methods using four simple 0.005 inch diameter platinum filaments each with a pair of potential lead wires. The filaments were incorporated into two stainless-steel block containers which possessed a high degree of symmetry in the construction. Each container held a pair of filaments. The two pairs of cells (one reference pair; one test pair) were connected in a WXheatstone bridge circuit as shown in Figure 3. In the bridge circuit the potential difference indicated is proportional to the temperature difference between the reference and test filament wires. Since the temperature difference between the filament and block can be given as At a ref ref (43)

I REFERENCE TEST CELL CELL POWER SUPPLY REFERENCE CELL CELL RECORDER Figure 3. Wheatstone Bridge Circuit for a Symmetrical Two Pair Hot Wire Thermal Conductivity Cell of Coffin and O'Neal (24)

29 where a is a constant involving the geometry of-the-cells and the power dissipated by a wire, the potential output of the bridge circuit is =a ( Tref c)+ B (44) where B is a correction for any inherent unbalance of the bridge. By operating with gases of known thermal conductivity, Coffin and O'Neal found the values of the two constants. Then operating with nitrogen as a standard reference gas they were able to evaluate the thermal conductivity of other gases from Equation 44. Hot Ribbon Filaments The hot ribbon filaments method is a variation of the hot wire in which a thick wire or ribbon is used in lieu of a fine wire. Kannuluik and Martin (62) used a 0.0587 inch diameter platinum wire and solved the heat conduction equation for their case to yield the thermal conductivity. More recently Gottlieb and Zollweg (43) experimented with a hot ribbon filament at filament temperatures up to 2400~F. The filament was a 0.079 inch wide tungsten strip and the collector was a pair of nickel plates located 0.005 inches away. End effects were eliminated by using two cells with the filaments in one twice as long as the other. Radiation efforts were studied extensively to determine radiation losses for different filament temperatures. The emissivity at constant emitter temperature was found to change less than 023 percent for alkali metal vapors at different pressures.

30 Heat Transfer Theory (53) and experimental efforts (37) have shown-that for low Graetz numbers, the Nusselt number becomes independent of the Reynolds number and becomes asymotically equal to hD Nu -= - 3.658 (45) Low Graetz numbers are easily obtained for laminar flow in a long tube having a small diameter and a constant wall temperature. If the convective heat transfer coefficient is determined experimentally, the thermal conductivity is found from Equation 45. Although accurate heat flux measurements are difficult to make at high temperatures, Achener (1) and Fisher (34) proposed to make such measurements for cesium and rubidium up to temperatures of 18000F. using a capillary tubing with a 1/16 inch inside diameter and 1.5 foot length as a heat exchanger. The capillary tube was to be placed above a pool of boiling liquid metal whose temperature would be controlled by an overpressure of argon. In this way a nearly uniform wall temperature could be maintained. For conditions where the liquid metal condensing resistance and wall metal resistance are small, the thermal conductivity can be found from k 3.658 ln tw 3.658 (46)

31 Porous Beds The effective thermal conductivity of porous beds can be used to determine the thermal conductivity of the gas contained intersitially. Israel, et al. (58) found the thermal conductivity of hydrogen at 20000F. to 47000F. by measuring the effective conductivity of porous tungsten specimens filled with pressurized hydrogen. Effective conductivities were determined from temperature measurements on the upper flat surface of the right circular cylindrical porous specimen heated by high frequency induction currents. The values of effective conductivities were calculated by equating the axial, centerline heat flux at the surface of the specimen, determined from the solution of the heat conduction boundary valve problem, to the radiation and thermal convection heat losses at the same point. Prandtl Number Method Any method for measuring a property value such as thermal conductivity must be based on a fundamental relationship which contains besides the desired property only quantities which can be accurately determined. The Prandtl number expressed as cV' Pr= - k (47) could be used to find the thermal conductivity of a gas providing the Prandtl number could be determined independently based on measurable quantities other than those appearing in Equation 47. Pohlhausen (81) derived a unique solution for high-velocity, steady,

32 two-dimensional flow in which heat is transferred by convection only. He related the Prandtl number to a recovery factor defined as t - t r s t t (48) t 5 For Prandtl numbers between 0.5 and 5, the relationship between the Prandtl number and the recovery factor is expressed accurately as 1/2 r = Pr (49) Eckert and Irvine (29) designed a high-velocity flow device to accurately evaluate the recovery factor by measuring temperatures and pressures. Their results for air between 60~F. and 360~F. calculated from Equations 47-49 agreed within 4 percent with National Bureau of Standards data. 2. Transient Methods In the past, steady state methods have been preferred because of general reliability. However, with improved instrumentation and experience the dynamic and transient methods are becoming more and more useful. Thermal conductivity measurements by any method seldom give any indications of poor values. The data will normally be self-consistent and only by comparing different methods can self-consistent errors be detected. Dynamic Probe Method The dynamic probe method (90,97,105) is an absolute, transient (dynamic) method. Heat is generated for short time periods in a long, thin probe positioned centrally in a

33 cylindrical reservoir and the time-temperature history of the sample fluid recorded during the heating period at some radial distance away from the probe. The thermal conductivity of the fluid may be calculated from the time-temperature record and the power input to the probe by a method developed by Carslaw and Jaeger (19). The temperature rise 0 at a point r in an infinite mass of fluid heated by a very long and very small diameter heat source is 0(Tr) = _2k I (x) (50) ih ere r X 1/72 (51) 2 (ar) and 2 4 I(x) = 0.5772 - in x + 2 (52) For small values of x, i.e., large T and small r, the higher order terms in x may be neglected and Q2k [0.5772 - In 2( 1/2 (53) From Equation 53, the temperature rise between times 11 and z2 is given by A0=2 02 1 4Tk T1 (54)

34 for-negligible changes in the thermal diffusivity or in terms of the thermal conductivity -2 (55) k= in - (55) 4ArrAe'r Experimentally the thermal conductivity is found by measuring the slope k of the straight line obtained from a plot of 0 versus 4lTk in T. Data taken during the first few seconds are usually disregarded since the higher order terms in Equation 52 may be significant. This is usually apparent in the time-temperature history. Allen (2) devised a technique which combined continuous measurements with constant power dissipation. The power dissipation was maintained constant by using an electrical circuit having a high impedance thermionic valve (a power pentode) with a mutual conductance equal to the reciprocal of the wire resistance. In such a circuit, changes in voltage correspond directly to changes in resistance such that the power output is constant. Changes in voltage (thus equivalent to changes in temperature) were recorded by a cathode ray oscillograph. Thermal capacity effects were reduced by using a 0.001 inch diameter platinum wire. Shock Wave Method In recent years several investigators (18, 25,50,80,88) have deduced the thermal conductivity of gases at high temperatures from the measurement of heat transfer rates from the heated gases to an end well of a shock tube in a reflected

35 shock wave. Shock speeds are determined with the aid of a raster oscilloscope display by noting temperature changes in a series of thin film temperature detectors placed along the shock tube. The heat transfer from the end wall is related to the temperature change occurring at the wall upon reflection of shock wave. The wall temperature is measured with some type of thin-film temperature gauge. Collins and Menard (25) used a gauge consisting of a platinum film sputtered onto a quartz substrate. The gauge was connected to a differential amplifier and the resulting voltage change was presented on an oscilloscope. Camac and Feinberg (18) built an end wall heat transfer element consisting of a thin opaque carbon layer on a transparent sapphire window. They then measured the temperature of the element with a calibrated infrared detector. In the determination of the thermal conductivity, the region behind the reflected shock is idealized to consist of a hot semiinfinite gas adjacent to a semi-infinite solid and the continuity and energy equations written for such conditions. The equations lead to a second order differential equation for which one boundary condition can be measured with a temperature gauge and a second boundary condition approximated by assuming that the thermal' conductivity is related to k = a T (56)

36 In — the dimensionless form of the differential equation the constant a cancels out. The best values of b are found by an iterative procedure in which values of b are assumed and the solution of the differential equation for the end wall heat flux compared to the experimental values of the heat flux. The best value of b is found by minimizing the sum of the square of the deviations between the experimental data and the theoretical curve. Since only the temperature dependence of the thermal conductivity is found in this method, i.e., the constant b, values of the constant a must be obtained from other data in order to give absolute values of thermal conductivity. Thermal Diffusivity Method Analysis of transient heat transfer systems involve the temperature distribution with respect to time as well as distance. For example the unsteady state heat conduction equation in cylindrical coordinates is ae [r a2 1 ae -= -+ —- aT lr2 r 3r (57) In such systems the thermal diffusivity, a = k, is an important Oc parameter which may be evaluated from the individual terms or may be determined experimentally as a group as originally suggested by Groeber (49). Experimental determinations of thermal diffusivity provide a good independent check on the consistency of the individual terms.

37 The theory of operation of a device to measure the thermal diffusivity of a fluid. contained in: a cylindrical system was developed by Van Zee and Babcock (98). They made thermal diffusivity measurements of molten glass. Later, Harrison, Boteler and Spurlock (51) made similar measurements on nitrogen. In the system of Harrison, Boteler and Spurlock (51) the current through the cylindrical container was varied by changing the field current in a motor-driven direct current generator. Changes in the field current generator were controlled by a function generator such that the temperature fluctuation measured by a thermocouple located at a distance R from the center and near the container wall could be represented by o (R,T) AR cos (WT) (58/ When the temperature fluctuations at R are given by Equation 58, the temperature fluctuations at the center of the cylinder are given by (51) 8(0,) =R A cos(WT)[ber + sin(wT)[bei VRR] Liber R + bei 2 R (59) a. a Equation 59 can be written as AR -1 t O(O,T)L lIber2 - R+ bei2V R R t berl R (60)

38 From Equation 60, the ratio of the amplitude at the center Ao to 0 the amplitude at R, AR is A o 1 er2 R + bei2 R (61) R a and the phase shift ~ at the center is bei — R -1 a =t tan 7e R (62) Experimentally the amplitude attenuation Ao/AR and the phase shift t are measured for known values of w. Since the only unknown in Equations 61 and 62 is a, the thermal diffusivity is readily determined. Harrison, Boteler and Spurlock (51) estimated the accuracy of their nitrogen data at about 5 percent and indicated that significant improvements are not likely. It should be noted that in the dynamic probe and shock wave methods that the thermal diffusivity is effectively eliminated from the problem by suitable manipulations. E. Experimental Cells for Alkali Metal Vapors Several investigators have constructed and experimented with cells designed to measure the thermal conductivity of alkali metal

39 vapors at elevated temperatures. There were unfortunately very limited results. Gottlieb and Zollweg (43) obtained thermal conductivity data on cesium, potassium and rubidium vapors at vapor temperatures of 1400-16000F. in a hot ribbon filament cell at low pressures. The maximum vapor pressure for potassium was 0.88 mm Hg. or 0.017 lbs./ sq. in. They reported an accomodation coefficient of 0.57 for potassium as determined from a plot of l/k versus 1/P. They further reported that the thermal conductivity of potassium was 0.0104 Btu/ hr.-ft.-~F. at 14300F. with no significant (less than 10 percent) temperature dependence between 12500F. and 16100F. In 1963, Lemon et al. (68) built and checked out a 0.001 inch diameter bare wire dynamic probe thermal conductivity cell. Calibration checks with air and nitrogen were very satisfactory at ambient temperatures but thermal conductivity measurements on potassium vapor at various degrees of superheat from 750-14700F. showed a marked dependence upon the power input to the probe. Several tests were made to locate the source of trouble. After the tests proved to be unsuccessful, the program was terminated. Blum (8) reported upon a concentric cylinder cell similar to the cell of Vines (100). The thermal conductivities of sodiumand potassium vapors were to be measured but no data have been presented as yet.

40 Fisher and Achener (34) made a comprehensive analytical investigation of a dynamic method of measuring the diffu-sivities- of alkali metal vapors in 1964. In such a device, the thermal conductivity is obtained from k = ac p p (63) They concluded that it would be necessary to use sheathed thermocouples to detect temperatures if alkali metal vapors at high temperatures were used. This proved to be a serious disadvantage since sheathed thermocouples would have an adverse effect on the definition of the response curve which could not be improved without decreasing the sensitivity. On the basis of their findings they concluded that this transient method of measuring the diffusivity of alkali metal vapors at elevated temperatures had too many inherent problems to warrant construction. -In 1966 Achener (1) designed and proposed to build a long tube small diameter heat exchanger from which he would deduce thermal conductivities from convective heat transfer coefficients at low Graetz numbers. In 1964, Tepper, Zelenak, Roehlich and May (95) reported on plans to measure the thermal conductivity of cesium and rubidium vapor by a transient hot wire technique. Recently Staub (91) indicated that measurements had been made by Tepper on cesium, rubidium and potassium vapors but the report could not be obtained. Timrot and Totskii (96), two Russian scientists, developed a dilatometric method for the determination of the thermal conductivity of corrosive gases at high temperatures. The temperature drop

41 across the layer of the gas to be investigated is determined from the thermal expansion of the walls enclosing the gas layer. End effects are eliminated with guard heaters. Measurements of the thermal conductivity of helium with their device showed good agreement with published' experimental data. Stefanov, Timrot, Totskii, and Chu Wen-hao (93) made measurements of the thermal conductivity of potassium and sodium by the dilatometric method. The potassium measurements were in the range of 10500F. to 17800F. and from 0.3 lbs./sq.in. to 13.4 lbs./sq.in, pressure. They indicated an average maximum error in the data of 20 percent. Figure 4 was prepared from a table in Reference 93. In view. of the work attempted and under progress and after examining all the possible methods of measuring the thermal conductivity of vapors, the guarded top plate parallel plate thermal conductivity cell seemed to offer considerable promise. The construction of such a cell is reasonably simple even when refractory metals are used. Since no bare electrical wires are required in contact with potassium vapor, the containment of potassium and the operation of the cell are greatly improved. The accuracy possible with a guarded top plate parallel plate thermal conductivity cell should be comparable with concentric cylinder cells. F. Physical Properties of Potassium Many investigators have measured various thermodynamic and transport properties of the alkali metals and of potassium in particular during the past decade. A summary of these efforts for potassium

42.018 LL 0 2 atm. U. Saturated Vapor.016.0140:.012 0iH.008 M -Monomeric Vapor.006 800 1000 1200 1400 1600 1800 2000 VAPOR TEMPERATURE -~F Figure 4. Experimental Thermal Conductivity Results for Potassium Vapor Measured with a Dilatometric Thermal Conductivity Cell (93)

43 through 1965' is given by Coe (23). The two properties of-most importance in this investigation are the vapor pressure and the viscosity of the vapor. A review- of- all the available vapor pressure data for-potassium indicates that the most reliable data are those of Ewing et al. (32, 33) of the U.S. Naval Research Laboratory. Their vapor pressure data cover the range of 1200~F. to 24000F. and is given by the equation 8128.77 log 0P = 6.12758 - T - 0.53299 loglOT (64) where the pressure is in atmospheres and the temperature in ~R. The average deviation of their experimental data from the correlating equation is + 0.31 percent. In the analysis of their data Ewing and co-workers found the first four virial coefficients for potassium and as a result developed a virial equation of state for potassium. The second virial coefficient which can be used to estimate the force constants for the Lennard-Jones potential is given as 4890.7 loglo B = - 3.8787 + T + loglT (65) where B < 0 Ewing and co-workers also verified the existence of the tetramer of potassium in the analysis of the vapor pressure data. The

44 existence of-the dimer-had previously been verified spectroscopically. (55) They further found the equilibrium constants for the reactions nK + K (66) These constants are given by 5312.5 og10 k2 = 3.8611 T (67) and log10 k - 10.1453 + 13745 (68) The enthalpies for the two reactions were obtained from Van't Hoff's isochore equation and are given by 2K = K2, AH' = - 24,296 Btu/lb-mole (69) 4K + K4, AHO = - 6 2,860 Btu/lb-mole (70) Since the equilibrium mole fractions of the monomer, dimer and tetramer are related by x k n n (X )n n- (71) Equations 67, 68, and 71 can be used to find the equilibrium concentration of monomer, dimer and tetramer as a function of temperature and pressure.

45 The only known viscosity data for potassium vapor are those of Stefanov et al. (93) who made measurements with a falling - weight apparatus. A Geiger counter was used to monitor the position of a weighted piston- carrying a Co-60 specimen. They estimated their data were accurate to 3 percent. The data are given in Figure 5 which was-prepared from a table in Reference 93. These data are useful in the estimation of the force constants for the LennardJones potential. G. Theoretical Predictions of Thermal Conductivity of Potassium Vapor Weatherford (102) et al. made predictions for the frozen thermal conductivity for the saturated vapor of potassium and the other alkali metals for the temperature range of 8400F. to 22400F. Their results for potassium are shown in Figure 6. The results were calculated assuming that the Prandtl number k of the vapor was constant and equal to 0.73. The values of the frozen specific heat and the viscosity were taken from theoretical calculations of Shapiro and Meisl (87) and Weatherford (103), respectively.

0.09 0.08 0.07 IL 00604 0 0atuMonome ric ated Vapor 0.03 800 1000 1200 1400 1600 1800 2000 2200 TEMPERATURE- OF Figure 5. Experimental Viscosity Results for Potassium Vapor Measured with a Falling Piston Apparatus (93)

47 Cr 0 0. E 0.010 ao 0.009 - u.I I — 0.008 - LL ucE 0.007 z LuJ 0.005' r E - 800 1000 1200 1400 1600 1800 2000 VAPOR TEMPERATURE -F Figure 6. Theoretical Thermal Conductivity of Saturated Potassium Vapor (102)

CHAPTER III DESCRIPTION OF EQUIPMENT The parallel plate apparatus developed to measure the thermal conductivity of potassium vapor at elevated temperatures in this investigation is quite similar in design to the thermal conductivity cell used by Michels, Sengers and Van Der Guilk (75) for the measurement of the thermal conductivity of carbon dioxide vapor close to its critical temperature and pressure. Several differences in design were necessitated by the corrosion (3, 26,59,76), containment and loading problems (27) which exist when working with alkali metal liquids and vapors. Some of the principal differences involved the choice of materials of construction, type heaters, temperature measuring methods and guard plate insulation. Figure 7 gives a view of the disassembled cell and Figures 8 and 9 give a schematic representation of the cell construction. The cell consists of three principal sections; the top plate assembly, the guard cover assembly and the bottom plate. Molybdenum was selected for the thermal conductivity cell material because of its desirable characteristics. Ideally, the cell material should have a high thermal conductivity to insure uniformity of temperature, a low emissivity to reduce the effects of radiation and a surface stability with regard to corrosion and changes in?emissivity. Of all the materials that can be considered 48

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Disassembled View of the Thermal Conduct 1V 1 ty Cell

Cell Container 8-32 Molybdenum Screws Wall 01, 6 L4-I ff A\ h \\l3g.0535" Figure 8. Schematic Representation of the Thermal Conductivity Cell Showing Heaters and Thermocouples

51 C) //~~I\I //~~~ / 1~~~~~~~~/ c, //~~~~~~~/ < / 6~~~~ Figure 9. Top View of the Thermal Conductivity Cell /Showing Exact Placement of Heaters and Thermocouples\ ~,- ~ I -?'~ 1 ~, 4 L —, - ----- _ —— _~_.-',, \~ _ I X x~ I'-' / /~~~~C Y1 Figure 9. Top View of the Thermal Conductivity Cell Showing Exact Placement of Heaters and Thermocouples

52 corrosion resistant to alkali metals at elevated temperatures (3,59, 76), molybdenum has one of the highest thermal conductivities (89) (69 Btu/hr.-sq.ft.-~F/ft. at 10000F.) and one of the lowest emissivities- (89) (0.12 at 18000F.). The top plate assembly of the cell which is 2.0135 inches in diameter consists-of two pieces held together by three number 8-32 molybdenum- flat heat machine screws as shown in the lower portion of Figure 7 and *in Figure 8. Each piece is 0.246 inches thick. The cell heater fits into a 1.500 inch diameter by 0.070 inch thick cavity formed by the two pieces when screwed together. A molybdenum guard cover assembly consisting of two pieces which contain the guard heater fits over the top plate. The assembly is 3.0135 inches in diameter. The top piece is 0.2515 inches thick and the bottom piece is 0.8701 inches thick at the outer edge, the center portion being machined out to a depth of 0.5403 inches to receive the top plate assembly. The two pieces when screwed together with three number 8-32 molybdenum flat head machine screws form a 2.745 inch diameter by 0.078 inch thick cavity within which the guard heater is situated. Figure 7 shows a disassembled view of the guard plate assembly and Figures 8 and 9 give additional representations. It is the function of the guard cover assembly to prevent the transfer of heat from the top plate assembly in every direction except toward the lower plate of the cell. This was accomplished by providing a vapor space between the top plate assembly and the guard cover assembly to increase the resistance to heat transfer in those

53 directions and by employing a guard heater to keep the guard cover assembly at or very close to the top plate assembly temperature. The top plate assembly is held in place within the guard cover assembly-by three number 8-32 molybdenum flat head machine screws which extend through the top plate as shown in Figure 8. Three 1/16 inch diameter synthetic sapphire balls (99.99 percent A1203) placed-between the-guard —cover and top plate as shown in Figure 8 maintain a vapor gap of 0.0483 inches in the vertical direction. Small indentations were made in the guard cover to receive the sapphire balls and prevent movement and misalignment. The radial vapor gap spacing is 0.0557 inches. Although the molybdenum screws constitute a potential path for heat transfer the effect is minimal when the top plate assembly and the guard cover assembly are maintained at the same temperature. Synthetic sapphire balls were selected as the spacer material because they are resistant to potassium at temperatures up to 15000F. (26) Upon completion of the machining of all the individual parts of the top plate and guard cover, the pieces were assembled and the bottom surface of the top plate and guard cover were surface ground to give a flat surface. The surface was then lapped with Linde A abrassive until a mirror like surface resulted. A 3.0135 inch diameter and 1.0088 inch thick piece of molybdenum constitutes the lower plate of the cell. The top and bottom plates of the cell are separated by three 1/32 inch diameter synthetic

54 sapphire balls as shown in Figure 8. Because of the indentations in the guard cover surface, the vapor gap distance between plates is 0.0182 inches. The top surface of the lower plate was also surface ground- and lapped. A stainless steel yoke holds the assembled thermal conductivity cell together as shown in Figure 10. The cell rests upon three 1/16 inch diameter stainless steel balls which in turn rest upon the lower yoke plate. The top yoke plate rests upon the top of the guard cover assembly. Three 1/8 inch diameter stainless steel rods pass through the two yoke plates and hold the cell in the proper place. The bottom yoke plate is welded to the rods so that the bottom of the cell is approximately 1/2 inch above the bottom of the cell container. The upper portion of the rods are threaded for 8-32 machine screw nuts which hold the top yoke plate tightly against the top of the cell. The point contacts between the yoke and bottom plate are essential in reducing the undesirable heat transfer paths between the upper and lower plates. Heaters for the cell were manufactured by Pyro Electric. Inc. The main top plate heater consists of two 0.0095 inch diameter nichrome wires insulated from each other by magnesium oxide and enclosed in a 1/16 inch diameter stainless steel sheath and coiled tightly with the lead wires in the center as shown in Figure 7. Nickel lead wires of the same diameter were welded to the nichrome wires at approximately the point where the coiling stops and the straight lead section begins. This was done at the time the wires

55 Vacuum tI;??~~~~~~~~~~~~~~~~I-_'-"',X\" "'CV~' f 7, ~ ~ ~ ____ vTemal Conductivit~ 9~~~~~~~~~~Cl oti r,,,.7 " " " I Ilk oo-,d 1.Hoke Bellows Z4Valve/ -!!i'~1~~~~~~~~~~~~~.Y~ I;;':,''T j-quid Metal ~'Container (Boiler) Z 1, -1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-

56 wereinsertedinto the sheath and prior to coiling. The total resistance of the top plate heater is approximately 32 ohms with the greatest portion of the resistance occurring within the coil. The nickel lead wires are each 10 3/8 inches long from the coil to the pointwherethe voltage taps are connected. The guard heater was manufactured similarily to the top plate heater except that the heating element was made of alumel and the coil was wound such that the lead wires were at the outer edge of the coil. Figure 7 shows a view of the guard heater which has a resistance of approximately 9 ohms. A Kepco Model SC-32-5, 0-32 DC semi-conductor voltage regulated power supply provides the direct current power for the main and guard heaters. The power supply and heaters are connected as shown schematically'in Figure 11. The trim rheostats shown in the main heater circuit consist of two 10-turn 0-25 ohm potentiometers anld a 0-4000 ohm resistance box. A Honeywell Type NBS 0.99998 ohm standard resistor'is also located'in the circuit to provide an accurate way to measure the current through the main heater. A 10-turn 0-25 ohm potentiometer'is located in the guard heater circuit to facilitate the balance between the main and guard heater circuits. The current through the main heater is determined by measuring the voltage drop across the standard 1 ohm resistor with a Leads and Northrup K-3 potentiometer and null detector. The voltage drop across the main heater is measured with the potentiometer when the voltage drop is

Trim Rheostat Guord Heater Thermal Conductivity Cell Top Plate Assembly I l Std. Shunt,0 0 T Is Jo. --— Vh d~ ~ A, --— V s ---- Resistance Box Rheostat' I S KEPCO Power Supply Figure 11. Thermal Conductivity Cell'Heater and Guard Heater Wiring Circuit

58 the voltage drop is greater. A 0-10 volt Simpson D.C. volt meter and a 0-2 ampere Simpson D.C. ampere meter are used to measure the voltage drop across the guard heater and the amperage through the guard heater, respectively. Ungrounded chromel-alumel thermocouples placed as indicated in Figures 8 and 9 are used to determine the temperatures at the desired locations. Each thermocouple contains 28 gauge wires within a 1/16 inch diameter stainless steel sheath. Cold junction thermocouples of a similar design are connected to each thermocouple with the itive lead going to a selector switch. The e.m.f. generated by each thermocouple is measured with the K-3 potentiometer and null detector. Thermocouples 3 and 4 are located within 1/8 inch of the surface of the top and bottom plates respectively and are used to determine the temperature difference between the two plates. Thermocouples 3, 5,6 and 7 are used to determine a null temperature reading for the top plate and guard cover assemblies. Two additional thermocouples pass through the top of the cell container with the tips of the thermocouples approximately 1/8 inch from the top of the guard cover. One is used to determine the vapor temper~ature and the other is connected to the furnace temperature control system. The thermal conductivity cell is housed in a container constructed of a 4 inch length of 4 inch diameter, 0.083 inch wall thickness Type 304 stainless steel tube. Three-quarter inch thick pieces of

59 Type 304 stainless steel round stock form the bottom and top of the container as shown schematically in Figure 10, Type-316 stainless steel Swagelok fittings were welded into the top of the container to permit the thermocouple and heater leads to pass out through the top of the cell container and to provide a leak tight seal. A 3/8 inch diameter type 316 stainless steel tube vapor line and a high temperature-Hoke bellows valve, Type THY442 were also welded to the cell container as shown in Figure 10. The vapor line connects to the vacuum system. em. A liquid metal boiler is connected to the cell container. The boiler is constructed of a 3 1/4 inch long section of 3/16 inch wall, Type 304 stainless steel. One-half inch thick sections of Type 304 stainless steel round stock form the bottom and top of the boiler. A 3/8 inch diameter vapor line, a 3/8 inch diameter alkali metal fill tube and a thermocouple Swagelok fitting are welded to the top of the boiler. The vapor line is connected to a 3/8 inch diameter tube on the bottom of the cell container with a Swagelok union. A high temperature Hoke bellows valve, Type 445,'is connected into the line between the two' containers., The fill line was capped off with a Swagelok cap after charging the container with potassium. A chromelalumel thermocouple similar to those used in the thermal conductivity cell is used to determine the alkali metal liquid temperature in the boiler. The potassium pressure in the cell and boiler is determined using the boiler temperature and the vapor pressure data of

60 The thermal conductivity cell container and liquid metal container (boiler) rest upon a stainless steel frame within a Lindberg/Hevi-Duty Type M-6018-S vertical hinged combustion tube furnace. The furnace contains two 9 inch long heating zones, each rated at 2800 watts and a 3 inch long vestibule at the top of the furnace as shown in Figure 10. The heating chamber is 5 3/4 inches in diameter. A high temperature insulation was placed around the thermocouple and cell heater leads coming out of the cell container. The insulation fills most of the space between the top of the cell container and the top of the vestibule and reduces convection heat losses from the top of the furnace. Transite was placed over the vestibule to further reduce convection losses. Figure 12 shows schematically the furnace heating circuit and temperature controller. Control of the temperature within the thermal conductivity cell container is accomplished with a Wheelco Model 407 Capitrol null seeking galvanometer, a Wheelco Model 350 reference voltage source and a Wheelco Model 610A pilot amplifier. A chromelalumel thermocouple within the cell container is connected to the galvanometer where the difference in e.m.f. between the thermocouple and reference voltage is indicated by the galvanometer and becomes the input signal to the pilot amplifier which produces a direct current output to control the 5 KVA Lindberg saturable reactor. A variable transformer is located in the lower heating zone to permit adjustment of the temperature level in the lower portion of the

61 TEMPERATURE Fr - -~ - - - CONTROLLER 5000 WATT THERMOCOUPLE SATURABLE REACTOR i_________ LINt VOLTAGE 19. 89l 19.8iS VARIABLE TRANSFORMER 5600 WATT OMBUSTION ITemperature ControI l CircuitF

62 furnace with respect to the upper half. This is necessary to insure that the temperature within the thermal conductivity cell is always sufficiently above the saturation temperature of potassium to prevent condensation in the cell. The vacuum system is connected to the vapor line leading from the top of the thermal conductivity cell with a 3 foot length of flexible copper tubing. A Welch Duo-Seal No. 1405H vacuum pump is the forepump for a Consolidated Vacuum Corporation two-stage oil diffusion pump, type VMF-20 (air cooled) operating with Dow Corning 704 Silicone Oil. A calibrated RCA 1946 thermocouple type vacuum gauge was used to determine the pressure. Gas pressures of 1-2 microns were readily obtained with the vacuum system. The accuracy of the vacuum gauge below 1-2 microns is limited because of the steepness of the calibration curve. An overall view of the equipment is given in Figure 13.

63 Figure 13. Overall View of the Experimental Equipment

CHAPTER IV EXPERIMENTAL PROCEDURES As originally planned the equipment was designed to obtain an individual thermal conductivity value from two sets of data, one set for isothermal conditions and the second for heated conditions. The isothermal data would be required to establish the temperature profile in the top and guard plate and to determine the temperature difference between the top plate and bottom plate under "isothermal conditions". Since, as will be discussed later, the thermal conductivity cell was apparently never at a uniform temperature when only the furnace heater was used, the temperature profile or null between the top and guard plates and the temperature difference between plates were needed. Isothermal conditions always refer to conditions where neither the top plate heater or guard heater are being- heated. As further planned, data for the second phase of an experiment would be taken with the passage of a direct current through the top plate heater. The heater input would provide the heat flux for the cell and would cause an increase in the temperature difference between top and bottom plates. The guard heater would be used to establish the same temperature profile or null between the top plate and the guard plate as existed during the isothermal portion of the experiment. The actual temperature difference due to the top plate heater input would be the net increase in the temperature difference between the top and bottom 64

65 plates over-the temperature difference under isothermal conditions. The total-heat transfer rate in terms of an apparent thermal conductivity would then be QtXs kt AAt (72) The apparent thermal conductivity would include the effects of radiation and conduction through the spacers. Because of operational difficulties with the furnace, the proposed operating procedure could not be used. The experimental procedure actually used for the vacuum, nitrogen and potassium data was established after several weeks of experimentation to determine the operating characteristics of the equipment. During initial tests, the furnace temperature control system was found to be less than satisfactory. In order to obtain the best possible furnace temperature control conditions, extensive trials were performed to establish the best proportional control setting, to determine the effect of insulation both inside and outside of the furnace and to find the optimium location for the furnace control thermocouple. Under the best possible conditions the variation in the cell temperature over a 24-hour period was as much as 7~F. During the duration of a 30minute run, the maximum variation in temperature from the mean temperature was generally no more than 0.2~F. but upon occasion varied by as much as 1-2~F. depending upon the time of day and line voltage fluctuations

66 The most stable operating conditions were obtained with a proportional control band setting of 1.5 percent of meter span with extensive insulation around the outer edge of the vestibule and upon the top of the furnace and with the control thermocouple located within the cell container. The top of the furnace was covered with pieces of Transite cut to fit around the thermocouples and Fiberfrax was placed upon the Transite to minimize the loss of heat from the furnace by bulk convection. During preliminary runs thermocouples 3 and 6 in the top plate and thermocouples 5 and 7 in the guard plate were connected together to give a null value with a single potentiometer reading. In effect- the single reading was the difference in e.m.,f. between the averages of the e.m.f's of thermocouples 3 and 6 and thermocouples 5 and-7.' The potentiometer millivolt reading can be converted directly into a null temperature difference. Similarly thermocouples 3 and 4 were connected to give the difference in e.m.f. generated by the two thermocouples. This difference can be converted to a difference in temperature between the upper and lower cell plates. A switching arrangement was used to permit the use of thermocouples 3 in both the null and temperature difference circuits. The wiring diagram is given in Reference (10), All the thermocouples used in the two circuits were manufactured with ungrounded

67 hot junctions-to prevent short-circuiting between thermocouples through thermocoup-le sheaths and cell connections. It was during- these preliminary runs that the null was found to be larger than-the null values that one might predict from the thermocouple calibration data. Preliminary calibration indicated a maximum -null of +0.1 ~F. at 12000F. In addition, the null fluctuated and varied considerably during the run. Apparently the fluctuations were due to the furnace temperature variations. The temperature difference between plates varied but not nearly as much as the null temperature. Because of the unexpected magnitude of the null temperature (%200F.) and the difference in temperature between plates under isothermal conditions as well as fluctuations in the readings, the two thermocouple circuits were disconnected and each thermocouple was connected individually to a selector switch with each thermocouple having its own cold junction. Several runs were made which verified that the null and temperature difference between plates were the same as previously measured with the two thermocouple circuits. Subsequent runs indicated that a temperature gradient existed along the length of the furnace and that the thermocouple e.m.f. characteristics may have changed somewhat since being calibrated probably due to the bending that was required in assembling the thermal conductivity cell. The change in calibration was not of major importance since the most

68 important measurements involved the difference in two temperatures and the temperature differences were accurately determined in the method by which the data were taken. The accuracy of any absolute temperature was probably within 5-100F. This estimate was based on the fact that all thermocouples generated approximately the same e.m.f. except for thermocouple 6 which was consistently lower by approximately 25-400F. depending upon the temperature level. The e.m.f.'s generated by the thermocouples were always consistent with respect to each other during the course of a series of runs at the same general conditions, but frequently changed when the temperature level and heating conditions were changed. Before the final operating procedure was established it was decided that each thermocouple would be left connected to an individual post on the selector switch with its own cold junction rather than connecting the thermocouples into the two circuits described previously. This procedure had a slight disadvantage in that the precision of a single temperature difference would be less because of the one less significant figure indicated on the potentiometer. However, fluctuations in the temperature differences during the course of a run were generally such that the advantage obtained when using the two circuits was small. By taking individual thermocouple readings it was possible to obtain much more information about the

69 temperature profile in the cell and to develop some history for each thermocouple. In this way the system behavior was better understood and abnormal behavior if any could be more quickly noticed. Sufficient data were always taken and averaged so that the accuracy of any run taken with individual thermocouples was comparable to data obtained with the two thermocouple circuits. Operating-Procedure The experimental procedure used for obtaining thermal conductivity data for nitrogen and potassium and for obtaining the radiation effects for vacuum conditions was the same once the cell was charged or evacuated, The furnace temperature controller was set at the desired temperature and the controller and furnace turned on. Steady state conditions were reached in approximately 6-8 hours. Once steady state was reached as indicated with thermocouple 3, the isothermal data runs could be begun. Each run consisted of 10 sets of readings and each set consisted of reading the e.m.f. of thermocouples 3,4,5,6,7,8 in order. The potassium boiler temperature, as indicated with thermocouple 9, was also determined when potassium data were being taken, A typical run for potassium is given in Table I. The raw data were reduced by averaging the potentiometer millivolt readings for each thermocouple as shown in Table I. Next the millivolt reading of thermocouple 3 was subtracted from the millivolt readings of thermocouples 4,5,6,7, and 8 respectively.

Table I. Representative Sample of Original Data for Potassium Run 206955, Data Set 32 Thermocouples - my Heater 3 4 5 6 7 8 Boiler Volts Amps 24.671 24.538 24.480 24.341 23.735 24.741 17.492 3.10 0.09568 24.669 24.535 24.484 24.336 23.736 24.745 17.496 24.670 24.540 24.485 24.341 23.740 24.746 17.496 24.674 24.539 24.488 24.339 23.743 24.745 17.502 24.673 24.544 24.483 24.335 23.742 24.750 17.500 24.672 24.544 24.489 24.345 23.745 24.750 17.504 24.678 24.542 24.488 24.348 23.750 24.750 17.504 24.679 24.545 24.481 24.351 23.746 24,746 17.504 24.677 24.544 24.492 24.348 23.745 24.751 17.501 24.677 24.547 24.495 24.349 23.735 24.751 17..504 3.10 0,09568 Avg. 24.6740 24.5418 24.4865 24.3433 23.7417 24.7475 17.5003 3.10 0.09568 3-3 4-3 5-3 6-3 7-3 8-3 0 -0.1322 -0.1875 -0.3307 -0.9323 +0.0735 mv 0 -5.608 -7.944 -14.01Z -39.504 +3.114 OF Null = +33.436 Guard Heater: 7.15 Volts 0.42 Amps

71 These differences were then divided by the millivolts/~F. at the absolute temperature of thermocouple 3 to give the temperature difference in ~F. between each thermocouple and thermocouple 3. This in effect made thermocouple 3 the base thermocouple and all the cell temperatures were determined relative to thermocouple 3. Since the millivolts/~F. generated by the thermocouples is rather constant over a wide range of temperatures, temperature differences are much more accurate than absolute temperature measurements. This procedure served as a continuous calibration check of the thermocouples. Preliminary thermocouple calibrations against a N.B.S. calibrated thermocouple indicated a very close agreement between thermocouples and a maximum.deviation from the standard of approximately 30F. at 12000F. A null temperature-was calculated from Null = (t3 + t6) - (t5 + t7) (73) where the subscripts refer to the thermocouple number. The temperature difference between plates was calculated from At = (t3 - t4) (74) The null and temperature differences were plotted for 5-10 runs as shown in Figure 14. Because of the temperature variations within the furnace, runs were taken at the same temperature set

1.0 UL cO..0.0 ISOTHERMAL L _ I + MEAN VALUES Z -_1.0. - 4.0 HEATED-GUARD HEATER VOLTAGE zo U:Jo E 6.55 VOLTS W D, 2 s4s715 VOLTS w I — 7 bdJ 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 CELL NULL- OF [THERMOCOUPLES (3+6)- (5+7)] Figure 14. Typical Experimental Results for Potassium Vapor Thermal Conductivity - Data Set 32

73 point until a definite null temperature difference relationship was determined. Each run required approximately 30 minutes to take and approximately 10 minutes to calculate the null and temperature difference. Once the null temperature difference relationship was established for the isothermal runs, the heated top plate data runs could be begun with the furnace at the same temperature set point. The constant voltage direct current power supply was turned on and set at the desired voltage. The top plate trim potentiometers as shown in Figure 11 were adjusted to give the desired voltage drop across the top plate heater. The guard plate trim potentiometer was then adjusted so that the voltage drop across the guard heater would result in a heat input per unit surface area comparable to that generated in the top plate heater. When steady state was reached, several runs were taken as in the isothermal case to establish the null temperature difference relationship for the heated top plate condition. If after the first few runs, it was apparent that the guard heater voltage was incorrectly set because of a significantly different null as compared to the isothermal case, the guard plate trim potentiometer was adjusted to compensate for the discrepancy and the runs continued after steady state was again reached. In addition to the thermocouple readings, voltage dropg across-the top plate heater, the guard plate heater and the 1 ohm standard shunt

74 were measured and recorded. The current through the top plate heater was calculated from the voltage drop across the 1 ohm standard shunt and the current through the guard heater was measured with an ampere meter. Data for the heated top plate were plotted in the same figure as the isothermal data as shown in Figure 14. If the guard voltage drop had been properly adjusted, the null values for the isothermal and heated top plate conditions would be identical as indicated by- either the range of null values or the average of the null values. Two series of runs having the same range of null values will generally have the same average null if the runs are evenly spaced with time and 6-8 runs are taken. Because of the time required for a single run and for a series of runs, it was not always possible to space the runs evenly with time. Whenever the average nulls for the isothermal and heated top plate conditions were within 0.2~F. the range of null values was generally coincidental with the same midpoints. The null temperature as defined in Equation 73 is equal to twice the temperature difference between the average temperatures of the top plate and the guard plate. When after a series of runs the null values for the heated conditions differed significantly from those under isothermal conditions, the guard heater trim potentiometer was adjusted to bring the two null points closer together and another set of runs taken. All the data for a single operating condition were then plotted as in Figure 14.

75 Vacuum Runs Upon initiation of a series of vacuum runs, the valve between the potassium boiler and the cell was closed and the valve between the cell and the vacuum system opened. The cell and vacuum system were allowed to out-gas at ambient temperatures for approximately- one day before heating the thermal conductivity cell. The furnace was then turned on and brought up to temperature (900-1200~F.) slowly over a period of a half day. During all the vacuum- runs the vacuum system was always open to the cell. The absolute pressure within the system was measured with a calibrated thermocouple type vacuum gauge. During vacuum runs the low absolute pressure greatly reduced the heat transfer by convection and conduction within the cell container. As a- result the temperature fluctuations and the temperature difference -between thermocouples were substantially greater than during the nitrogen and potassium runs. A set of vacuum runs was taken prior to each set of nitrogen data during the cell calibration phase of the investigation. The vacuum runs were used to measure the combined contribution of radiation and spacer conduction. Nitrogen Runs The nitrogen used in the investigation was manufactured by Liquid Carbonic Division of General Dynamics and had a minimum purity of 99.7%. The nitrogen was admitted to the cell through the vacuum system with the system initially under a vacuum and at ambient temperature, The nitrogen was then removed by evacuation and additional nitrogen added until the pressure was

slightly above atmospheric pressure. This process was repeated several times to insure a minimum amount of impurities. The system was left under a pressure of approximately 1000 mm Hg pressure. The pressure-was measured with a calibrated compound Bourdon tube gauge. Potassium Runs The potassium used in the investigation was a high purity potassium (less than 10 ppm oxygen and less than 50 ppm sodium) obtained from Mine Safety Appliances Company in a stainless steel shipping container. The container was designed to facilitate the transfer of potassium to other containers. The potassium boiler, the potassium shipping container, the vacuum system and a helium gas cylinder were connected together with tubing and fittings to effect the transfer of the desired amount of potassium to the boiler. A vacuum was pulled on the entire system except for the shipping container and the system checked for leaks. When found leak free, the boiler and the shipping container and the line between the two containers were then heated to approximately 2000F. with electrical heating tapes to melt the potassium (melting point 146~F.) and to keep the transfer lines above the melting point. The load valve on the potassium container was opened and the helium in the container evacuated and then refilled with helium to a pressure of approximately 780 mm Hg. The load valve was then closed. The empty boiler was next filled with helium to a pressure of 350 mm Hg and the valve leading-to the boiler-closed. By slowly opening thevalve in the fill line which connected the potassium container

77 and boiler, potassium began to flow into the boiler because of the small pressure differential and continued to flow until the helium being compressed in the boiler was at the same pressure as the helium in the container. After the pressures had equalized the valve in the fill line was closed and the helium pressure in the boiler increased to approximately 1500 mm Hg. Residual potassium in the fill line was then forced back into the container by the pressurized helium in the boiler by opening the fill line valve. The entire system was then cooled down to room temperature. With a helium pressure on the system slightly above atmospheric pressure, the boiler was removed and capped for weighing. The weight of the boiler before and after filling indicated that 3 1/4 ounces of potassium had been added to the boiler. This was sufficient potassium to fill 3/4 of the container at operating conditions and more than sufficient to keep the top of the thermocouple sheath submerged in liquid potassium. The cap was then removed from the boiler and the boiler connected to the thermal conductivity cell container which had also been filled with helium. A vacuum was then pulled on the system and the system flushed with helium several times. The valve between the cell container and the boiler was then closed leaving helium in the vapor space of the boiler at essentially atmospheric pressure. The thermal conductivity cell and vacuum system was thoroughly out-gassed and a set of vacuum runs taken at 1000~F.-data set 9.

78 It has been planned to determine the radiation effects under vacuum conditions prior to each set of potassium data, but when the equipment was cooled down the valve between the boiler and cell container could not be opened, The valve stem was sheared twice attempting to open the valve because of seizing of the valve stem threads. Before any additional attempts to open the valve, three additional vacuum data sets were then taken at 1100, 1200, and 13000F.-data sets 10-12. Upon completion of the vacuum runs, the cell container and boiler were removed from the furnace and the valve bonnet and the residual valve stem plug removed from the valve body. With the plug removed the bellows was free to expand - opening the valve. An identical Hoke Type TY445 valve was purchased in order to obtain a new bonnet and valve stem plug. A thread lubricant and anti-seize compound sold by Crawford Fitting Company under the name of Silver Goop was applied to the valve parts and the old valve rebuilt. The secondary valve packing was left out upon reassembly because it had charred previously contributing to the valve trouble. The valve operated satisfactorily after reassembly. The cell container and boiler were than placed back into the furnace and connected to the vacuum system. The thermocouples and the heater circuits were also reconnected. Upon completion of a thorough out-gassing the system was ready to begin a series of potassium runs. Potassium runs were made with the valve between the cell container and the vacuum system closed and the valve between the cell container and the boiler opened. The furnace was brought up

79 to temperature slowly. -Once close to the desired cell temperature, the furnace temperature controller was allowed to operate normally. The temperature of the liquid potassium in the boiler was brought to the desired level by adjusting the variable transformer in the lower heating element circuit of the furnace as shown in Figure 12. The boiler temperature was maintained at a temperature approximately 100~F. less than the cell temperature to insure that only potassium vapor was present in the cell. The pressure of the potassium vapor in the cell was assumed to be equal to the vapor pressure of the liquid potassium in the boiler as determined from the boiler temperature and the vapor pressure data of Ewing (33). Two sets of potassium data were taken at 10000F., data sets 13 and 14, and with the boiler temperatures at approximately 800 and 9300F., respectively. Upon completion of these runs the system was cooled down to room temperature and the top valve opened to determine if there had been any leakage into the system during the week that data were being taken. No significant leakage was apparent as indicated on the thermocouple vacuum gauge. The top valve was again closed and the system out-gassed and heated to 11000F. for additional potassium data. Upon completion of each data set at 11000F., data sets 15-17, preliminary calculations were made to determine the total thermal conductivity kt. The value of kt for data set 15 was lower than that obtained for a corresponding pressure condition at 10000F, and the values became progressively

80 less for data sets 16 and 17 which were at higher cell pressures. Since this was contrary to what was expected, it was postulated and later verified that the emissivity of the molybdenum surface had changed since the beginning of the potassium runs. Additional runs at 12000F. were made with the hope that the proper radiation correction could be found later. The top high temperature valve became inoperable after the completion of data set 20. Fortunately the valve was taken apart without serious damage to the bonnet and valve stem plug. After repairs were effected and the valve parts coated with Silver Goop and reassembled, the valve worked satisfactorily during the balance of the investigation. The runs for data set 21 were then taken at the same temperature and pressure conditions as data set 13. The calculated valve of the total thermal conductivity kt for data set 21 was substantially less than the value for data set 13. The system was cooled down and the valve between the cell and the boiler closed. Checks to determine if the two high temperature valves were functioning properly revealed that potassium was in the short length of 3/8 inch diameter tubing connecting the top high temperature valve to the cell container. After some initial attempts to evacuate the potassium through the vacuum system were unsuccessful, the line between the top valve and the vacuum system was wrapped with heating tape and the furnace heated to 1300~F. The system was

81 out-gassed under these conditions for several days. A later check indicated that the line was substantially free of potassium at that time. This was again verified when vacuum data runs were taken at 1000 and 12000F.-data sets 24 and 25. Vacuum runs taken at 10000F. and 1200~F. for data sets 24 and 25 revealed that the apparent thermal conductivity under vacuum conditions k was significantly lower than in the vacuum runs rad. taken prior to the potassium runs. This verified that the emissivity of the molybdenum surface had changed. When the appropriate values of k were subtracted from the values of the total thermal rad. conductivity kt for data sets 13 and 21, the values of the thermal conductivity of potassium vapor kc for the two data sets were in good agreement. A small heater was constructed of nichrome wire and ceramic insulators and attached to the 3/8 inch diameter tube between the top valve and the cell container. During the balance of the potassium runs, data sets 26-32, the heater was used to keep the tube hot and prevent condensation in the line. The heater kept the temperature in the vestibule considerably hotter than before, but if the voltage drop across the heater was too great, the temperature fluctuations in the cell became excessive. This was quite apparent for data sets 26 and 27. The voltage drop across the heater was normally kept at about 20 volts.

CHAPTER V EXPERIMENTAL DATA AND ANALYSIS The experimental data were processed to the extent illustrated in Table I and Figure 14 at the time the data were taken. This step consisted of averaging the thermocouple millivolt readings and computing the average temperature differences between each cell thermocouple and thermocouple 3. The cell null temperature was also computed. These data and results are given in Appendices A and B. Each data set was processed in a similar method whether for vacuum, nitrogen or potassium runs. From each set of data it was necessary to determine the mean overall temperature differences between the top and bottom plates due to conduction and radiation and to determine the net heat input to the top plate. The mean temperature difference At between the top and bottom plates due to conduction and radiation from the heated top plate was determined by a statistical analysis of the data. For each guard heater voltage value, least squared deviation lines of equal slope were placed through the isothermal data points and the heated top plate data points as previously illustrated in Figure 14 for data set 32. Although the lines through the data of data set 32 are nearly horizontal, lines of definite positive or negative slopes were obtained for other data sets depending upon the gas or vapor and the furnace temperature 82

83 conditions. The difference in the ordinate values of the two lines is the mean temperature difference between plates. The equations of the lines, the temperature difference, the mean error in the temperature difference, the mean temperatures and the mean null temperatures were computed using the Ford Motor Company's GE 265 computer. The computer program and a typical output is given in Appendix C. Table II gives a summary of the operating conditions for all the data sets and the preliminary results as processed with the digital computer. The net heat input to the top plate by the top plate heater was found by a four part process. As indicated in the discussion of equipment, the heater consisted of a heating coil and two nickel lead wires which extended from the coil to a point approximately 10 inches from the coil and outside the cell container. First, the total resistance of the top plate heater and ltad wires as listed in Table III was calculated using the average voltage drop across the heater and lead wires and the average current through the heater and lead wires. Next the resistance of the lead wires were estimated from Figure D.3 in Appendix D using the temperature indicated by thermocouple 8 which was positioned in the cell container immediately above the cell. The heater resistance was found by subtracting the lead wire resistance from the total resistance. Lastly, the heat input to the top plate by the top plate heater was determined from

Table II. Summary of Operating Conditions for the Experimental Data - Data Sets 1-32 Average Average Guard Null At Standard Gas System Null Heater Heated Heater Heater from Error of Data or Top Plate Pressure Isothermal Voltage Top Plate Voltage Current Heating At Set Vapor Temp. OF mm Hg OF Volts d.c. 0F Volts d.c. Amps d.c. OF 0 1 vac. 932.5 0.004 25.681 Isothermal vac. 948.2 0.002 25.681 4.0 25.753 1.199 0.03637 9.731 0.376 2 N2 924.3 1210 13.996 Isothermal N2 925.8 1190 13.996 5.8 13.991 3.497 0..10671 1.999 0.255 3 vac. 1031.3 0.002 27.982 Isothermal vac. 1033.6 0.002 27.982 3.05 28.484 1.807 0.05630 3.652 0.231 4 N2 1028.4 1299 16.144 Isothermal co N2 1028.5 1305 16.144 5.95 15,690 3.595 0.11084 2.118 0.071 5 vac. 1117.6 0.002 30.502 Isothermal vac. 1Ml8M5 0.001 30.502 3.15 31.060 1.849 0.05729 2.599 0.351 6 N2 1113.2 1363 17.401 Isothermal N2 1114.0 1360 17.401 5.95 17.002 3.585 0.10989 1.860 0.119 7 vac. 1211.9 0.001 30.324 Isothermal vac. 1214.9 0.002 30.324 4.6 30.651 2.415 0..07435 2.776 0.292 8 N2 1209.8 1362 20.760 Isothermal N2 1214.1 1380 20.760 6.8 20.975 3.511 0.10779 1.643 0.082 9 vac. 1005.1 0.002 34.352 Isothermal vac. 1009.4 0.002 34.352 4.0 34.483 1.800 0.05508 3.617 0.103 10 vac. 1109.3 0.002 37.777 Isothermal vac. 11114.1 0.002 37.777 3.9 35.571 1.900 0.05775 2.299 0.159

Table II. (continued) System * Average Pressure Average Guard Null At Standard Gas mm Hg or Null Heater Heated Heater Heater from Error Data or Top Plate lbt./ Isothermal Voltage Top Plate Voltage Current Heating of At Set Vapor Temp. ~F sq.in. OF -Volts d.c. OF Volts d.c. Amps. d.c. OF 11 vac. 1201.6 0.002 39.710 Isothermal vac. 1204.0 0.002 39.710 4.5 43.162 2.300 0.06960 2.605 0.131 vac. 1208.9 0.002 39.710 5.0 40.378 2.300 0.06964 3.254 0.214 12 vac. 1298.7 0.002 43.009 Isothermal vac. 1308.5 0.002 43.009 5.0 43.615 2.300 0.06932 2.202 0.132 vac. 1304.0 0.002 43.009 5.25 42.894 2.300 0.06915 3.009 0.201 13 K 1004.5 0.168 37.189 Isothermal K 1014.3 0.163 37.189 8.2 36.272 3.600 0.11065 7.061 0.059 K 1013.4 0.166 37.189 7.6 36.873 3.600 0.11023 6.554 0.061 K 1012.2 0.167 37.189 7.3 36.644 3.600 0.10993 6.058 0.062 K 1012.4 0.168 37.189 6.9 37.335 3.600 0.11000 5..688 0.058 14 K 1011.6 0.630 44.225 Isothermal K 1018.0 0.606 44.225 6.9 43.754 3.600 0.11044 5.762 0.042 K 1023.3 0.646 44.225 6.5 44.604 3.600 0.11030 5.173 0.055 15 K 1105.1 0.180 35.164 Isothermal K 1109.1 0.172 35.164 6.7 35.904 3.600 0.11004 5.183 0.063 K 1109.3 0.173 35.164 8.0 35.139 3.600 0.10986 6.573 0.070 16 K 1107.7 0.517 40.452 Isothermal K 1111.3 0.494 40.452 8.0 41.847 3.600 0.10997 6.870 0.038 K 1113.8 0.501 40.452 9.0 40.259 3.600 0.11015 7.961 0.096 K 1111.1 0.518 40.452 5.5 42.842 3.600 0. 10974 4.145 0.040 17 K 1108.3 1.235 45.882 Isothermal' K 1117.7 1.201 45.882 8.0 44.577 3.110 0.09494 6.336 0.172 K 1113.1 1.150 45.882 7.0 46.302 3.110 0.09518 5.151 0.074 *Pressure for vacuum runs in mm Hg; K runs in lbs./sq.in.

Table II. (continued) System Average Pressure Average Guard Null At Standard Gas mm Hg or Null Heater Heated Heater Heater from Error Data or Top Plate lbs. / Isothermal- Voltage Top Plate Voltage Current Heating of At Set Vapor Temp.0F sq.in. OF Volts d.c. OF Volts d.c. Amps. d.c. OF 18 K 1186.6 0.470 38.149 Isothermal K 1190.4 0.459 38.149 7.0 38.149 3.100 0.09448 4.399 0.083 19 K 1187.2 1.155 43.428 Isothermal K 1194.5 1.155 43.428 7.0 43.542 3.100 0.09469 4.197 0.202 20 K 1195.6 1.187 50.578 Isothermal K 1203.2 1.184 40.578 7.0 50.560 3.100 0.09523 4.388 0.150 21 K 998.7 0.161 38.609 Isothermal K 1005.6 0. 155 38.609 6.2 39.206 3.100 0. 09491 5.397 0.022 K 1008.0 0.155 38.609 7.0 38.535 3.100 0.09455 6.474 0.028 22 vac. 997.0 0.003 36.232 Isothermal vac. 999.4 0.003 36.232 5.0 36.473 2.200 0.06651 3.702 0.134 vac 1001.2 0.003 36.232 6.0 35.897 2.200 0.06669 4.757 0.255 23 vac. 993.9 0.002 33.527 Isothermal vac. 1003.3 0.002 33.527 6.5 33.939 2.600 0.07903 5.515 0.126 vac. 1002.5 0.002 33.527 7.2 33.376 2.600 0.07906 6.779 0.157 24 vac. 998.3 0.002 29.910 Isothermal vac. 1005.6 0.001 29.910 5.6 29.908 1.400 0.04269 7.621 0.208 25 vac. 1187.1 0.002 33.206 Isothermal vac. 1193.0 0.002 33.206 5.6 32.789 1.400 0.04265 4.714 0.099 vac. 1193.8 0.002 33.206 5.1 33.423 1.400 0.04268 3.825 0.096 *Pressure for vacuum runs in mm Hg; K runs in lbs./sq.in.

Table II. (continued) Average System Average Guard Null At Standard Gas Pressure Null Heater Heated Heater Heater from Error Data or Top Plate lbs.! Isothermal Voltage Top Plate Voltage Current Heating of At Set Vapor Temp. OF sq.in. OF Volts d.c. OF Volts d.c. Amps.d.c. OF 26 K 1012.0 0.483 40.929 Isothermal K 1018.9 0.450 40.929 6.95 40.599 3.110 0.09591 6.586 0.325 27 K 1010.9 0.489 40.105 K 1018.1 0.492 40.105 6.60 40.163 3.109 0.09553 4.658 0.469 28 K 1090.0 0.159 35.033 Isothermal K 1098.4 0.158 35.033 6.8 35.676 3. 098 0.09479 5.236 0.101 K 1097.0 0.150 35.033 7.6 34.421 3.100 0.09490 6.484 0.112 29 K 1095.3 0.430 38.522 Is-othermal K 1103.1 0.411 38.522 7.42 38.440 3.119 0. 09560 6. 232 0.105 K 1099.1 0.403 38.522 7.0 38.715 3.120 0.095 70 5.933 0.078 K 1099..3 0.405 38.522 6.6 39.358 3.110 0.09547 5. 634 0.078 30 K 1185.8 0.189 33.011 Isothermal K 1192.8 04y92 33.011 6.80 33.848 3.113 0.09522 4.619 0.121 K 1194.4 0.195 33.011 7.75 33.530 3.110 0.09509 5. 162 0.081 K 1193.7 0.187 33.011 8.50 32.690 3.110 0.09508 6.302 0.062 31 K 1189.2 0.397 35.494 Isothermal K 1194.1 0.394 35.494 8.50 34.176 3.114 0.09540 6.190 0.140 K 1192.4 0.395 35.494 7.55 35.239 3.120 0.09541 5.070 0.135 32 K 1094.7 0.162 33.994 Isothermal K 1101.8 0.156 33.994 7.15 33.504 3.109 0. 09569 5.895 0.050 K 1102.2 0.163 33.994 6.55 34.678 3.110 0.09561 4.974 0.045

88 Table III. Summary of the Top Plate Heater Temperatures and Resistances - Data Sets 1-32 Data Heater Heater Total Heater Heater Lead Wire Heater Set Voltage Current Resistance Lead Wire Resistance Resistance Temperature Volts Amps Ohms OF Ohms Ohms 1 1.199 0.03637 32.961 980 4.02 28.941 2 3.497 0.10671 32.771 980 4.02 28.751 3 1.807 0.05630 32.096 1070 4.19 27.906 4 3.595 0.11084 32.425 1070 4.19 28.235 5 1.849 0.05729 32.274 1165 4.36 27.914 6 3.585 0.10989 32.623 1165 4.36 28.263 7 2.415 0.07435 32.481 1265 4.54 27.941 8 3.511 0.10779 32.576 1265 4.54 28.036 9 1.800 0.05508 32.680 1013 4.11 28.570 10 1.900 0.05775 32.900 1108 4.31 28.590 11 2.300 0.06962 33.036 1197 4.47 28.566 12 2.300 0.06924 33.218 1291 4.64 28.578 13 3.600 0.11020 32.668 1005 4.10 28.568 14 3.600 0.11037 32.618 996 4.08 28.538 15 3.600 0.10995 32.742 1109 4.31 28.432 16 3.600 0.10995 32.742 1102 4.30 28.442 17 3.110 0.09506 32.716 1096 4.29 28.426 18 3.100 0.09448 32.811 1190 4.46 28.351 19 3.100 0.09469 32.738 1184 4.45 28.288 20 3.100 0.09523 32.553 1181 4.45 28.103 21 3.100 0.09473 32.725 999 4.07 28.650 22 2.200 0.06661 33.028 996 4.07 28.958 23 2.600 0.07905 32.890 1000 4.09 28.800 24 1.400 0.04269 32.795 1005 4.10 28.695 25 1.400 0.04266 32.817 1194 4.46 28.357 26 3.110 0.09591 32.426 999 4.07 28.356 27 3.109 0.09553 32.545 997 4.07 28.475 28 3.099 0.09485 32.673 1099 4.30 28.373 29 3.116 0,09559 32.598 1094 4.28 28.318 30 3,111 0.09513 32.702 1202 4.48 28.222 31 3.117 0.09541 32.671 1196 4.46 28.211 32 3.110 0.09565 32.514 1105 4.30 23.214

89 Qt 3.413 Btu/hr (i (75) t 34 watt ( ) Values of the heat input Qt are tabulated in Tables IV, V, and VI for the vacuum, nitrogen, and potassium data, respectively. As indicated in Table II for most data sets the average values of the null for the heated top plate data did not agree sufficiently close with the average value of the null for the isothermal data. When this occurred the guard heater voltage was adjusted to bring the heated top plate null closer to the null value for the isothermal data. The top plate heater voltage and current were always kept the same throughout the duration of a data set. Each guard heater voltage setting gave a definite temperature difference between plates and average null temperature as shown in Figure 14. By taking data at two or more guard heater voltages it was possible to closely estimate by interpolation the temperature difference that would exist between plates if the null values for the isothermal and heated top plate conditions were the same. The interpolated estimates of the temperature difference between plates are listed in Tables IV, V, and VI for the vacuum, nitrogen and potassium data, respectively. The effective area of the top plate for heat transfer to the bottom plate was determined using the analog to the effective area of a Thomson condensor (75). This dilemma arises because the guard plate and top plate are separated by a radial gap while

Table IV. Experimental Results for Apparent Thermal Gonductivity Under Vacuum Conditions Data T P Q At k Set cell celll OF mm Hg Btu. /hr. Btu./hr.ft.-OF 1 943.3 0.003 0.13066 9.731 0.00089 3 1031.8 0.002 0.30189 3.652 0.00547 5 1117.2 0.001 0.31269 2.599 0.00797 7 1213.5 0.002 0.52717 2.776 0.01257 9 1007.6 0.002 0.29582 3.617 0.00541 0 10 1113.0 0.002 0.32543 2.299 0.00937 11 1204.7 0.002 0.47256 3.420 0.00915 12 1304.8 0.002 0. 46760 2.875 -0401077 22 998.1 0.003 0.43851 4.140 0.00701 23 999.7 0.002 -0.61424 6.480 0.00628 24 100l.-8 0.002 0.17860 7.621 0.00155 25 1191.3 0.002 0.17613 4.129 0.00282

Table V. Experimental Results for Thermal Conductivity of Nitrogen Data T P Q At k k k Set cell cell Btu/hr. OFt rad. OF mmlg Btu/hr.ft.`F Btu./hr.ft.-tF Btu-/hrOft.-0F 2 924.8 1190 1.1174 1.999 0.03701 0.00391 0.03310 4 1027.4 1305 1.1839 2.117 0.03702 0.00542 0.03160 6 1113.1 1360 1.1649 1.860 0.04147 0.00727 0.03420 8 1213.3 1380 1.1118 1.643 0.04479 0.00972 0.03507

Table VI. Experimental Results for Thermal Conductivity of Potassium Vapor at Various Saturation Temperatures Data T T P Q At k k k Set cell Boiler cell Btu./hr. OF t rad c lbs./sq.in. Btu./hr.ft.-0F Btu./hr.ft.-0F Btu./hr.ft.-0F 13 1010.1 805.6 0.166 1.1841 5.910 0.01327 0.00472 0.00855 14 1017.9 930.9 0.626 1.1865 5.410 0.01452 0.00435 0.01017 15 1105.9 809.8 0.173 1.1731 6.520 0.01191 0.00522 0.00669 16 1108.2 911.2 0.504 1.1735 7.783 0.00998 0.00461 0.00537 17 1112.6 1006.8 1.160 0.8767 5.445 0.01066 0.00409 0.00657 18 1189.9 899.7 0.459 0.8637 4.399 0.01300 0.00460 0.00840 19 1192.4 1003.4 1.155 0.8657 4.197 0.01366 0.00418 0.00948 20 1201.0 1106.5 1.184 0.8698 4.388 0.01312 0.00383 0.00929 21 1003.6 798.3 0.155 0.8775 6.360 0.00913 0.00165 0.00748 26 1015.6 897.4 0.450 0.8902 6.000 0.00982 0.00161 0.00821 27 1015.8 906.8 0.492 0.8869 4.658 0.01260 0.00161 0.01099 28 1094.8 797.9 0.154 0.8712 5.884 0.00980 0.00215 0.00765 29 1097.4 885.4 0.406 0.8831 5.950 0.00983 0.00216 0.00767 30 1190.7 817.5 0.191 0.8717 5.600 0.01020 0.00281 0.00739 31 1190.8 882.3 0.395 0.8764 4.805 0.01208 0.00283 0.00925 32 1099.2 800.8 0.160 0.8810 5.502 0.01060 0.00218 0.00842

93 the bottom plate is a continuous surface. The effective area is given by 2 2 2 ~2 2 Lh - r -rrD/r-r i (76) where r = inside radius of guard plate r = outside radius of top plate u D = thickness of the upper plate d = distance between top and bottom plates The effective area was 0.022858 sq. ft. compared to a nominal area of 0.022110 sq. ft. The distance between top and bottom plates was 0.0182 in. Upon heating the effective area increases because of expansion but so does the thickness of the gap between plates. The two expansion factors tend to compensate for each other. Using the thermal expansion coefficient of molybdenum for the area expansion and the thermal expansion coefficient of the sapphire balls for the gap expansion, the ratio of the gap expansion to the area expansion was such that between 900 and 14000F. s _ (0.998)(0.0182/12 ft.) 0.06621 ft A 0..022858 sq.ft.

94 with a maximum error at either temperature extreme of 0.02 percent, The constant expansion factor simplified the calculations. For each data set, the total thermal conductivity can be calculated from QtXs t Ant (72) where kt includes the contribution of radiation as well as thermal conductivity. Vacuum Runs Vacuum runs were made to determine the exact magnitude of the effects of radiation between plates and conduction through the spacers. Since the spacers offer nearly point contacts on at least one surface, the amount of energy transferred should be small in comparison with radiation effects at elevated temperatures. This was verified by Rothman (84). The total heat transferred by radiation is given by Qrad A F eFa (T1 T ) (37) rad, ea 1 2 when T1 T2, Equation 37 can be written as Qrad 4 oA F F (T ) t (78) radwhere At = TT (79) where At = T1-T2 (79)

95 In terms of an equivalent thermal conductivity, the radiation contribution can be expressed as Qrad. X k = rad. AAt (80) in which k = 4o X F F TF rad. s ea 1 (81) The radiation data are given in Figure 15 and Table IV in terms of krad For infinite parallel plates (13), F 1 (82) and F1 e 1 + 1 (83) E 1 E2 which becomes for plates of equal emissivity F = 1 e 2 e -1 (84) Therefore, krad, and e are related through Equations 81 and 84 and either quantity can be computed from a knowledge of the other. The first set of vacuum runs prior to the first nitrogen runs gave a value of krad 000089 Btu/hr.-ft.-~F. at 9340F. which rad t agreed closely with wh-at one would calculate using Goldsmith's (42)

0.018 o DATA SET I 016 DATA SETS 3,5,and 7 0.016 o DATA SETS 9,10, Il,and 12,| |v DATA SETS 24,and25 L. OXIDIZED / oa 0.014 /, II~~/ / $ aoln // / 0.012 // M>~~~~ / z 0.010 / H // / / 00~/ / / j 0.006 / / / / / - Figure 15. The Apparent Therma1 Conductivity'0..02.OUnder Vacuum ConditionsLEAN a.! -.000 80 90 100 10 // 20 Io CELL TEMPERATUR. "" Fi-r 15 Th ApaetTemlCnutvt Une Va ~u C ntANs

97 emissivity values for a clean molybdenum surface. Subsequent vacuum runs, data sets 3,5, and 7, gave values of krad considerably higher than one would predict for a clean surface. The surface had apparently been oxidized by the small amount of oxygen present in the nitrogen. In order to analyze and correlate the radiation data, Goldsmith's (42) emissivity data for oxidized molybdenum surfaces was used. For a surface which is partially oxidized, emissivity increases slightly with temperature. Using the same temperature effect as for the data of Goldsmith, a series of lines were drawn which represented emissivity versus temperature for various degrees of oxidization. From these curves, the dashed lines in Figure 15 were computed using Equations 81 and 84. The top line in Figure 15 for a partially oxidized surface represents a variation in emissivity from 0.260 at 9400F. to 0.385 at 13400F. The bottom line for a clean surface represents a variation in emissivity from 0.059 at 9400F. to 0o101 at 1340~F. The vacuum runs taken prior to the exposure of the cell surface to potassium revealed more or less a consistent pattern. The best curve through these data is shown as the upper smooth curve in Figure 15. There is a fair amount of scatter in these data. The temperature fluctuations are much more severe for low pressure runs because of the reduced heat transfer and the results are apt to be less consistent. The standard error of At for these data sets was in the order of 0.3~F. for a At of 3.0~F, After the

98 molybdenum surface had been exposed to potassium for some time the surface emissivity decreased. This was verified by the results obtained from data sets 24 and 25 which gave a consistent picture with a minimum of temperature fluctuations. The standard error in At was 0.2 for a At of 7.6 for data set 24 and 0.1 for a At of approximately 4.0 for data set 25, The results shown in Figure 15 indicated that the surface was nominally oxide free —giving values of krad comparable to those for a clean surface. Nitrogen Runs A series of nitrogen runs was made between 900 and 1200~F. to serve as a calibration of the cell and to check on the method of analysis. A summary of the operating conditions is given in Table V, The nitrogen pressure for the runs was approximately 1.5 atmospheres. The total rate of heat transfer in terms of a thermal conductivity was calculated from QtX k t s t = At (72) The thermal conductivity of nitrogen was then obtained from k = k -k c -krad. (85) Where krad was taken from the top solid line of Figure 15 at the cell temperature. Values of the thermal conductivity of nitrogen for the test conditions are given in Table V and in Figure 16, As

o,- 0.050 IL oz 0040 0 f~~~ ROTHMAN I 0040 0.030 O 0.020 0 0 "< 0.010 I — 0.000 800 900 1000 1100 1200 1300 1400 TEMPERATURE -OF Figure 16. Comparison of the Experimental Thermal Conductivity Results for Nitrogen with the Results of Rothman (84)

100 can be seen from Figure 16, there is very good agreement with the data of P.othman (84) at 1 atm. Rothman's data is in very close agreement with the data of other investigators. Since the thermal conductivity of gases increases with pressure about 1 percent per atmosphere in the range from roughly 1 mm to 10 atm., the data should be nominally 1/2 percent higher than the data of Rothman. If this correction were applied to the data in Figure 16, the agreement would be even better than indicated. The exceptionally good agreement of the experimental thermal conductivity values for nitrogen with the data of Rothman and others, demonstrated that the method of taking and analyzing the data was satisfactory. The standard error in the determination of At for the nitrogen data was approximately 6 percent. Except for the first nitrogen set, the average deviation from the data of Rothman is +1 percent. Potassium Runs The thermal conductivity of potassium at each test condition was obtained from Equations 72 and 85 as in the case of nitrogen. The results are given in Table VI and Figure 17. Because of the change in emissivity of the molybdenum surface during some intermediate potassium runs, there was some question of the value of krad. as given in Table VI for data sets 15-20 and especially those of data sets 15-17. For data sets 13 and 14, the apparent contribution of radiation k d to the total conduction,

101 0.012 LL 0, o 0.010 \ | \ 1000OF BOILER E I ~ TEMPERATURE U) 0.009 h9_ 800 ~F _u_ 0.008 ~-~.....E RATURE ra 9 U. 0.008: ~ _ _._._ —- MONOMER o ) 00 8'r 800 0F 0.006 BOILER a 900 ~F TEMPERATURE n IOO0OF z. 0.005. 9 0l.. 800 900 1000 1100 1200 1300 1400 CELL TEMPERATURE -OF Figure 17, Experimental Thermal Conductivity Results for Potassium Vapor

102 kt, was taken from the top solid line of Figure 15 for the partially oxidized surface. For data sets 21 and 26 through 32, k ad was taken from the bottom solid line of Figure 15 for the nominally clean surface at the cell temperature. For the intermediate runs, data sets 15-20, values of krad were predicted based on the knowledge that the surface emissivity would be changing with time such that in Figure 15 one would always go for a higher dashed line to a lower such line. Based upon the elapsed time between the start of data set 15 and the completion of data set 20, values of krad. were interpolated between the two solid lines of Figure 15 at the cell temperature. Except for the intermediate runs at a cell temperature of 11000F., the results agree closely with the balance of the data. Apparently there was a much greater change in the surface emissivity initially followed by a gradual change in time until the surface had stabilized. Except for the data in data sets 26 and 27, the mean standard error in At was approximately 1 1/2 percent for all the potassium data. The lower deviations as compared to the nitrogen data was due to improvements in furnace control and stability as a result of the experience gained in operating the system. The range of the cell null values was also substantially less because of improved control. During the runs for data sets 26 and 27, the small heater attached to the tube between the top valve and cell container was operated with a voltage drop of 40-60 volts to

103 prevent condensation of potassium in the line while running at conditions close to the saturation temperature in the vestibule area. These higher voltages resulted in greater temperature fluctuations in the cell - the standard error in At being 5 percent for data set 26 when a voltage drop of 40 volts was used and being 10 percent for data set 27 when a voltage drop of 60 volts was used. There is, as evidenced from the data in Figure 17 and predicted from fundamental considerations, a significant effect of pressure on the conductivity of potassium vapor. This effect is due to the heat of reaction involved with the association - dissociation reactions in potassium vapor as discussed in the section on thermal conductivity of gas mixtures in chemical equilibrium. Because of the significance of pressure, the data in Figure 17 were corrected to constant values of cell pressure which is equivalent to constant boiler temperatures. The magnitude of the corrections, listed in Table VII, were based on theoretical considerations. There is a fair amount of scatter in the potassium data as shown in Figure 17. In order to present a valid correlation of the data, it was felt that any correlating curves through the data for constant boiler temperatures would be consistent with kinetic theory. Kinetic theory was used in conjunction with the experimental data to determine the shape and the relative position of

Table VII. Correction of Experimental Values of Thermal Conductivity of Potassium Vapor to Constant Boiler Temperature and Comparison to Correlating Curve Correction Deviation Data T T k to constant from CorrelaSet Cell Boiler t T Boiler corr ting Curve Btu./hr.ft.-~F Btu./hr.ft.-~F Btu./hr.ft.-~F Btu./hr.ft.-~F 13 1010.1 805.6 0.00855 -0.00014 0, 00841 +0.00050 21 1003.6 798.3 0.00748 +0.00004 0.00752 -0,00039 28 1094.8 797.9 0.00765 +0.00002 0.00767 -0,00022 30 1190.7 817.5 0.00739 -0.00009 0.00730 -0.00074 32 1099.2 800.8 0.00842 -0.00001 0,00841 +0,00051 a =0 00056 14 1017.9 930.9 0.01017 -0.00082 0.00935 -0.00001 18 1189.9 899.7 0.00840 +0.00000 0.00840 -0.00020 26 1015.6 897.4 0.00821 +0.00l007 0.00828 -0.00109 27 1015.8 906.8 0.01099 -0.00022 0.01077 +0,00134 29 1097.4 885.4 0.00767 +0, 00013 0. 00780 -0,00098 31 1190.8 882.3 0,00925 +W0 0011 0.00936 +0.00075 a- 0.00095 19 1192,4 1003.4 0.00948 -0.00007 0.00941 -0.00036

105 the correlating isotherms through the data in Figure 17. Before kinetic theory could be used, the composition of the vapor and the force constants a and e for the Lennard-Jones potential had to be found. The composition of potassium vapor at various degrees of superheat was determined from Equations 67, 68 and 71 using the Ford Motor Company's GE 265 computer. The results are tabulated in Table VIII. As can be seen in Table VIII the mole fractions of the tetramer of potassium at the operating conditions in this investigation were negligible. This permitted the system to be treated as a binary mixture. Values of the force constants a and ~ were estimated from viscosity, vapor pressure, and normal boiling point data, From the saturated vapor viscosity data of Stefanov et al. (93), using the technique suggested by Hirschfelder, Curtiss and Bird (56), e/k and a12 were found to be 430~K and 5.32 A~, respectively. Since both the monomer and dimer are present for these data, the computed values of ~/k and a12 are taken as being the mean values for the binary mixture. An attempt was made to compute the force constants from the monomeric viscosity data of Stefanov et al. (93), but the method of Hirschfelder, Curtiss and Bird (56) would not give a convergent solution. From the second virial coefficient data of Ewing et al. (33), s/k and a12 were computed by a method

Table VIII. Equilibrium Vapor Composition of Potassium T T P X1 X X cell boiler atm.1 2 Mol. Wt. OF OF mol fractions 1000 800 0.0106 0.9938 0.0062 2x10-7 39.346 1000 900 0.0302 0.9825 0.0175 5x10-6 39.786 _8 1100 800 0.0106 0.9963 0.0037 5x10 39.246 1100 900 0. 0302 0.9896 0.0104 lx10-6 39.508 1100 1000 0.0745 0.9751 0.0249 2x10-5 40.077 1200 800 0.0106 0.9977 0.0023 lx10-8 39.192 1200 900 0.0302 0. 9935 0.0065 4x10-7 39.357 1200 1000 0.0745 0.9842 0.0158 5x10-6 39.721 1200 1100 0.1641 0. 9665 0.0335 5x10-5 40.417

107 outlined by Hirschfelder, Curtiss, and Bird (56). The values of E/k and a12 were found to be 3800K and 3.48 A', respectively. The normal boiling point and liquid potassium density data of Ewing et al. (33) gave values of s/k and a12 of 14300K and 4.60 A~, respectively, when calculated by the procedure suggested by Wilke and Lee (104). There is a significant difference in the values as computed from the three sets of data. Hirschfelder, Curtiss and Bird (56) indicate that the results from viscosity data are preferable for computing transport properties from kinetic theory. From the three sets of computed values of the force constants, the collision integral QD and the product a 2D were found and tabulated in Table IX for temperatures of 1000, 1100 and 1200~F. The, diffusion coefficients D12 for -these temperatures and vapor pressures corresponding to saturated vapor temperatures of 800, 900, 1000, and 1100~F. were computed from Equation 18. D = 0.001858 T3/2 [(M1+M2)/M1M2] 1/2 12 2 P12 D (18) For these same conditions and using the compositions listed in Table VIII, the heat of reaction contribution to conduction k was r determined from Equation 86. 2 p AH2 X1 X2 k =D - 2 l 2(86) which is RT RTm as Equation 2(86) which is the same form as Equation 28.

108 Table IX. Summary of Force Constants for Lennard-Jones 6-12 Potential Predicted from Experimental Results T T kT Q2 OF OK kT D 12 D Constants predicted from 2nd virial coefficient data (33 ) e/k = 3800K; a12= 3.48 A~ 1000 811.1 2.134 1.052 12.74 1100 866.7 2.281 1.028 12.45 1200 922.2 2.427 1.007 12.20 Constants predicted from saturated vapor viscosity data ( 93 ) s/k = 4300K; a12 = 5.32 AO 1000 811.1 1.886 1.096 31.02 1100.866.7 2.016 1.072 30.34 1200 922.2 2.145 1.050 29.72 Constants predicted from normal boiling point data ( 33 ) E/k = 14300K; o12 = 4.60 A~ 1000 811. L 0.567 1.930 40.84 1100 866.7 0.605 1.860 39.36 1200 922.2 0.645 1.805 38.19 Constants predicted from best fit with experimental thermal conductivity data C/k = 4000K; a12 = 5.17 A0 1000 811.1 2.028 1.070 28.55 1100 866.7 2.167 1.046 27.91 1200 922.2 2.306 1.025 27.35

109 The frozen thermal conductivity kf was computed from Equation 13 using the force constants listed in Table IX 1/2 -4 (T/M) k = 1.9891 x 10 vrs2__ (13) v The collision integral Q is tabulated in Reference (82) as a function of kT/e. The molecular weight of the monomer was used in Equation 13. This is believed to be justified because of the relatively small amount of the dimer which exists at the operating conditions —less than 2 percent. It also should be noted in Equation 15 that the increased molecular weight for the dimer and the Eucken factor are self-compensating which tends to reduce the effect of the molecular weight increase when estimating thermal conductivities of diatomic molecules. Further, it is not possible, to assign independent values of the force constants from the calculated values of a and e in Table IX. Finally, the method of averaging thermal conductivities (82) is such that with such a small fraction dimer the average thermal conductivity would be essentially equal to the thermal conductivity of the monomer at the same temperature. Therefore, the frozen thermal conductivity and the monomeric thermal conductivity are essentially identical for the operating conditions encountered in this investigation. The total effective thermal conductivity k of potassium vapor as estimated from kinetic theory for the various conditions was

110 computed from Equation 26. The results for the three sets of estimated force constants are given in Tables X, XI, and XII. These results were then compared with the data in Figure 17. As can be seen from the values of kc listed in Tables X, XI, and XII, the predicted values based on the viscosity data as recommended by Hirschfelder, Curtiss, and Bird (56) are in closest agreement with the experimental data although somewhat low. By interpolation from 2 plots of s/k and a12 versus a 12D for the three sets of values, it was possible to estimate values of the force constants which, when used as before, gave predicted values of k which fit the experimental data with a least mean squared deviation. The values of e/k and a12 were 4000K and 5.17 A', respectively,as indicated in Table IX. The values of kc predicted from the constants above are given in Table XIII and are-plotted in Figure 17. Taking the predicted values of k for the vapor pressures corresponding to saturated vapor pressures of 800, 900, and 1000~F,, the experimental potassium data were corrected to either a 800, 900 or 10000F. boiler temperature. The correction, the corrected values k and the deviation corr from the predicted values are given in Table VII. Standard deviations between the corrected and predicted values of k for the 800 and 9000F. boiler isotherms are 0.00056 and 0.00095 Btu/hr.-ft.-~F., respectively, which correspond to standard errors of k of 7 and 10 p percent.

Table X. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Deteimined from the Second Virial Coefficient 2 k 0+5 T T P - - 2 rl T T P a~~~~~~12 QD D12 D k kf cell Boiler cell sf r12 r c Atm. ~~~~sq. ft./hr. 1 O~~F O~F ~ Atm.'ft/r Btu Btu./hr.ft.-~F Btu./hr.ft.-~F Btu./hr.ft.-~F ft. 3-~F 1000 800 0.0106 12.74 241.50 0.84 0.00203 0.01570 0.01773 1000 900 0.0302 12.74 84.78 7.02 0.00595 0.01570 0.02165 1100 800 0.0106 12.45 273.10 0.41 0.00112 0.01661 0.01773 1100 9J0 0.0302 12.45 95.86 3.26 0.00313 0.01661 0.01974 1100 1000 0.0745 12.45 38.86 18.45 0.00717 0.01661 0.02378 1200 800 0.0106 12.20 305.80 0.21 0.00064 0.01748 0.01814 1200 900 0.0302 12.20 107.30 1.71 0.00183 0.01748 0.01931 1200 1000 0.0745 12.20 43.51 9.98 0.00434 0.01748 0.02182 1200 1100 0.1641 12.20 19.75 44.24 0. 00874 0.01748 0.02622

Table XI. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Determined from Saturated Vapor Viscosity Data k 10+5 r xlO 2 D 12D D 12 k k k cell Boiler cell 12 Btu r fc ~F ~F Atm. sq.ft./hr. ft3 0F Btu./hr.ft.-~F Btu./hr.ft.-~F Btu./hr.ft.-~F 1000 800 0.0106 31.02 99.20 0.84 0.00083 0.00645 0.00728 1000 900 0.0302 21.02 34.82 7.02 0.00244 0.00645 0.00889 1100 800 0.0106 30.34 112.02 0.41 0.00046 0.00682 0.00728 1100 900 0.0302 30.34 39.32 3.26 0.00128 0.00682 0.00810 1100 1000 0.0745 30.34 15.94 18.45 0.00294 0.00682 0.00976 1200 800 0.0106 29.72 125.52 0.21 0.00026 0.00718 0.00744 1200 900 0.0302 29.72 44.06 1.71 0.00075 0.00718 0.00793 1200 1000 0.0745 29.72 17.86 9.98 0.00178 0.f00718 0.00896 1200 1100 0.1641 29.72 8.11 44.24 0.00359 0.00718 0.01077

Table XII. Predicted Values for the Thermal Conductivity of Potassium Vapor Based Upon Lennard-Jones Force Constants Determined from Normal Boiling Point Data 2 krk x10+5 2 r xlO T T P aD12 D12 k kf k cell Boiler cell D 12 D12 r f`F OF Atm. Btu./hr.ft.-~F Btu./hr.ft-~F Btu./hr.ft.-~F 1000 800 0.0106 40.84 75.35 0.84 0.00063 0.00490 0,00553 1000 900 0.0302 40.84 26.45 7.02 0.00186 0.00490 0.00676 1100 800 0.0106 39.36 86.35 0.41 0.00035 0.00525 0.00560 1100 900 0.0302 39.36 30.31 3.26 0.00099 0.00525 0.00624 1100 1000 0.0745 39.36 12.29 18.45 0.00223 0.00525 0.00748 1200 800 0.0106 38.19 97.68 0.21 0.00021 0.00558 0.00579 1200 900 0.0302 38.19 34.29 1.71 0.00059 0.00558 0.00617 1200 1000 0.0745 38.19 13.90 9.98 0.00139 0.00558 0.00697 1200 1100 0.1641 38.19 =6,31 44.24 0.00279 0.00558 0.00837

Table XIII. Predicted Values for the Thermal Conductivity of Potassiun Vapor Based Upon Lennard-Jones Force Constants Wi ich Give a Least Squared Deviation Fit with the Experimental Data k +5~ k T T P 2 k~~~~~~~~ ~ ~~ ~ ~~~~r x10' k kf kT T P 2 D r f c cell Boiler cell 012% 12 D12 Btu./hr.ft.-OF Btu./hr.ft-0F Btu./hr.ft.-1 F 0F OF Atm. sq.ftr./hr. Btu ft. -3F 950 800 0.0106 28. 90 101.05 1.19 0.00120 0.00684 0.00804 950 800 0.0106 28.90 0.~~~000684 0.0104, 950 900 0.0302 28.90 35.47 10.19 0.00361 1000 800 0.0106 28. 55 107.80 0.84 0.00091 0.00702 0.00793 1000 900 0.0302 28.55 37.830.00702 0.0096 37.83 7.02 0.002663 00079 1050 800 0. 0106 28.21 114.73 0.61 0.00070 0.00723 0.0079 1050 800 0.0106 28.21 ~~~0.00723 0.00909 1050 900 0.0302 28.21 40.27 4.62 0.00186 0.00723 0.0190 1050 1000 0.0745 28.21 16.32 24.50 0.00400 12138.4 0.005 000741 0.00791 1100 800 0.0106 27.91 121.78 0.41 0.00741 0.00 1100 900 0.0302 27.91 42.74 3.26 0.00139 0.00741 0.008 0.00741 0.01061 1100 1000 0.0745 27.91 17.33 18.45 0.00320 0.00760 ~ 0.00799 1150 800 0.0106 27.62 129.01 0.30 0.00039 0.00760 0.0079 1150 900 0.0302 27.62 45.28 2.35 0.00106 0.00760 0.008 1150 1000 0.0745 27.62 18.36 13.48 0.00247 1200 800 0.0106 27.35 136.40 0.21 0.00029 0.00779 0.00808 1200 900 0.0302 27.35 47.87 1.71 0.00082 0.00779 0.00861 1200 1000 0.0745 27.35 19.41 9.98 0.00194 0.00779 0.00973 1200 1100 0.1641 27.35 8.81 44.24 0. 00390 0.00779 0.01169 1250 800 0.0106 27.07 144.09 0.15 0.00022 0.00797 0.00819 1250 900 0.0302 27.07 50.57 1.25 0.00063 0.00797 0.00860 1250 1000 0.0743 27.07 20.50 7.74 0.00159 0.00797 0.00956

CHAPTER VI DISCUSSION OF RESULTS The thermal conductivity of potassium vapor in the temperature range of 1000 to 1200~F. and the pressure range of 0.01 to 0.075 atmospheres is-given- in Figure 17. There is as predicted from theory, a significant effect of pressure on the thermal conductivity of potassium vapor. This is caused by the heat of reaction associated with changes in equilibrium composition with pressure and temperature. The mean values presented in Figure 17, for saturated pressures corresponding to 800, 900 and 10000F. are estimated to have an accuracy of + 10 percent. Kinetic theory was used to establish the mean values through the experimental data. Although limited in absolute accuracy kinetic theory does provide tremendous insight into the relative effects of pressure and temperature once the absolute magnitude of the thermal conductivity is established by experimental results. Some will argue that the Lennard-Jones (6,12) potential as used for the intermolecular force potential does not apply to potassium. If, however, the force constants are obtained from experimental data for the same temperature range as the values to be predicted, the theory should give a reasonable approximation to the effect of pressure and temperature providing the temperature range is not too great. As can be seen from Equationsl3 and 18, the most 115

116 significant consequence-in the choice of the intermolecular force potential is in the values of the two collision integrals which are only slightly a function of temperature. This temperature effect of the collision integrals is small when compared to the effects of the absolute temperature in the theory. The variation of the vapor composition for the operating conditions of this investigation are also quite small which support the validity of the theory. The values of the monomeric vapor (or the frozen thermal conductivity of the vapor at lower pressures) estimated from the theory and the experimental results agree closely with the experimental data of Stefanov et al. (93) and the theoretical estimates of Weatherford et al. (102) over the temperature range of this investigation. A comparison of the data is given in Figure 18. The maximum deviation- is -6 percent when compared to the results of Stefanov at 12000F. It should be noted that the thermal conductivity of the monomeric vapor and the frozen thermal conductivity of the vapor are not synonymous except for low pressures where the equilibrium composition consists predominately of the monomer. The maximum deviation in the total effective thermal conductivity when compared to the data of Stefanov is -8 percent. Stefanov indicated a maximum average error in his data of 20 percent. There were several factors which could have contributed to the scatter in the experimental data. The most significant of these are those related to the temperature variations and fluctuations in the furnace during operation. The standard error between the

0.0095 THIS INVESTIGATION 0.0090 - STEFANOV (93) WEATHERFORD (102).LL / * 0.0085 - LL -: 00080 / >>I ~~~/ 0.0070 07/ 0.006570 0060 0.0060 900 1000 1100 1200 1300 1400 800 900 1000 1100 1200 1300 1400 VAPOR TEMPERATURE- OF Figure 18, Comparison of Thermal Conductivity Data for Potassium Monomer with Results of Stefanov (93) and Weatherford (102)

118 data and correlating lines for the temperature difference between plates versus null for the potassium runs as illustrated in Figure 14 were on the average 1.5 percent. The standard error for data sets 26 and 27 was higher because of the high voltage drop across the auxiliary heater in the furnace vestibule. Since the standard error applies to both the isothermal and heated top plate lines, the total error in the mean temperature difference At is estimated to be 3 percent. The average null values are estimated to be accurate to 0.20F. Upon interpolation for At as indicated in Chapter IV, this could lead to an additional error in the At of approximately 4 percent. Any thermocouple drift or errors in reading the potentiometer would be included in the estimated errors of the At and the null temperature. The measured values of the voltage drop across the heater and the standard 1 ohm shunt are accurate to 0.2 percent —with the greatest error being in the voltage drop across the heater. A 10 percent error in the estimate of the lead wire resistance would represent only a 1.4 percent error in the calculation of the value of the heat generated in the top plate heater because of the relative magnitude of the resistances. The actual error in the amount of heat generated by the top plate heater is estimated to be less than 0,5 percent. Any additional effect on the calculated value of the heat input Qt due on imbalance between the top plate temperature and the guard plate temperature should already be accounted for in the estimate of the null error.

119 The only additional factors which come into the calculation of the total heat transfer from -Equation 72 are the area and the plate spacing. Both are accurate to within 1 percent. The estimated errors in At, null, Qt' A, and Xs were used as indicated by Equation 72 to obtain the maximum estimated error in the total conductivity kt. The maximum error of k was found to be 9.8 percent. The pressure in the thermal conductivity cell was determined by measuring the temperature of the liquid potassium in the potassium. boiler with a thermocouple and then computing the vapor pressure from the vapor pressure data of Ewing et al. (33). Errors in the.thermocouple readings could cause a deviation of 1 to 2 percent in the reported values as shown in Figure 17. Two additional potential sources of difficulty were the valve between the cell-and boiler and the surface condition of the liquid potassium. Temporary plugging of the valve due to condensation or liquid surface oxidation could cause variations in the vapor pressure from the predicted values. Since the radiation contribution must be subtracted from the total apparent thermal conductivity to obtain the actual value of k the errors in radiation values are extremely important. Based c on the results presented in Figure 15 and the standard errors in the At's, the radiation data for the partially oxidized surface and the nominally clean surface are estimated to be accurate to within 10 percent. In terms of the error to the effective thermal conductivity kc, the radiation errors represent possible errors in

120 k of 9 percent and 2,5 percent for the partially oxidized surface c and the nominally clean surface, respectively. As it is unlikely for all the errors to occur at the same time in a way which maximizes the absolute error, an experimental error of + 10 percent seems reasonable. This is also consistent with the deviations from the least squared deviation isotherms predicted from kinetic theory. Estimates of the temperature jump caused by the accomodation coefficient of the cell surface calculated from Equation 22 indicated that the measured thermal conductivities could be lower than the actual value of the thermal conductivity because of the small distance between plates. For a boiler temperature of 8000F. or a pressure of 0.0106 atmospheres, the estimate is 2.5 to 5.9 percent lower for accomodation coefficients of 1.0 and 0.57, respectively. At a boiler temperature of 900~F. or a pressure of 0.0302 atmospheres the estimate is 1 to 2.5 percent lower for accomodation coefficients of 1.0 and 0.57, respectively. For a given vapor temperature, kinetic theory would indicate, from Equations 13, 18, and 86, that the difference in the effective thermal conductivity kc between two different pressure levels is caused by the difference in the heat of reaction effect kr because of the change in the equilibrium composition. The products D12P, 2 12 D, and a12 v remain constant independent of pressure. Since the experimental data show good correlation with respect to the

121 deviation from the predicted values in Table VII (no bias), it is concluded that any reduction in thermal conductivity because of the surface temperature jump is small and consistent with the higher values of the accomodation coefficient.

CHAPTER VII CONCLUSIONS AND RECOMMENDATIONS The guarded top plate, parallel plate thermal conductivity cell developed and used in this investigation is a satisfactory cell for accurate measurements of the thermal conductivity of alkali metal vapors at elevated temperatures. This steady state method requires longer operating periods to obtain experimental data compared to the transient techniques, but does have the advantage that no bare electrical wires have to be insulated from the cell walls in the presence of alkali metal vapors as is true for the hot wire cell and the dynamic probe method. There are several equipment changes which would improve the operation of the cell and would greatly reduce the time necessary to take the data. There should be separate furnaces or constant temperature baths for the cell and the liquid metal boiler. High temperature molten salt baths would be preferable but furnaces which are insulated from all sides and both ends would be satisfactory. Furnace temperature control is extremely important. Ideally the temperature variation should not exceed 0.2 to 0.30F. during the period of a day. The furnace temperature control in this investigation-was inadequate and as a result of the temperature variations and fluctuations it frequently took 4 or 5 days to obtain a single data set. 122

123 The vapor line connecting the cell and the boiler, located in separate furnaces, should have an inside diameter of at least 1/2 inch and should contain an appropriately large high temperature bellows valve. Connections to the vacuum system should be made to this line between the cell and bellows valve. This would eliminate potential problems of vapor condensation with any condensation occurring in the lines below the cell where no harm would result. The vacuum line should contain a large high temperature bellows valve placed as close as possible to the vapor line. All the lines and the valve bodies should be thoroughly insulated and heated as necessary. Chromel-alumel thermocouples were used in the cell. No significant thermocouple drift was ever apparent during the investigation or at least none could be distinguished from the furnace temperature variations. There are some changes in the thermocouples as a result of bending when the cell was fabricated. The magnitude of the change could not be accurately determined because the furnace was incapable of maintaining an isothermal condition throughout the length of the cell container. Chromel-alumel thermocouples do generate a higher emf/~F. than platinum - platinum rhodium thermocouples, but the possible advantage of chromel-alumel thermocouples because of the greater accuracy in reading is balanced by the possible drift. In future investigations platinum - platinum rhodium thermocouples are recommended.

124 A high temperature corrosion resistance pressure transducer would be very beneficial for measuring the pressure in the cell. This would provide an independent check on the conditions in the cell in the- event of oxidation of the liquid potassium surface or plugging of —-the valve between cell container and boiler.

APPENDIX A ORIGINAL DATA Table A.i Original Data for Data Set 1 —Vacuum Runs at 9430F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Volts Amps my my my my my my ISOTHERMAL 199465 20.5570 19.9231 20.6471 20.4644 19.7936 21.6574 199466 20.7126 20.0838 20.7845 20.6112 19.9052 21.6758 199467 20.7450 20.0910 20.8162 20.6518 19.9448 21.7463 199468 20.5251 19.8782 20.5933 20.4157 19.7490 21.6184 199469 20.7022 20.0492 20.8123 20.6142 19.9100 21.8344 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.0 VOLTS 199472 21.0702 20.1873 21.1557 20.9996 20.3167 22.0372 1.191 0.03612 199474 21.1768 20.2961 21.2387 21.0780 20.4066 22.0544 1.179 0.03571 199475 20.8261 19.9685 20.9018 20.7595 20.0597 21.6659 1.227 0.03729

Table A.2 Original Data for Data Set 2 —Nitrogen Runs at 9250F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 mv mv mv mv mv mv Volts Amps ISOTHERMAL 199488 20.4485 20.5556 20.5200 20.2474 18.8421 21.4979 199489 20.8595 20.9854 20.9632 20.6776 20.2117 21.9881 199490 20.7966 20.8936 20.8531 20.5316 20.1897 21.9828 199491 20.5527 20.6775 20.6662 20.3835 19.9307 21.6702 199494 20.2001 20.3066 20.2904 20.0176 19.5609 21.3039 199495 20.1975 2.0.2969 20.2847 20.0003 19.5852 21.3105 a 199497 20.2669 20.3753 20.3589 20.0756 19.6689 21.3677 199498 20.2886 20.3996 20.4147 20.1401 19.6910 21.4079 199499 20.5126 20.6285 20.6800 20.4025 19.8939 21.6583 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.8 VOLTS 205505 20.4449 20.4974 20.5400 20.2504 19.8576 21.4577 3.517 0.10777 205506 20.4407 20.5109 20.5511 20.2618 19.8104 21.4662 3.500 0.10709 205507 20.4970 20.5709 20.6541 20.3982 19.8762 21.5374 3.480 0.10588 205508 20.5309 20.5863 20.6320 20.3463 19.9320 21.5550 3.490 0.10614 205509 20.5505 20.6132 20.6570 20.3870 19.9624 21.5581 3.500 0.10673 205511 -20.4971 20.5620 20.6496 20.3739 19.8668 21.5301 3.495 0.10666

Table A.3 Original Data for Data Set 3 —Vacuum Runs at 10320F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Volts Amps mv my mv mv mv mwx ISOTHERMAL 205517 22.9755 22.1076 23.0787 22.1921 22.1630 24.0144 205521 23.0183 22.1492 23.1310 22.9731 22.2047 24.0491 205522 22.9860 22.1002 23.0809 22.9262 22.1655 24.0165 M 205523 22.9900 22.1084 23.0900 22.9533 22.1778 24.0266 205524 22.9859 22.0997 23.0949 22.9433 22.1753 24.0251 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 3.05 VOLTS 205532 23.0183 22.0505 23.0857 22.9238 22.1884 23.9835 1.800 0.05615 205533 23.0455 22.0819 23.1360 22.9938 22.2242 23.9994 1.810 0.05628 205534 23.0449 22.0825 23.1184 22.9708 22.2170 23.9921 1.810 0.05651 205536 23.0548 22.0762 23.1244 22.9808 22.2283 24.0051 1.810 0.05606 205540 23.0702 22.1038 23.1741 23.0199 22.2649 24.0045 1.810 0.05624

Table A.4 Original Data for Data Set 4 —Nitrogen Runs at 10270F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 my myv y myv y mVol ISOTHERMAL 205541 22.8990 22.9978 23.1288 22.8321 22.2412 24.0749 205542 22.9099 23.0068 23.0941 22.8137 22.2576 24.0823 205543 22.9336 23.0335 23.1187 22.8459 22.2824 24.0769 205544 22.9411 23.0345 23.1107 22.8300 22.2740 24.0942 205545 22.9355 23.0357 23.1167 22.8407 22.2752 24.0901 205546 22.9000 22.9943 23.1111 22.8274 22.2087 24.0573 205547 22.9370 23.0355 23.1251 22.8413 22.2760 24.0949 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.95 VOLTS 205702 22.9230 22.9702 23.1358 22.8508 22.2508 24.0338 3.605 0.11089 205703 22.9350 22.9824 23.1442 22.8564 22.2858 24.0648 3.580 0.11976 205704 22.9147 22.9655 23.1204 22.8332 22.2653 24.0445 3.600 0.11067

Table A.5 Original Data for Data Set 5 —Vacuum Runs at 11170F. RUN THERMOCOUPLES ______ ______ ______ ______ ______ ______ ______ ______HEATER 3 4 5 6 7 8 my my my m m my Volts mps ISOTHERMAL 205710 25.1948 24.4017 25.2847 25.1441 24.3508 26.2737 205712 25.0308 24.2373 25.0876 24.9258 24.1796 26.1206 205713 25.0014 24.1717 25.0665 24.9563 24.1597 26.0553 205715 25.0540 24.2708 25.1255 24.9687 24.1959 26.1220 205716 24.9398 24.1225 24.9910 24.8820 24.0837 26.0315 205717 24.9824 24.1707 25.0653 24.9459 24.13'-9 26.0850 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 3.15 VOLTS 205718 25.0489 24.1718 25.1237 25.0282 24.1978 26.0719 1.860 0.05760 205719 25.0510 24.1824 25.1364 25.0308 24.2061 26.0558 1.870 0.05785 205720 25.0535 24.1770 25.1419 25.0311 24.2143 26.0820 1.860 0.05755 205721 25.0483 24.1630 25.1338 25.0288 24.2081 26.0752 1.860 0.05753 205722 25.0642 24.1981 25.1702 25.0318 24.2163 26.1118 1.815 0.05636 205723 25.0775 24.2150 25.1784 25.0527 24.2405 26.1240 1.830 0.05685

Table A.6 Original Data for Data Set 6 —Nitrogen Runs at 11130F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Volts Amps my my my my my my ISOTHERMAL 205724 24.9095 24.9797 25.1239 24-.8252 24.2194 26. 1156 205725 24.9528 25.0340 25.1718 24.8852 24.2673 26. 1514 205726 24.9038 24.9795 25.1215 24.8340 24.2098 26.0938 205727 24.9242 24.9973 25.1542 24.8722 24.2204 26.1100 205728 24.9217 24.9955 25.1419 24.8547 24.2228 26.1142 205729 24.9605 25.0328 25.1756 24.8908 24.2520 26.1515 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.95 VOLTS 205732 24.9587 24.9911 25.1788 24.8866 24.2814 26.1170 3.570 0.10967 205733 24.9464 24.9737 25.1645 24.8722 24.2427 26.1048 3.590 0.11021 205734 24.9334 24.9622 25.1479 24.8559 24.2330 26.0921 3.590 0.10981

Table A.7 Original Data for Data Set 7 —Vacuum Runs at 12130F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Volts Amps my my my Tmyv myV my ISOTHERMAL 205735 27.2570 26.6156 27.3619 27.2032 26.4027 28.3616 205736 27.2594 26.6152 27.3644 27.2119 26.4023 28.3581 205737 27.2190 26.5633 27.3183 27.1694 26.3581 28.3321 205739 27.2738 26.6184 27.3794 27.2257 26.4123 28.3854 205741 27.2336 26.5859 27.3510 27.1990 26.3569 28.3530 205743 27.2956 26.6518 27.4277 27.2665 26.4228 28.4161 205744 27.3045 26.6562 27.4372 27.2771 26.4362 28.4255 205745 27.2313 26.5625 27.3286 27.1809 26.3473 28.3618 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.6 VOLTS 205600 27.3431 26.6168 27.4783 27.3286 26.4789 28.3839 2.470 0.07584 205601 27.3564 26.6308 27.5005 27.3444 26.4712 28.4147 2.385 0.07324 205602 27.3656 26.6522 27.5142 27.3492 26.4849 28.4177 2.395 0.07365 205605 27.3303 26.6277 27.4443 27.2651 26.4228 28.3815 2.410 0.07431 205606 27.3158 26.5899 27.4430 27.2604 26.4020 28.3709 2.413 0.07447 205607 27.2634 26.5457 27.3516 27.1419 26.3508 28.3339 2.420 0.07461

Table A.8 Original Data for Data Set 8 —Nitrogen Runs at 12130F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Volts Amps my my my my my my ISOTHERMAL 205608 27.1575 27.1987 27.3242 27.0632 26.3990 28.3922 205609 27.2425 27.2782 27.4044 27.1284, 26.4995 28.4825 205610 27.2658 27.3029 27.4265 27.1513 26.5213 28.4947 205611 27.1894 27.2284 27.3329 27.0580 26.4520 28.4113 205612 27.1986 27.2358 27.3761 27.1091 26.4386 28.4381 205613 27.2039 27.2383 27.4086 27.1554 26.4129 28.4363 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.8 VOLTS 205614 27.3300 27.3301 27.4996 27.2315 26.5713 28.4847 3.510 0.10781 205615 27.2833 27.2862 27.4539 27.1849 26.5320 28.4437 3.540 0.10875 205616 27.3365 27.3367 27.4985 27.2318 26.5748 28.4866 3.505 0.10737 205617 27.3482 27.3461 27.5046 27.2349 26.5913 28.4981 3.505 0.10779 205619 27.2848 27.2823 27.4119 27.1337 26.5354 28.4251 3.500 0.10721 205620 27.2467 27.2442 27.3889 27.1176 26.4836 28.4050 3.510 0.10768 205621 27.2735 27.2717 27.4250 27.1690 26.4922 28.4337 3.510 0.10793 205622 27.2635 27.2587 27.4007 27.1252 26.4882 28.4160 3.510 0.10750

Table A.9 Original Data for Data Set 9 —Vacuum Runs at 10080F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 mv mn my my my my Volts Amps ISOTHERMAL 205626 22.4422 22.2485 22.1940 22.0796 21.5189 22.6509 205627 22.3734 22.1731 22.1142 22.0180 21.4500 22.5418 205628 22.3421 22.1386 22.0932 21.9941 21.4363 22.5156 205629 22.3138 22.1101 22.0639 21.9614 21.3948 22.5051 205630 22.3948 22.1962 22.1471 22.0423 21.4783 22.5818 205631 22.4013 22.2010 22.1514 22.0506 21.4866 22.5759 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.0 VOLTS 205638 22.4758 22.1878 22.2261 22.1297 21.5732 22. 5796 1.800 0.05507 205639 22.5114 22.2245 22.2549 22.1607 21.5888 22.6070 1.800 0.05500 205640 22.5388 22.2561 22.2868 22.1901 21.6169 22.6384 1.800 0.05497 205641 22.4377 22.1519 22.1957 22.0946 21.5373 22.5440 1.800 0.05514 205642 22.3914 22.1065 22.1401 22.0446 21.4687 22.4883 1.800 0.05519

Table A.10 Original Data for Data Set 10 —Vacuum Runs at 11130F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 mv my mv mv y m mv Volts Amps ISOTHERMAL 205644 24.7385 24.6095 24.4005 24.2666 23.7197 24.6645 205645 24.7933 24.6676 24.4615 24.3291 23.7686 24.7202 205646 24.8700 24.7472 24.5416 24.4093 23.8622 24.8015 205647 24.9350 24.8102 24.5973 24.4741 23.9149 24.8495 205648 24.9121 24.7939 24.5842 24.4536 23.8957 24.8226' 205649 24.8820 24.7644 24.5438 24.4179 23.8532 24.7808 205550 24.7870 24.6706 24.4666 24.3450 23.7658 24.6870 205551 24.7889 24.6719 24.4560 24.3253 23.7637 24.7054 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 3.9 VOLTS 205556 24.9378 24.7625 24.6409 24.5097 23.9269 24.7781 1.900 0.05779 205557 24.8968 24.7219 24.6087 24.4806 23.8856 24.7361 1.900 0.05780 205558 24.8514 24.6698 24.5464 24.4458 23.8209 24.6731 1.900 0.05782 205559 24.9200 24.7536 24.6314 24.4919 23.9191 24.7906 1.900 0.05782 205560 25.0221 24.8431 24.7358 24.6075 24.0093 24.8576 1.900 0.05771 205561 25.0431 24.8691 24.7438 24.6198 24.0291 24.8713 1.900 0.05770 205562 24.9635 24.7885 24.6722 24.5446 23.9582 24.8147 1.900 0.05773

Table A.l1 Original Data for Data Set 11 —Vacuum Runs at 12050F. RUN THERMOCOUPLES 3 4 5 6 7 8 3_ ul Volts Amps ISOTHERMAL 205564 27.0069 26.9530 26.7191 26.5797 25.9271 26.8754 205565 27.0567 27.0033 26.7688 26.6244' 25.9826 26.9218 205566 27.0922 27 0407 26.8032 26.6563 26.0240 26.9616 205567 27.0798 27.0205 26.7894 26.6458 26.0013 26.9203 205568 26.9974 26.9318 26.6891 26.5496 25.9181 26.8267 205569 26.9687 26.9139 26.6625 26.5191 25.8982 26.8304 205570 26.9255 26.8626 26.6240 26.4885 25.8508 26.7706 HEATED TOP PLATE - GUARD VOLTAGE = 4.5 VOLTS 205571 27.0071 26.8640 26.7167 26.6135 25.9024 26.7803 2.30 0.06965 205572 27.1400 27.0034 26.8618 26.7145 26.0621 26.9030 2.30 0.06954 HEATED TOP PLATE - GUARD VOLTAGE = 5.0 VOLTS 205573 27.1400 27.0034 26.8618 26.7145 26.0621 26.9030 2.30 0.06954 205574 27.1776 27.0409 26.8972 26.7617 26.0926 26.9210 2.30 0.06951 205575 27.1676 27.0284 26.8818 26.7502 26.0875 26.9080 2.30 0.06953 205576 27.1769 27.0422 26.8969 26.7559 26.1160 26.9252 2.30 0.06953 205577 27.2550 27.1258 26.9437 26.8192 26.1503 26.9881 2.30 0.06971 205578 27.1862 27.0467 26.8698 26.7384 26.0921 26.9245 2.30 0.06972 205579 27.1992 27.0635 26.8862 26.7459 26.1185 26.9555 2.30 0.06971 205580 27.1972 27.0773 26.9006 26.7613 26.1124 26.9812 2.30 0.06975 205581 27.1920 27.0538 26.8626 26.7321 26.0988 26.9334 2.30 0.06974

Table A.12 Original Data for Data Set 12 —Vacuum Runs at 13050F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 mv my my my my mv Volts Amps ISOTHERMAL 205582 29.1300 29.1149 28.8170 28.6874 28.0108 28.9498 205585 39.3198 29.3022 28.9780 28.8594' 28.1848 29.0904 205586 29.2962 29.2811 28.9572 28.8372 28.1657 29. 0726 205587 29.3112 29.3022 28.9833'28.8484 28.1884 29.0955 205588 29.3108 29.2949 28.9673 28.8340 28.1797 29. 0812 205589 29.4244 29.4153 29.0869 28.9590 28.2775 29.1996 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.0 VOLTS 205590 29.4831 29.4130 29.1720 29.0367 28.3310 29.2003 2.30 0.06925 205591 29.5542 29.4887 29.2260 29.0878 28.3980 29.2572 2.30 0.06935 205592 29.5455 29.4853 29.2487 29.1041 28.3870 29.2562 2.30 0.06937 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.25 VOLTS 205593 29.4393 29.3520 29.1254 29.0053 28.3060 29.1364 2.30 0.06916 205594 29.4058 29.3152 29.0925 28.9652 28.2757 29.1031 2.30 0.06913 205595 29.4016 29.3161 29.0820 28.9415 28.2706 29.1067 2.30 0.06916 205596 29.4480 29.3582 29.1150 28.9849 28.3070 29.1227 2.30 0.06912 205597 29.4170 29.3323 29.0972 28.9636 28.2849 29.1109 2.30 0.06913 205598 29.4244 29.3521 29.1039 28.9623 28.2780 29.1302 2.30 0.06916 205599 29.4188 29.3426 29.0942 28.9)29 28.2788 29.1090 2.30 0.06916

Table A.13 Original Data for Data Set 13 —Potassium Runs at 10100F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv mv mv - Volts Amps ISOTHERMAL 206004 22.3240 22.5324 22.0849 21.9963 21.3558 22.2892 17.6139 206005 22.3542 22.5616 22.1129 22.0302 21.3966 22.3100 17.6224 206006 22.3858 22.5957 22.1463 22.0626 21.4284 22.3458 17.6803 206007 22.3688 22.5791 22.1206 22.0441 21.4002 22.2996 17.6956 206008 22.3798 22.5925 22.1384 22.0576 21.4157 22.3219 17.7321 206009 22.3256 22.5391 22.0814 22.0058 21.3652 22.2629 17.6721 HEATED TOP PLATE - GUARD VOLTAGE = 8.2 VOLTS 206010 22.5925 22.6322 22.3620 22.2725 21.6436 22.3363 17.6212 3.60 0.11064 206011 22.5837 22.6225 22.3535 22.2635 21.6338 22.3285 17.6043 3.60 0.11066 HEATED TOP PLATE - GUARD VOLTAGE = 7.6 VOLTS 206013 22.5155 22.5683 22.2774 22.1915 21.5515 22.2911 17.5834 3.60 0.11031 206014 22.5689 22.6237 22.3310 22.2458 21.6136 22.3408 17.6438 3.60 0.11023 206015 22.5898 22.6449 22.3514 22.2698 21.6334 22.3571 17.6647 3.60 0.11022 206016 22.5897 22.6434 22.3493 22.2700 21.6378 22.3447 17.6648 3.60 0.11015 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.3 VOLTS 206017 22.5198 22.5828 22.2804 22.2019 21.5720 22.2948 17.6336 3.60 0.10990 206018 22.5010 22.5654 22.2621 22.1844 21.5579 22.2796 17.6218 3.60 0.10994 206019 22.5976 22.6638 22.3592 22.2807 21.6484 22.3796 17.7340 3.60 0.10994 HEATED TOP PLATE - GUARD VOLTAGE = 6.9 VOLTS 206020 22.5483 22.6247 22.2978 22.2254 21.5891 22.3285 17.6909 3.60 0.10997 206021 22.5438 22.6185 22.2956 22.2251 21.5888 22.3253 17.6911 3.60 0.10998 206022 22.5380 22.6145 22.2907 22.2167 21.5812 22.3227 17.6890 3.60 0.11001 206023 22.5424 22.6204 22.2964 22.2217 21.5820 22.3281 17.6938 3.60 0.11001 206024 22.5412 22.6167 22.2936 22.2198 21.5831 22.3279 17.6742 3.60 0.11001

Table A.14 Original Data for Data Set 14 —Potassium Runs at 10180F. RUN THERMOCOUPLES HEATER 3 4 5' 6 7 8 Boiler my my my my my my my VOLTS A]PS ISOTHERMAL 206025 22.4604 22.9492 22.1235 22.1289 21.4245 22.0232 20.5790 206026 22.4984 22.9876 22.1637 22.1702 21.4749 22.0691 20.6024 206027 22.4931 22.9817 22.1538 22.1620 21.4556 22.0488 20.5786 206028 22.4903 22.9806 22.1529 22.1611 21.4518 22.0527 20.5983 206029 22.5032 22.9947 22.1657 22.1711 21.4543 22.0642 20.6135 206030, 22.4921 22.9831 22.1529 22.1597 21.4329 22.0427 20.6034 206031 22.6291 23.1306 22.2890 22.2974 21.5903 22.1888 20.7585 cc 206032 22.6262 23.1181 22.2832 22.2945 21.5844 22.1697 20.7104 HEATED TOP PLATE - GUARD HEATER VOLTAGE= j6.9 VOLTS 206035 22.6622 23.0159 22.3215 22.3332 21.6318 22.0781 20.5318 3.60 6( 1l046 206036 22.6887 23.0425 22.3448 22.3604 21.6666 22.0948 20.5496 3.60 0.11038 206037 22.6784 23.0301 22.3337 22.3508 21.6553 22.0807 20.5317 3.60 0.11037 206038 22.6793 23.0319 22.3334 22.3509 21.6631 22.0823 20.5372 3.60 0.11035 206039 22.6820 23.0345 22.3366 22.3528 21.6647 22.0864 20.5449 3.60 0111040 206040 22.6674 23.0169 22.3217 22.3391 21.6501 22.0711 20.5198 3.60 0.11040 206041 22.8010 23.1702 22.4483 22.4651 21.7573 22.2216 20.6910 3.60 0.11046 206042 22.7976 23.1659 22.4445 22.4650 21.7522 22.2108 20.6705 3.60 0.11052 206043 22.7906 23.1606 22.4449 22.4647 21.7555 22.2140 20.6908 3.60 0.11017 206044 22.7971 23.1617 22.4.496 22.4715 21.7644 22.2178 20.6829 3.60 0.11016 206045 22.8051 23.1748 22.4626 22.48ll 21.7739 22.2345 20.7129 3.60 0.11017

Table A.15 Original Data for Data Set 15 —Potassium Runs at 1106~F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv m mv Volts Amps ISOTHERMAL 206046 24.7299 24.7550 24.5273 24.3803 23.7657 24.8970 17.75 76 206047 24.7405 24.7670 24.5385 24.3954 23.7626 24.9049 17.7988 206048 24.7357 24.7620 24.5321 24.3880 23.7625 24.8967 17.7869 206049 24.7357 24.7636 24.5327 23.3883 23,7505 24.8986 17.7959 206050 24.7515 24.7805 24.5508 24.4037 23.7811 24.9242 17.8176 206051 24.7612 24.7906 24.5566 24.4110 23.7854 24.9255 17.8255 206052 24.7469 24.7790 24.5386 24.3979 23.7725 24.9012 17.8257 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.7 VOLTS 206055 24.8308 24.7379 24.6128 24.4799 23.8586 24.8639 17.7248 3.60 0.11000 206056 24.8436 24.7510 24.6230 24.4928 23.8673 24.8645 17.7483 3.60 0.11004 206057 24.8350 24.7419 24.6127 24.4828 23.8559 24.8537 17.7466 3.60 0.11005 206058 24.8378 24.7472 24.6148 24.4845 23.8527 24.8565 17.7609 3.60 0.11005 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.0 VOLTS 206061 24.8705 24.7409 24.6637 24.5201 23.8961 24.8612 17.7242 3.60 0.10993 206062 24.8277 24.7007 24.6198 24.4830 23.8540 24.8025 17.7225 3.60 0.10985 206063 24.8442 24.7159 24.6360 24.4980 23.8801 24.8173 17.7538 3.60 0.10983 206064 24.7990 24.6719 24.5877 24.4496 23.8365 24.7691 17.7297 3.60 0.10985 206065 24.8591 24.7330 24.6487 24.5093 23.8930 24.8319 17.7943 3.60 0.10985 206066 24.8489 24.7241 24.6387 24.4967 23.8760 24.8324 17.7901 3.60 0.10988

Table A.l6 Original Data for Data Set 16 —Potassium Runs at 11080F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv my my my my r my Volts Amps ISOTHERMAL 206070 24.6069 24.8482 24.3383 24.2593 23.5770 24.5372 20.1165 206071 24.6059 24.8497 24.3358 24.2532 23.5686 24.5427 20.1089 206072 24.7889 25.0328 24.5147 24.4349 23.7498 24.7144 20.2823 206073 24.7794 25.0246 24.5073 24.4289 23.7538 24.7044 20.2782 206074 24.7686 25.0138 24.4967 24.4172 23.7278 24.6907 20.2673 HEATED TOP PLATE - GUARD HEATER VOLTAGE,= 8.0 VOLTS 206075 24.8704 24.9536 24.5969 24.5162 23.7960 24.6355 20.0679 3.60 0.11003 206076 24.8957 24.9779 24.6177 24.5412 23.8264 24.6596 20. 0946 3.60 0.10998 206077 24.8890 24.9718 24.6131 24.5356 23.8199 24.6561 20.0960 3.60 0.10996 206078 24.8869 24.9701 24.6122 24.5339 23.8258 24.6574 20.1021 3.60 0.10995 206079 24.9012 24.9845 24.6268 24.5492 23.8397 24.6694 20.1152 3.60 0.10995 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 9.0 VOLTS 206080 24.9013 24.9568 24.6375 24.5494 23.8591 24.6375 20.0671 3.60 0.11009 206081 24.9778 25.0384 24.7124 24.6271 23.9382 24.7024 20.1501 3.60 0.11014 206082 24.9530 25.0141 24.6927 24.6027 23.9226 24.6953 20.1469 3.60 0.11014 206083 24.9913 25.0563 24.7314 24.6381 23.9668 24.7393 20.1953 3.60 0.11016 206084 24.9206 24.9749 24.6565 24.5641 23.8707 24.6634 20.0779 3.60 0.11022 206085 24.9238 24.9751 24.6571 24.5680 23.8773 24.6603 20.0766 3.60 0.11019 206086 24.9288 24.9829 24.6708 24.5807 23.8792 24.6706 20. 0922 3. 60 0.11017 206087 24.9486 25.0045 24.6890 24.5982 23.8988 24.6915 20.1207 3.60 0.11015 206088 24.9279 24.9846 24.6625 24.5753 23.9029 24.6642 20.1111 3.60 0.11007 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.5 VOLTS 206089 24.8767 25.0236 24.5809 24.5235 23.8156 24.7076 20.2317 3.60 0.10975 206090 24.8955 25.0407 24.6024 24.5443 23.8189 24.7264 20.2484 3.60 0.10973

Table A.17 Original Data for Data Set 17 —Potassium Runs at 11130F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv mv mv Volts Amps ISOTHERMAL 206091 24.7412 25.1934 24.3939 24.3810 23.6203 24.4466 22.3385 206092 24.7326 25.1895 23.3960 24.3771 23.6328 24.4576 22.3857 206093 24.7714 25.2324 24.4340 24.4185 23.6770 24.4899 22.4432 206094 24.8557 25.3179 24.5073 24.4993 23.7599 24.5489 22.5128 206095 24.8399 25.3070 24.5020 24.4875 23.7670 24.5537 22.5411 206096 24.8531 25.3152 24.5059 24.4958 23.7628 24.5459 22.5158 206097 24.8450 25.3089 24.5000 24.4901 23.7585 24.5451 22.5213 206098 24.8742 25.3334 24.5236 24.5132 23.7773 24.5716 22.5244 206099 24.8494 25.3121 24.5042 24.4936 23.7507 24.5538 22.5169 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.0 VOLTS 206101 25.0096 25.3173 24.6786 24.6549 23.9399 24.5804 22.3854 3.11 0.09504 206102 25.0201 25.3323 24.6847 24.6617 23.9562 24.5863 22.4090 3.11 0.09501 206103 25.0035 25.3479 24.6983 24.6745 23.9570 24.6039 22.4380 3.11 0.09497 206104 25.0994 25.4241 24.7665 24.7451 24.0270 24.6618 22.5212 3.11 0.09477 206105 25.0285 25.3462 24.6967 24.6749 23.9602 24.5980 22.4600 3.11 0.09488 206106 25.0443 25.3674 24.7090 24.6876 23.9654 24.6036 22.4650 3.11 0.09494 206107 25.0321 25.3509 24.6954 24.6763 23.9533 24.5850 22.4420 3.11 0.09496 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206108 24.8887 25.2225 24.5458 24.5275 23.7696 24.4922 22.3092 3.11 0.09521 206109 24.8999 25.2338 24.5526 24.5389 23.7776 24.4921 22.3123 3.11 0.09515 206110 24.9032 25.2404 24.5680 24.5496 23.7878 24.5093 22.3588 3.11 0.09513 206111 24.9473 25.2836 24.6071 24.5920 23i8462 24.5454 22.4047 3.11 0.09502 206112 24.9518 25.2910 24.6133 24.6015 23.8498 24.5452 22.4154 3.11 0.09503 206113 24.9612 25.3013 24.6194 24.6022 23.8681 24.5544 22.4220 3.11 0.09510 206114 24.9452 25.2823 24.6075 24.5916 23.8386 24.5404 22.4046 3.11 0.09518

Table A.18 Original Data for Data Set 18 —Potassium Runs at 11900F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv mv mv Volts Amps ISOTHERMAL 206139 26.6482 26.7204 26.4067 26.2752 25.6135 26.7572 19.9829 206140 26.6516 26.7264 26.4152 26.2813 25.6242 26.7699 19.9020 206141 26.6567 26.7346 26.4162 26.2822 25.6194 26.7686 19.9261 206142 26.6379 26.7135 26.3958 26.2633 25.6071 26.7450 19.8976 206143 26.6529 26.7265 26.4166 26.2817 25.6301 26.7746 19.9049 206144 26.7078 26.7791 26.4641 26.3354 25.6729 26.8072 19.9505 206145 26.7046 26.7730 26.4667 26.3358 25.6905 26.8186 19.9595 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206147 26.7607 26.7297 26.5222 26.3941 25.7440 26.7523 19.8708 3.10 0.09447 206148 26.7422 26.7134 26.5038 26.3769 25.7149 26.7386 19.8563 3.10 0.09448 206149 26.7527 26.7245 26.5111 26.3844 25.7274 26.7458 19.8676 3.10 0.09444 206150 26.7485 26.7197 26.5079 26.3818 25.7281 26.7402 19. 8626 3.10 0.09449 206151 26.7653 26.7345 26.5291 26.4016 25.7377 26.7549 19.8856 3.10 0.09446 206152 26.7634 26.7310 26.5265 26.3999 25.7397 26.7529 19.8816 3.10 0.09452

Table A.19 Original Data for Data Set 19 —Potassium Runs at 11920F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv my mv my my mv volts Amps ISOTHERMAL 206153 26.6216 26.9338 26.3179 26.2572 25.5410 26.5018 22.3087 206154 26.6772 26.9894 26.3713 26.3082 25.5834 26.5544 22.3595 206155 26.6564 26.9691 26.3495 26.2881 25.5550 26.5309 22.3338 206156 26.6687 26.9712 26.3685 26.3115 25.5755 26.5437 22.3389 206157 26.7129 27.0167 26.4141 26.3560 25.6251 26.5879 22.3677 206158 26.7345 27.0273 26.4326 26.3786 25.6555 26.5945 22.3688 206159 26.7006 27.0116 26.4058 26.3401 25.6245 26.5877 22.3543 p. 206160 26.6794 26.9801 26.3807 26.3205 25.5998 26.5542 22.3138 206161 26.6790 26.9812 26.3842 26.3206 25.5868 26.5581 22.3226 206162 26.6287 26.9284 26.3387 26.2768 25.5563 26.5175 22.2563 206163 26.6603 26.9552 26.3687 26.3061 25.5897 26.5456 22.2873 206164 26.-6681 26.9698 26.3713 20.3033 25.5967 26.5554 22.3108 206165 26.7225 27.0324 26.4235 26.3577 25.6511 26.6027 22.3787 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206166 26.7968 26.9989 26.4872 26.4275 25.7186 26.5523 22.2837 3.10 0.09474 206167 26.8400 27.0446 26.5279 26.4676 25.7486 26.5951 22.3199 3.10 0.09473 206168 26.8558 27.0612 26.5465 26.4850 25.7812 26.6148 22.3380 3.10 0.09469 206169 26.8775 27.0864 26.5675 26.5069 25.7933 26.6328 22.3564 3.10 0.09464 206170 26.8909 27.1003 26.5814 26.5224 25.8100 26.6434 22.3676 3.10 0.09464 206171 26.8861 27.0923 26.5759 26.514I 25.8009 26.6402 22.3702 3.10 0.09466 206172 26.8592 27.0653 26".5462 26.4876 25.7672 26.6056 22.3296 3.10 0.09467 206173 26-.8354 27.0428 26.5236 26.4652 25.7532 26. 5826 22.3136 3.10 0.09475 206174 26.8324 27.0360 26.5235 26.4635 25.7519 26.5834 22.3054 3.10 0.09472

Table A.20 Original Data for Data Set 20 —Potassium Runs at 12010F. RUN TIHERMIOCOUPLES HEATER 3 4 5 6 7 8- Boiler fy my mv nmv y my my Volts Amps ISOTHERMAL 206175 26.9335 27.5105 26.5330 26.5629 25.7653 26.4904 24.8181 206176 26.9169 27.4900 26.5204 26.5490 25.7390 26.4819 24.7907 206177 26.8633 27.4431 26.4656 26.4901 25.6944 26.4365 24.7654 206178 26.8682 27.4415 26.4766 26.5041 25.7089 26.4393 24.7806 206179 26.8756 27.4624 26.4736 26.4967 25.7194 26.4518 24.7855 206180 26.8543 27.4356 26.4516 26.4758 25.6929 26.4228 24.7403 206181 26.8337 27.4163 26.4330 26.4537 25.6749 26.4123 24.7371 206182 26.8507 27.4373 26.4511 26.4696 25.6814 26.4329 24.7607 206183 26.8918 27.4854 26.4963 26.5126 25.7319 26.4840 24.8386 206184 26.8936 27.4764 26.4918 26.5110 25.7201 26.4663 24.7898 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206185 27.0308 27.5126 26.6328 26.6469 25.8599 26.5108 24.7720 3.10 0.09526 206186 27.0470 27.5229 26.6445 26.6634 25.8768 26.5122 24.7551 3.10 0.09519 206187 27.0750 27.5587 26.6771 26.6911 25.9022 26.5519 24.8229 3.10 0.09519 206188 27.0717 27.5541 26.6732 26.6883 25.9071 26.5461 24.8135 3.10 0.09521 206189 27.0891 27.5708 26.6897 26.7069 25.9131 26.5544 24.8179 3.10 0.09520 206190 27.0753 27.5500 26.6685 26.6892 25.8991 26.5317 24.7738 3.10 0.09519 206191 27.0286 27.5029 26.6293 26.6468 25.8598 26.4979 24.7234 3.10 0.09531 206192 27.0388 27.5144 26.6395 26.6566 25.8675 26.5063 24.7297 3.10 0.09532

Table A.21 Original Data for Data Set 21 —Potassium Runs at 10040F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler my my my my my my my Volts Amps ISOTHERMAL 206197 22.2269 22.4259 22.0447 21.9753 21.2422 22.1537 17.5533 206198 22.2125 22.4098 22.0265 21.9601 21.2251 22.1237 17.5276 206199 22.2048 22.4037 22.0287 21.9611 21.2297 22. 1377 17.5504 206200 22.2190 22.4176 22.0389 21.9722 21.2395 22.1422 17.5558 206201 22.2168 22.4164 22.0392 21.9700 21.2409 22.1517 17.5671 206202 22.2431 22.4412 22.0644 22.0043 21.2639 22.1616 17.5804 206203 22.2412 22.4415 22.0641 21.9950 21.2637 22.1699 17.5854 206204 22.2579 22.4562 22.0696 22.0045 21.2634 22.1817 17.5754 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.2 VOLTS 206205 22.3987 22.4672 22.2067 22.1431 21.4011 22.1846 17.5071 3.10 0.09497 206206 22.3861 22.4563 22.1974 22.1332 21.3900 22.1722 17.4947 3.10 0.09498 206207 22.3558 22.4252 22.1690 22.1035 21.3624 22.1460 17.4641 3.10 0.09496 206208 22.3576 22.4273 22.1734 22.1052 21.3678 22. 1536 17.4721 3.10 0.09492 206209 22.4040 22.4745 22.2144 22.1518 21.4106 22.1899 17.4931 3.10 0.09481 206210 22.3936 22.4628 22.2078 22.1452 21.4020 22.1836 17.4751 3.10 0.09479 HEATED TOP PLATE - GUARD HEATER VOLTAGE - 7.0 VOLTS 206211 22.4659 22.5109 22.2854 22.2200 21.4799 22.2234 17.4741 3.10 0.09452 206212 22.4443 22.4887 22.2688 22.2003 21.4622 22.2132 17.4600 3.10 0.09557 206213 22.4720 22.5170 22.3012 22.2297 21.4944 22.2504 17.4876 3.10 0.09445 206214 22.4890 22.5342 22.3120 22.2424 21.5018 22.4890 17.4847 3.10 0.09458 206215 22.4148 22.4593 22.2321 22.1646 21.4253 22.1665 17.4716 3.10 0.09461 206216 22.4057 22.4511 22.2259 22.1571 21.4213 22.1612 17.4713 3.10 0.09459 206217 22.3906 22.4384 22.2158 22.1412 21.4115 22.1637 17.4701 3.10 0.09454 206218 22.4334 22.4801 22.2575 22.1841 21.4536 22.2058 17.4904 3.10 0.09447

Table A.22 Original Data for Data Set 22 —Y-acuum Runs at 9980F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 my my my my my my Volts Amps ISOTHERMAL 206219 22.1524 22.2375 21.9829 21.8926 21.1969 22.1804 206220 22.2175 22.3152 22.0574 21.9579 21.2658 22.2700 206221 22.2315 22.3192 22.0658 21.9897 21.2752 22.2092 206222 22.2150 22.3004 22.0501 21.9656 21.2645 22.2254 206223 22.2098 22.2952 22.0498 21.9648 21.2615 22.2212 206224 22.2105 22.2987 22.0429 21.9568 21.2550 22.2194 206225 22.0978 22.1818 21.9368 21.8496 21.1553 22.1142 206226 22.0831 22.1674 21.9212 21.8401 21.1397 22.0883 206227 22.1180 22.2076 21.9706 21.8774 21.1896 22.1675 206228 22.2018 22.2893 22.0543 21.9618 21.2704 22.2475 206229 22.2382 22.3274 22.0765 21.9863 21.2901 22.2678 4> HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.0 VOLTS 206230 22.2001 22.1944 22.0294 21.9515 21.2491 22.1017 2.20 0.06672 206231 22.1810 22.1764 22.0177 21.9339 21.2337 22.0939 2.20 0.06670 206232 22.2406 22.2433 22.0749 21.9873 21.2930 22.1638 2.20 0.06649 206233 22.2747 22.2782 22.1021 22.0207 21.3230 22.1819 2.20 0.06646 206234 22.2475 22.2480 22.0734 21.9998 21.2910 22.1321 2.20 0.06644 206235 22.2180 22.2161 22.0547 21.9737 21.2769 22.1355 2.20 0.06641 206236 22.1998 22.2003 22.0375 21.9571 21.2580 22.1194 2.20 0.06644 206237 22.3206 22.3227 22.1671 22.0773 21.3867 22.27 46 2.20 0.06646 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.0 VOLTS 206238 22.2602 22.2169 22.0969 22.0109 21.3157 22.1391 2.20 0O06672 206239 22.1897 22.1573 22.0376 21.9441 21.2528 22.0804 2.20 0.06672 206240 22.1972 22.1661 22.0425 21.9493 21.2608 22.0937 2.20 0.06671 206241 22.2113 22.1845 22.0525 21.9537 21.2708 22.1062 2.20 0.06660 206242 22.2248 22.2034 22.0697 21.9715 21.2874 22.1253 2.20 0.06664 206243 22.2276 22.2020 22.0677 21.9761 21.2871 22.1126 2.20 0.06664 206244 22.3929 22.3811 22.2318 22.1415 21.4440 22.2804 2.20 0.06673 206245 22.3822 22.3629 22.2202 22.1311 21.4340 22.2662 2.20 0.06672 206246 22.3716 22.3536 22.2065 22.1145 21.4152 22.2530 2.20 0.06674

Table A.23 Original Data for Data Set 23 —Vacuum Runs at 1000~F. THERMOCOUPLES HEATER RUN 3 4 5 6 7 8 mv my my mv mv mv Volts Amp s ISOTHERMAL 205654 22.0218 21.9638 21.8981 21.7880 21.1034 22.1568 205655 22.0108 21.9574 21.8914 21.7767 21.1004 22.1566 205656 22.0307 21.9779 21.9096 21.7967 21.1137 22.1664 205657 22.1799 22.1323 22.0615 21.9452 21.2720 22.3235 205658 22.1531 22.1040 22.0362 21.9147 21.2446 22.2962 205659 22.1362 22.0891 22.0163 21.8950 21.2192 22.2783 205660 22.1115 22.0542 21.9911 21.8684 21.1945 22.2587 205661 22.1167 22.0644 22.0135 21.8923 21.2106 22.2895 205662 22.1617 22.1146 22.0428 21.9175 21.2466 22.3212 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.5 VOLTS 205663 22.3686 22.1859 22.2462 22.1274 21.4511 22.3568 2.60 0.07894 205664 22.3380 22.1553 22.2152 22.0989 21.4198 22.3259 2.60 0.07902 205665 22.3389 22.1555 22.2140 22.0955 21.4182 22.3245 2.60 0.07903 205666 22.3237 22.1326 22.2009 22.0881 21.4052 22.3040 2.60 0.07898 205667 22.2989 22.1051 22.1775 22.0642 21.3759 22.2821 2.60 0.07903 205668 22.3096 22.1221 22.1846 22.0703 21.3849 22.2926 2.60 0.07909 205669 22.3288 22.1456 22.2088 22.0865 21.4046 22.3221 2.60 0.07909 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.2 VOLTS 205670 22.3733 22.1641 22.2533 22.1276 21.4521 22.3317 2.60 0.07911 205671 22.3843 22.1771 22.2694 22.1409 21.4649 22.3540 2.60 0.07911 205672 22.2901 22.0742 22.1745 22.0495 21.3694 22.3568 2.60 0.07911 205673 22.3015 22.0871 22.1828 22.0547 21.3815 22.2711 2.60 0.07911 205674 22.3134 22.0982 22.1950 22.0685 21.3942 22.2816 2.60 0.07908 205675 22.3111 22. 0966 22.2024 22.082k5 21.4021 22.2807 2.60 0.07899 205676 22.2126 21.9952 22.0977 21.9771 21.3064 22.1660 2.60 0.07899 205677 22.2095 21.9949 22.0949 21.9667 21.3046 22.1740 2.60 0.07899 205678 22.3551 22.1469 22.2352 22.1140 21.4367 22.3038 2.60 0.07903 205679 22.3385 22.1334 22.2149 22.0874 21.4158 22.2952 2.60 0.07905

Table A.24 Original Data for Data Set 24 —Vacuum Runs at 10020F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 my my my my my my Volts Amps ISOTHERMAL 206763 22.1354 21.8328 21.9345 21.8251 21.3077 22.2501 206764 22.1247 21.8248 21.9299 21.8159 21.3025 22.2589 206765 22.1419 21.8401 21.9482 21.8335 21.3331 22.2782 206766 22.0913 21.7849 21.8914 21.7838 21.2764 22.2060 206767 22.0616 21.7589 21.8647 21.7542 21.2467 22.1859 206768 22.2328 21.9398 22.0408 21.9325 21.4191 22.3640 206769 22.2402 21.9466 22.0478 21.9401 21.4268 22.3802 206770 22.3457 22.0527 22.1492 22.0476 21.5234 22.4740 206771 22.3515 2.2.0617 22.1599 22.0537 21.5316 22.4933 206772 22.3678 22.0729 22.1764 22.0724 21.5528 22.5192 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.6 VOLTS 206757 22.3451 21.8741 22.1589 22.0449 21.5209 22.3252 1.40 0.04274 206758 22.3804 21.8955 22.1865 22.0680 21.5563 22.3579 1.40 0.04271 206759 22.4082 21.9270 22.2121 22.0972 21.5751 22.3813 1.40 0.04267 206760 22.4264 21.9515 22.2359 22.1118 21.6005 22.4173 1.40 0.04267 206761 22.3503 21.8704 22.1555 22.0409 21.5262 22.3235 1.40 0.04265 206762 22.3701 21.8953 22.1798 22.0601 21.5427 22.3591 1.40 0.04269

Table A.25 Original Data for Data Set 25 —Vacuum Runs at 1191~F. RUN THERMOCOUPLES HEATER 3 4. 5 6 7 8 my my mv my Um mv Volts Amps ISOTHERMAL 206773 26.7324 26.48-76 26.5227 26.3974 25.8196 26.8491 206774 26.6229 26.3761 26.3973 26.2756 25.7043 26.7074 206775 26. 6438 26.4089 26.4288 26.3019 25.7 360 26.7569 206776 26.6204 26.3799 26.3972 26.2679 25.7111 26.7142 206777 26.6222 26.3835 26.4098 26.2815 25.7228 26. 7469 206778 26. 6864 26.4466 26.4708 26. 3363 25. 7786 26.7979 206779 26.7032 26.4679 26.4872 26.3464 25.7961 26.8167 206780 26.7257 26.4821 26.5020 26. 3805 25.8185 26.8197 20'6781 26. 6964 26.4554 26.4781 26.3409 25.7777 26. 7985 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.6 VOLTS 206782 26.7519 26.4055 26.5403 26.4037 25.8504 26.7701 1.40 0.04270 206783 26.8198 26.4710 26.6120 26.4841 25.9226 26.8436 1.40 0.04265 206784 26.8174 26.4620 26.5998 26.4628 25.8965 26.8091 1.40 0.04263 206785 26.8122 26.4629 26.6009 26.4598 25.9049 26.8238 1.40 0.04263 206786 26.7909 26.4478 26.5828 26.4442 25.8-916 26.8144 1.40 0.04263 206787 26.8701 26.5255 26.6562 26.5313 25.9669 26.8752 1.40 0.04264 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.1 VOLTS 206788 26.7922 26.4629 26.5807 26.4703 25.9018 26.8257 1.40 0.04270 206789 26.7911 26.4573 26.5805 26.4609 25.8938 26.8242 1.40 0.04270 206790 26.7913 26.4582 26.5765 26.4434 25.8833 26.8159 1.40 0.04270 205791 26.8619 26.5320 26.6481 26.52k9 25.9592 26.8939 1.40 0.04266 206792 26.8795 26.5489 26.6577 26.5320 25.9613 26.8860 1.40 0.04267 206793 26.8323 26.5000 26.6152 26.4980 25.9218 26.8544 1.40 0.04267 206794 26.8382 26.5093 26.6190 26.5066 25.9302 26.8514 1.40 0.04268 206795 26.8670 26.5353 26.6517 26.5482 25.9753 26.8875 1.40 0.04267

Table A.26 Original Data for Data Set 26 —Potassium Runs at 10160F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv uv my my my m my Volts Am ps ISOTHERMAL 206801 22.5130 22.9536 22.1742 22.1746 21.5812 22.2188 20.0355 206802 22.4730 22.9022 22.1252 22.1310 21.5095 22.2148 19.9267 206803 22.4594 22.8888 22.1081 22.1164 21.4987 22.1073 19.9050 206804 22.6057 23.0348 22.2397 22.2504 21.6320 22.2589 20.0325 206805 22.6014 23.0396 22.2427 22.2491 21.6352 22.2621 20.0694 206806 22.5914 23.0234 22.2257 22.2346 21.6215 22.2494 20.0403 0 206807 22.5367 22.9471 22.1983 22.2028 21.5616 22.2145 19.9074 206808 22.4713 22.9053 22.1183 22.1209 21.5142 22.1400 19.9602 206809 22.5535 22.9880 22.1978 22.2121 21.5852 22.1799 20.0281 206810 22.5378 22.9751 22.1803 22.1917 21.5770 22.1840 20.0420 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.95 VOLTS 206811 22.7856 23.0516 22.4353 22.4414 21.8221 22.2807 19.8425 3.11 0.09588 206812 22.6767 22.9655 22.3434 22.3448 21.7124 22.1706 19.8587 3.11 0.09583 206813 22.6624 22.9540 22.3274 22.3315 21.6917 22.1486 19.8551 3.11 0.09584 206814 22.7043 22.9743 22.3771 22.3711 21.7257 22.2297 19.7802 3.11 0.09595 206815 22.6785 22.9459 22.3443 22.3417 21.7197 22.1929 19.7517 3.11 0.09595 206816 22.6579 22.9288 22.3320 22.3233 21.6922 22.1791 19.7605 3.11 0.09592 206818 22.6530 22.9285 22.3283 22.3211 21.6873 22.1759 19. 7734 3.11 0.09593 206819 22.7544 22.0380 22.4271 22.4164 21.8005 22.2884 19.9181 3.11 0.09593

Table A.27 Original Data for Data Set 27 —Potassium Runs at 10160F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv my my mv y my myv olts Amp s ISOTHERMAL 206821 22.4498 22.8553 22.1103 22-.1040 21.4985 22.1461 20.0156 206822 22.4802 22.8992 22.1293 22.1322 21.5249 22.1466 20.0986 206823 22.5069 22.9354 22.1565 22.1626 21.5436 22.1569 20.110'3 206824 22.5191 22. 913-0 22.1756 22.1726 21.5645 22.2202 19.9818 206825 22.4987 22.8845 22.1556 22.-15:53 21.5534 22.1996 19.9053 206826 22.4874 22.8738 22.1448 22.1429 21.5431 22.1992 19.9118 206827 22.5050 22.9109 22.1562 22.1533 21.5497 22.1876 20.0435 206828 22.5291 22.9334 22.1767 22.1765 21.5704 22.2086 20.0550 206829 22.5741 22.9785 22.2266 22.2314 21.6315 22.2574 20.0942 20.6830 22.5423 22.9358 22.1986 22.2000 21.6087 22.2442 20.0379 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.60 VOLTS 206831 22.7123 22.9811 22.3646 22.3603 21.7710 22.2742 19.9612 3.10 0.09572 206832 22.7064 22.9743 22.3570 22.3543 21.7489 22.2401 19.9418 3.11 0.09551 206833 22.7204 22.9937 22.3675 22.3648 21.7731 22.2589 20.0156 3.11 0.09558 206834 22.6235 22.9262 22.2970 22.2971 21.6721 22.1470 20.0464 3.11 0.09547 206835 22.6919 23.0081 22.3504 22.3448 21.7352 22.1759 20.1552 3.11 0.09542 206836 22.6524 22.9647 22.3011 22.2985 21. 6852 22.1188 20.0843 3.11 0.09550 206837 22.6306 22.9485 22.2822 22.27 6 21.6655 22.1129 20.1004 3.11 0.09551

Table A.28 Original Data for Data Set 28 —Potassium Runs at 10950F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler my my my my my my my Volts Amps ISOTHERMAL 206838 24.3909 24.4230 24.1954 24.0615 23.4330 24.5959 17.5543 206839 24.3903 24.4220 24.1941 24.0631 23.4328 24.5900 17.5484 206840 24.3590 24.3925 24.1617 24.0332 23.3959 24.5712 17.5299 206841 24.4025 24.4314 24.2029 24.0715 23.4579 24.6119 17. 5774 206842 24.4270 24.4597 24.2361 24.1012 23.4790 24.6439 17.6010 206843 24.4490 24.4782 24.2441 24.1187 23.4825 24.6421 17.6065 206844 24.3467 24.3752 24.1420 24.0006 23.3688 24.5515 17.4673 206845 24.3130 24.3412 24.1110 23.9732 23.:3468 24.5215 17.4590 206846 24.3114 24.3351 24.1116 23.9796 23.3557 24.4978 17.4576 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.8 VOLTS 206847 24.5808 24.4894 24.3751 24.2503 23.6085 24.6330 17.5365 3.09 0.09474 206848 24.5868 24.4944 24.3872 24.2607 23.6227 24.6416 17.5543 3.10 0.09477 206849 24.5481 24.4532 24.3476 24.2187 23.5796 24.5998 17.4943 3.10 0.09486 206850 24.5422 24.4456 24.3410 24.2128 23.5709 24.5880 17.4923 3.10 0.09480 206851 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.6 VOLTS 206852 24.5661 24.4472 24.3690 24.2242 23.6291 24.5953 17.4765 3.10 0.09482 206853 24.5684 24.4441 24.3719 24.2316 23.6227 24.5835 17.4641 3.10 0.09483 206855 24.4795 24.3514 24.2850 24.1486 23.5053 24.5074 17.3235 3.10 0.09495 206856 24.5347 24.4101 24.3470 24.2075 23.5732 24.5733 17.3911 3.10 0.09493 206857 24.5576 24.4359 24.3711 24.23l16 23.5937 24.5977 17.4265 3.10 0.09490 206858 24.5793 24.4588 24.3984 24.2571 23.6180 24.6157 17.4545 3.10 0.09491 206859 24.5831 24.4630 24.3905 24.2537 23.6130 24.6183 17.4630 3.10 0.09489 206860 23.5434 24.4216 24.3554 24.2238 23.6229 24.5839 17.4264 3.10 0.09492 206861 24.5286 24.4023 24.3376 24.2061 23.6101 24.5619 17.4037 3.10 0.09497

Table A.29 Original Data for Data Set 29 —Potassium Runs at 10970F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler my my my my my my my Volts Amps ISOTHERMAL 206862 24.4918 24.7113 24.2208 24.1547 23.5116 24.4629 19.6441 206863 24.5079 24.7338 24.2361 24.1636 23.5203 24.4859 19.6814 206864 24.5717 24.7935 24.2959 24.2335 23.6036 24.5308 19.7561 206865 24.5186 24.7356 24.2424 24.1807 23.5503 24.4766 19.6829 206866 24.4888 24.7092 24.2207 24.1515 23.5257 24.4719 19.6911 206867 24.4989 24.7196 24.2223 24.1557 23.5136 24.4696 19.6848 206868 24.4986 24.7193 24.2278 24.1633 23.5258 24.4710 19.7121 206869 24.4777 24.7010 24.2075 24.1404 23.5000 24.4556 19.6895 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.42 VOLTS 206870 24.6643 24.7329 24.4075 24.3361 23.6941 24.4783 19.5801 3.12 0.09560 206871 24.6084 24.6822 24.3617 24.2820 23.6158 24.4223 19. 5368 3.11 0. 09560 206872 24.6189 24.6959 24.3758 24.2935 23.6261 24.4417 19.5616 3.12 0.09559 206873 24.5377 24.6111 24.2917 24.2095 23.5527 24.3590 19.4849 3.12 0.09559 206874 24.5946 24.6753 24.3541 24.2649 23.6253 24.4398 19.5642 3.12 0.09559 206875 24.6774 24.7499 24.4289 24.3497 23.6874 24.5027 19.5981 3.12 0.09560 206876 24.6950 24.7693 24.4447 24.3655 23.6983 24.5225 19.6178 3.12 0.09560 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206877 24.6257 24.7044 24.3661 24.2970 23.6491 24.4587 19.5263 3.12 0.09570 206878 24.6063 24.6881 24.3530 24.2749 23.6116 24.4425 19.5175 3.12 0.09570 206879 24.5752 24.6570 24.3240 24.2459 23.5818 24.4189 19.4994 3.12 0.09570 206880 24.5880 24.6706 24.3369 24.2589 23. 5-976 24.4321 19. 5156 3. 12 0.09569 206881 24.5974 24.6813 24.3474 24.2679 23.6013 24.4393 19.5267 3.12 0.09569 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.6 VOLTS 206882 24.5573 24.6487 24.3078 24.2320 23.5515 24.4189 19.4977 3.11 0.09546 206883 24.5656 24.6541 24.3099 24.2392 23."5560 24.4082 19.4857 3.11 0.09546 206884 24.6627 24.7516 24.4023 24.3329 23.6707 24.5167 19.5735 3.11 0.09547 206885 24.6228 24.7119 24.3699 24.2918 23.6207 24.4812 19.5364 3.11 0.09549

Table A.30 Original Data for Data Set 30 —Potassium Runs at 11910F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler my mv mv m m my my Volts Amps ISOTHERMAL 206886 26.7352 26.6134 26.5578 26.3660 25.7754 27.1105 17.9247 206887 26.6590 26.5387 26.4832 26.2990 25.7010 27.0238 17.8945 206888 26.6190 26.4979 26.4377 26.2567 25.6630 26.9745 17.8684 206889 26.6532 26.5325 26.4679 26.2911 25.6907 27.0026 17.9582 206890 26.6277 26.5121 26.4428 26.2650 25.6660 26.9815 17.9408 206891 26.6148 26.4936 26.4304 26.2556 25.6629 26.9648 17.9043 206892 26.6269 26,5100 26.4428 26.2671 25.6767 26.9851 17.9116 206893 26.6266 26.5086 26.4458 26.2736 25.6813 26.9860 17.9106 206894 26.6559 26.5336 26.4693 26.3003 25.7167 27.0084 17.9339 HEATED TOP PLATE - GUARD HEATER VOLTAGE - 6.8 VOLTS 206895 26.8034 26.5699 26.6350 26.4627 25.8351 27.0336 17.9439 3.11 0.09519 206896 26.7999 26.5655 26.6286 26.4553 25.8241 27.0322 17.9339 3.11 0.09521 206897 26.7999 26.5747 26.6278 26.4550 25.8280 217.0222 17.9299 3.11 0.09522 206898 26.7932 26.5697 26.6230 26.4492 25.8265 27.0244 17.9273 3.11 0.09~22 206899 26.8716 26.6444 26.6789 26.5038 25.9092 27.1071 17.9764 3.12 0.09522 206900 26.8411 26,6146 26.6433 26.4709 25.8728 27.0680 17.9525 3.12 0.09527 HEATED TOP PLATE - GUARD HEATER VOLTAGE - 7.75 VOLTS 206901 26.8702 26.6309 26.7095 26.5259 25.9076 27.0902 17.9505 3.11 0.09512 206902 26.7877 26.5497 26.6269 26.4487 26.8164 26.9977 17.9076 3.11 0.09510 206903 26.9077 26.6637 26.7455 26.5640 25.9393 27.1198 17.9990 3.11 0.09509 206904 26.8948 26.6566 26.7326 26.5507 25.9288 27.1057 17.9930 3.11 0.09510 206906 26.8276 26.5881 26.6640 26.4869 25.8608 27.0345 17.9571 3.11 0.09506 206907 26.8297 26.5908 26.6650 26.4869 25.8627 27.0378 17.9602 3.11 0.09506 206908 26.8320 26.5902 26.6620 26.4849 25.8609 27.0306 17.9894 3.11 0.09507 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.5 VOLTS 206909 26.8246 26.5534 26.6696 26.4784 25.8783 27.0081 17.8587 3.11 0.09512 206910 26.8470 26.5789 26.6949 26.5042 25.8840 27.0356 17.8792 3.11 0,09510 206911 26.8217 26.5552 26.6648 26.4784 25.8598 27.0041 17.8719 3.11 0.09501 206912 26.8553 26.5872 26.7050 26.5165 25.8945 27.0315 17.8994 3.11 0.09504 206913 26.8508 26.5810 26.6991 26.5073 25.8985 27.0270 17.8986 3.11 0.09506 206914 26.8174 26.5460 26.6649 26.4716 25.8678 27.0005 17.8351 3.11 0.09515 206915 26.8396 26.5705 26.6846 26.4988 25.8Z38 27.0135 17.8833 3.11 0.09507 206916 26.8277 26.5596 26.6764 26.4875 25.8650 27.0076 17.8932 3.11 0.09507

Table A.31 Original Data for Data Set 31 —Potassium Runs at 1191~F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv mv mv Volts Amps ISOTHERMAL 206917 26.6417 26.6203 26.4194 26.2725 25.6665 26.8907 19.4194 206918 26.7140 26.6921 26.4916 26.3430 25.7322 26.9595 19.4763 206919 26.7096 26.6857 26.4705 26.3277 25.7212 26.9441 19.4825 206920 26.6675 26.6456 26.4396 26.2966 25.6908 26.9034 19.4551 206921 26.7060 26.6851 26.4977 26.3522 25.7251 26.9544 19.4893 206922 26.6454 26.6284 26.4209 26.2788 25.6626 26.8753 19.4568 206923 26.6395 26.6270 26.4209 26.2749 25.6707 26.8793 19.4697 206924 26.5797 26.5690 26.3572 26.2134 25.6123 26.8131 19.4374 206925 26.6648 26.6497 26.4255 26.2835 25.6780 26.8991 19.4980 206926 26.6978 26.6848 26.4614 26.3193 25.7167 26.9403 19.5303 206927 26.7070 26.6925 26.4773 26.3328 25.7341 26.9506 19.5333 Un HEATED TOP PLATE - GUARD HEATEX VOLTAGE = 8.5 VOLTS 206929 26.8682 26.6989 26.6605 26.5057 25.9188 26.9315 19.4515 3.11 0.09542 206930 26.7813 26.6152 26.5834 26.4278 25.8240 26.8289 19.4092 3.11 0.09540 206931 26.7795 26.6183 26.5815 26.4266 25.8209 26.8286 19.4154 3.11 0.09539 206932 26.7941 26.6351 26.5975 26.4435 25.8357 26.8515 19.4379 3.11 0.09539 206933 26.7842 26.6238 26.5882 26.4387 25.8159 26.8244 19.4262 3.12 0.09539 206934 26.9358 26.7745 26.7377 26.5788 25.9768 26.9988 19.5484 3.12 0.09540 206935 26.9231 26.7594 26.7191 26.5624 25.9676 26.9872 19.5355 3.12 0.09542 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.55 VOLTS 206936 26.8484 26.7080 26.6424 26.4938 25.8838 26.9443 19.4939 3.12 0.09542 206937 26.7403 26.6072 26.5386 26.3940 25.7649 26.8311 19.4289 3.12 0.09539 206938 26.7514 26.6183 26.5472 26.4045 25.7760 26.8356 19.4398 3.12 0.09538 206939 26.7508 26.6167 26.5478 26.4051 25.7796 26.8354 19.4409 3.12 0.09538 206940 26.7376 26.5994 26.5221 26.3832 25.7428 26.8186 19.4226 3.12 0.09538 206941 26.8356 26.6980 26.6306 26.4834 25. 8546 26.9234 19.4864 3.12 0.09544 206942 26.8304 26.6920 26.6275 26.4799 25.8605 26.9197 19.4802 3.12 0.09544 206943 26.8260 26.6893 26.6218 26.4762 25.8551 26.9090 19.4843 3.12 0.09543 206944 26.8313 26.6929 26.6241 26.4771 25.8664 26.9209 19.4849 3.12 0.09546

Table A.32 Original Data for Data Set 32 —Potassium Runs at 10990F. RUN THERMOCOUPLES HEATER 3 4 5 6 7 8 Boiler mv mv mv mv mv mv mv Volts Amps ISOTHERMAL 206948 24.4932 24.4927 24.2861 24.1529 23.5545 24.7147 17.5966 206949 24.4745 24.4781 24.2771 24.1434 23.5332 24.6997 17.5478 206950 24.4955 24.4975 24.2935 24.1632 23.5702 24.7235 17.5665 206951 24.4915 24.4967 24.2944 24.1604 23.5584 24.7225 17.5553 206952 24.5075 24.5103 24.3110 24.1773 23.5714 24.7304 17.5790 206953 24.4960 24.5025 24.3006 24.1658 23.5572 24.7226 17.5805 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.15 VOLTS 206954 24.6583 24.5242 24.4711 24.3299 23.7269 24.7313 17.4859 3.11 0.09571 206955 24.6740 24.5418 24.4865 24.3433 23.7417 24.7475 17.5003 3.10 0.09568 206956 24.6811 24.5466 24.4919 24.3497 23.7493 24.7469 17.5035 3.11 0.09568 206957 24.6634 24.5258 24.4700 24.3403 23.7446 24.7288 17.5040 3.11 0.09569 206958 24.6575 24.5209 24.4638 24.3335 23.7426 24.7181 17.4956 3.11 0.09570 206959 24.6539 24.5188 24.4605 24.3298 23.7431 24.7217 17.4933 3.11 0.09570 206960 24.6424 24.5071 24.4559 24.3164 23.7096 24.7163 17.4714 3.11 0.09571 206961 24.6682 24.5349 24.4796 24.3399 23.7288 24.7396 17.4933 3.11 0.09567 206962 24.6775 24.5428 24.4863 24.3471 23.7376 24.7443 17.5053 3.11 0.09566 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.55 VOLTS 206963 24.7006 24.5887 24.5092 24.3765 23.7568 24.7852 17.6024 3.11 0.09563 206964 24.7096 24.5969 24.5201 24.3870 23.7631 24.7901 17.6096 3.11 0.09562 206965 24.6489 24.5376 24.4561 24.3276 23.6949 24.7219 17.5622 3.11 0.09560 206966 24.6818 24.5692 24.4908 24.3626 23.7353 24.7633 17.5950 3.11 0.09559 206967 24.-6571 24.5419 24.4600 24.3351 23.7090 24.7257 17.5700 3.11 0.09559 206968 24.6451 24.5302 24.4476 24.3236 23.7020 24.7186 17.5645 3.11 0.09560

APPENDIX 3B PRELIMINARY PROCESSED DATA Table B.1 Preliminary Processed Data for Data Set 1 —Vacuum Runs at 9430F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 0F 0' OF OF OOF0F OmHg ISOTHERMAL 199465 928. 7 -26.747 3.8 02 -3.907 -32.211 46.430 24.502 0.004 1994 666 93-5.2 -26.532 3.034 -4.278 -34.067 40-.641 26.755 0.004 199467 936.5 - 2 7.595 3.004 -3.93,2 -33.76.3 42. 2,48 26.827 0.004 199468 927.2 -27.295 2.878 -4. 616 -32'. 747 46. 13-0 25.253 0.004 199469 934.7 -27.553 4..645 -3. 713 -33.426 47.772 25.068 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.0 VOLTS 199472 95 0;.0 -37.253 3.607 -2.979 -31.793 40.801 25.207 0.002 199474 954.6 -37.160 2.612 -4.169 -32.498 37.2209 25.717 0.002 199475 939.9 -36.186 3.194 -2.810 -32.338 35.434 26.334 0.002

Table B.2 Preliminary Processed Data for Data Set 2 —Nitrogen Runs at 9250F. THERMOCOUPLES NULL PRESSURE RUN 3 4-3 5-3 6-3 7-3 8-3 ~F mm Hg oF oF oF oF oF OF ISOTHERMAL 199488 923.9 4.519 3.017 -8.485 -25.586 44.278 14.084 1210. 199489 941.4 5.312 4.376 -7.675 -27.333 47.544 15.282 1210. 199490 938.7 4.093 2.384 -11.181 -25.608 50.051 12.043 1210. 199491 928.5 5.266 4.789 -7.139 -26.245 47.152 14.317 1210. 199494 913.3 4.494 3.810 -7.700 -26.970 46.573 15.460 1210. o 199495 913.1 4.194 3.679 -8.321 -25.835 46.962 13.835 1210. 199497 916.2 4.574 3.882 -8.072 -25.232 46.447 13.278 1210. 199498 917.0 4.684 5.321 -6.266 -25.215 47.228 13.628 1210. 199499 926.6 4.890 7.063 -4.646 -26.105 48.342 14.396 1210. HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.8 VOLTS 205505 923.7 2.215 4.013 -8.207 -24.781 42.734 12.561 1180. 205506 923.5 2.962 4.658 -7.548 -26.594 43.270 14.388 1180. 205507 926.0 3.118 6.628 -4.169 -26.194 43.898 15.397 1190. 205508 927.5 2.338 4.265 -7.789 -25.270 43.120 13.216 1190. 205509 928.3 2.646 4.493 -6.898 -24.814 42.514 13.423 1200. 205511 926.1 2.738 6.434 -5.198 -26.594 43.586 14.962 1200.

Table B.3 Preliminary Processed Data for Data Set 3 —Vacuum Runs at 10320F. RUN THERMOCOUPLES NULL PRESSURE 3. 4-3 5-3 6-3 7-3 8-3 OF -0 F F OF 0F: 0F OFmH I SOTHERMAL 205517- 1030.6 -36.775 4.372 -2.686 -3 4.427 44.021 27.369 0.002 205521 1032.4 -36.826 4.775 -1.915 - 34. 474 43.677 27.784 0.002 205522 103:1.1 -37.533 4.021 -2.533 -3:4.766 43.6,65 28.212 0.002 205523 1031.2 -37.355 4.237 -1.555 -34.415 43.924 28.623 0.002 205524 1031.1 -37.550 4.618 — 1.805 -34.347 44.033 27. 924 0.002 HEATED TOP PLATE. - GUARD HEATER VOLTAGE = 3.05 VOLTS 205532 1032.4 -41.008 2.855 -4.004 -35.165 40.898 28.306 0.001 205533 1033.6 -40.830 3.834 -2.190 -34.788 40.419 28.764 0.001 205534 1033.5 -40.779 3.114 -3.139 -35.080 4-0. 135 28.827 0.002 205536 1034.0 -41.466 2.949 -3.135 -35.02-1 40. 266 28. 937 0.002 205540 1034.5 -40.949 4.406 -2.131 -3-4. 122 39.588 27.585 0.002

Table B.4 Preliminary Processed Data for Data Set 4 —Nitrogen Runs at 10270F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF F F OF OF mmHg ISOTHERMAL 205541 1027.5 4.186 9.737 -2.834 -27.872 49.826 15.301 1270. 205542 1027.9 4.105 7.805 -4.076 -27.639 49.677 15.758 1285. 205543 1028.9 4.233 7.843 -3.716 -27.593 48.-444 16.034 1310. 205544 1029.2 3.957 7.186 -4.707 -28.266 48.860 16.373 1310. 205545 1029.0 4.245 7.677 -4.016 -27.978 48.923 16.285 1310. 205546 1027.5 3.995 8.944 -3.076 -29.292 49.038 17.272 1300. 205547 1029.1 4.173 7.970 -4.055 -28.008 49.063 15.983 1310. HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.95 VOLTS 205702 1028.4 2.000 9.016 -3.059 -28.483 47.067 16.408 1310. 205703 1029.0 2.008 8.864 -3.330 -27. 508 47.872 15.314 1305. 205704 1028.1 2.152 8.716 -3.453 -27.516 47.872 15.347 1300.

Table B,5 Preliminary Processed Data for Data Set 5 —Vacuum Runs at 11170~F RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF oF ~F oF OF OF mm Hg ISOTHERMAL 205710 1124.4 -33.748 3.825 -2.157 -35.914 45.910 29.932 0.003 205712 1117.6 -33.765 2.417 -4.468 -36.221 46.374 29.336 0.002 205713 1116.3 -35.306 2.770 -1.919 -35.817 44.846 31.128 0.002 205715 1118.5 -33.327 3.042 -3.629 -36.514 45.446 29.843 0.002 205716 1113.2 -34.778 2.178 -2.459 -36.429 46.455 31.792 0.001 205717 1115.5 -34.540 3.527 -1.553 -36.063 46.919 30.983 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 3.15 VOLTS 205718 1118.2 -37.323 3.182 -0. 880 -36.217 43.531 32.155 0.002 205719 1118.4 -36.961 3.634 -0.859 -35.953 43.182 31.460 0.001 205720 1118.5 -37.297 3.761 -0.953 -35.710 43.765 30.996 0.001 205721 1118.2 -37.672 3.638 -0.829 -35. 753 43.697 31.286 0.002 205722 1118.9 -36.855 4.510 -1.378 -36.080 44.578 30.192 0.001 205723 1119.5 -36.702 4.293 -1.055 -35.617 44.531 30.269 0.001

Table B.6 Preliminary Processed Data for Data Set 6 —Nitrogen Runs at 11130F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF OF OF mnHg ISOTHERMAL 205724 1112.5 2.987 9.123 -3.587 -29.365 51.323 16.655 1350. 205725 1114.2 3.455 9.319 -2.876 -29.170 51.004 16.975 1360. 205726 1112.2 3.221 9.263 -2.970 -29.531 50.638 17.298 1360. 205727 1113.0 3.110 9.787 -2.212 -29.948 50.459 17.949 1370. 205728 1112.9 3.140 9.370 -2.851 -29.740 50.744 17.519 1370. 205729 1114.6 3.076 9.153 -2.965 -30.148 50.680 18.030 1370. HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.95 VOLTS 205732 1114.5 1.417 9.676 -2.859 -30.170 49.097 17.635 1360. 205733 1114.0 1.153 9.195 -3.268 -29.446 49.378 16.983 1360. 205734 1113.5 1.378 9.365 -3.068 -28.821 49.289 16.388 1360.

Table B.7 Preliminary Processed Data for Data Set 7 —Vacuum Runs at 12130F. RUN THERMOCOUPLES NULL 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF OF FF mm Hg ISOTHERMAL 205735 1211.9 -27.293 4.463 -2.289 -36.353 47.004 29. 601 0.001 205736 1212.0 -27.412 4.468 -2.021 -36.472 46.753 29.983 0.001 205737 1210.1 -27.902 4.225 -2.110 -36.634 47.365 30.299 0.001 205739 1212.5 -27.889 4.493 -2.046 -36.659 47.302 30.120 0.001 205741 1210.8 -27.561 4.995 -1.472 -37.306 47.634 30.839 0.001 205743 1213.5 -27.395 5.621 -1.238 -37.140 47. 680 30.281 0.001 205744 1213.9 -27.587 5.646 -1.165 -36.948 47. 702 30.137 0.002 205745 1210.7 -28.459 4.140 -2.144 -37.617 48.106 31.333 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.6 VOLTS 205600 1215.5 -30.906 5.753 -0.617 -36.774 44.289 30.404 0.002 205601 1216.1 -30.876 6.131 -0.510 -37.668 45.034 31.027 O.001 205602 1216.6 -30.357 6.323 -0.697 -37.476 44.770 30.456 0.002 205605 1214.9 -29.897 4.851 -2.774 -38 617 44. 731 30.992 0.002 205606 1214.4 -30.889 5.412 -2.357 -38.885 44.897 31.116 0.002 205607 1212.1 -30.540 3.753 -5.170 -38.834 45.553 29.911 0.002

Table B.8 Preliminary Processed Data for Data Set 8 —Nitrogen Runs at 12130F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3. 5-3 6-3 7-3 8-3 OFP OF OF OF OF OF 0F mmHg ISOTHERMAL 205608 1207.5 1.761 7.903 -4.012 -32.276 52.540 21.171 1355. 205609 1211.2 1.519 6.889 -4.855 -32.617 52'.765 19.873 1360. 205610 1212.2 1.578 6.838 -4.872 -31.680 52.293 19.970 1365. 205611 1208.9 1.659 6.106 -5.591 -31.378 51.995 19.681 1365. 205612 1209.3 1.582 7.553 -3.808 -32.340 52.744 20.979 1365. 205613 1209.6 1.463 8.710 -2.063 -33.659 52.446 22.886 1365. HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.8 VOLTS 205614 1215.0 0.004 -7.217 -4.191 -32.285 49.136 20.877 1380. 205615 1213.0 0.123 7.259 -4.187 -31.970 49.378 20.524 1380. 205616 1215.2 0.008 6.893 -4.455 -32.412 48.940 21.064 1380. 205617 1215.7 -0.089 6.655 -4.821 -32.208 48.931 20.732 1380. 205619 1215.8 -0.106 5.408 -6.429 -31.889 48.523 20.052 1380. 205620 1213.1 -0.106 6.051 -5.493 -32.471 49.289 20.928 1380. 205621 1212.5 -0.076 6.446 -4.446 -33.246 49.370 22.354 1380. 205622 1212.1 -0.204 5.838 -5.885 -32.991 49.042 21.268 1380.

Table B.9 Preliminary Processed Data for Data Set 9 —Vacuum Runs at 10080FI RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF'O F F 0mmHg ISOTHERMAL 205626 1008.1 -8.172 -10.472 -15.299 -38.957 8.805 34.130 0.002 205627 1005.3 -8.451 -10.936 -14.995 -38.962 7.105 34.903 0.002 205628 1003.9 -8.586 -10.502 -14.683 -38.219 7.302 34.038 0.002 205629 1002.7 -8.594 -10.544 -14.869 -38.776 8.071 34.451 0.002 205630 1003.8 -8.379 -10.451 -14.873 -38.670 7.890 34.248 0.002 205631 1006.5 -8.451 -10.544 -14.797 -38.594 7.367 34.341 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 4.0 VOLTS 205638 1009.5 -12.151 -10.535 -14.603 -.38.084 4.379 34.016 0.002 205639 1011.2 -12.105 -10.822 -14.797 -38.928 4.003 34.953 0.002 205640 1012.2 -11.928 -10.632 -14.713 -38.898 4.202 34.817 0.002 205641 1007.9 -12.059 -10.210 -14.476 -37.991 4.485 33.725 0.002 205642 1006. 0 -12.021 -10.603 -14.632 -38.932 4.088 34.903 0.002

Table B.l0 Preliminary Processed Data for Data Set 10 —Vacuum Runs at 11130F. RUN THERMOCOUPLES NULL 3 4-3 5-3 6-3 7-3 8-3 OF F OF OF OF 0F F mmHg ISOTHERMAL 205644 1104.9 -5.466 -14.322 -19.995 -43.169 -3.135 37.496 0.002 205645 1107.2 -5.326 -14.059 -19.669 -43.419 -3.097 37.809 0.002 205646 ll10 i8 -5.203 -13.915 -19.521 -42.703 -2.902 37.097 0.002 205647 1113.5 -5.292 -14.309 -19.529 -43.224 -3.622 38.004 0.002 205648 1112.5 -5.008 -13.894 -19.427 -43.067 -3.792 37.534 0.002 205649 1111.5 -4.983 -14.330 -19.665 -43.593 -4.288 38.258 0.002 205550 1106.9 -4.932 -13.576 -18.728 -43.271 -4.237 38.119 0.002 205551 1107.0 -4.957 -14.105 -19.644 -43.440 -3.538 37.901 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 3.9 VOLTS 205556 1113.7 -7.427 -12.580 -18.139 -42.834 -6.766 37.275 0.002 205557 1111.9 -7.411 -12.207 -17.635 -42.847 -6.809 37.419 0.002 205558 1110.1 -7.694 -12.923 -17.186 -43.686 -7.555 39.423 0.002 205559 1112.9 -7.050 -12.228 -18.139 -42.411 -5.483 36.500 0.002 205560 1117.2 -7.584 -12.131 -17.567 -42.915 -6.970 37.479 0.002 205561 1118.1 -7.372 -12.682 -17.936 -42.966 -7.279 37.712 0.002 205562 1114.7 -7.415 -12.343 -17.750 -42.597 -6.305 37.190 0.002

Table B. 1 Preliminary Processed Data for Data Set 11 —Vacuum Runs at 12050F. RUN THERMOCOUPLES NUL 3 4-3 5-3 6-3 7-3 8-3 OF OF F F OF F F mmllg ISOTHERMAL 205564 1201.1 -2.293 -12.246 -18.178 -45.948 -5.595 40.016 0.002 205565 1203.3 -2.272 -12.251 -18.395 -45.706 -5.740 39.562 0.002 205566 1204.8 -2.191 -12.297 -18.548 -45.455 -5.557 39.204 0.002 205567 1204.2 -2.523 -12.357 -18.468 -45.893 -6.787 39.782 0.002 205568 1200.7 -2.791 -13.119 -19.055 -45.927 -7.263 39.991 0.002 205569 1199.2 -2.331 -13.029 -19.131 -45.553 -5.885 39.451 0.002 205570 1197.7 -2.676 -12.829 -18.595 -45.731 -6.591 39.965 0.002 HEATED TOP PLATE - GUARD VOLTAGE = 4.5 VOLTS 205571 1201.1 -6.204 -12.502 -15.987 -47.191 -10.042 43.706 0.002 205572 1206.8 -6.089 -12.357 -16.748 -47.008 - 9.651 42.617 0.002 HEATED TOP PLATE - GUARD VOLTAGE = 5.0 VOLTS 205573 1206.9 -5.812 -11.82C -18.106 -45.868 -10.085 39.600 0.002 205574 1208.5 -5.817 -11.931 -17.697 -46.170 -10.919 40.404 0.002 205575 1208.0 -5.923 -12.161 -17.761 -45.961 -11.046 40.361 0.002 205576 1208.4 -5.731 -11.914 -17.914 -45.144 -10.710 39.144 0.002 205577 1211.8 -5.497 -13.243 -18. 544 -47.008 -1L357 41.710 0.002 205578 1208.8 -5.936 -13.463 -19.055 -46.557 -11.136 40.965 0.002 205579 1209.4 -5.774 -13.319 -19.289 -45.987 -10.370 40.017 0.002 205580 1209.2 -5.102 -12.621 -18.548 -46.161 - 9.191 40.234 0.002 205581 1209.0 -5.880 -14.017 -19.570 -46.519 -11.004 40.966 0.002

Table B.12 Preliminary Processed Data for Data Set 12 —Vacuum Runs at 13050F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF F F OF mm Hg ISOTHERMAL 205582 1291.6 -0.642 -13.319 -18.834 -47.625 -7.668 42.110 0.002 205585 1299.7 -0.748 -14.669 -19.759 -48.712 -9.845 43.622 0.002 205586 1298.5 -0.648 -14.549 -19.699 -48.519 -9.596 43.369 0.002 205587 1299.2 -0.386 -14.072 -19.862 -48.188 -9.257 42.398 0.002 205588 1299.3 -0.682 -14.742 -20.463 -48.545 -9.854 42.824 0.002 205589 1304.0 -0.390 -14.484 -19.974 -49.223 -9.648 43.733 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.0 VOLTS 205590 1306.6 -3.008 -13.351 -19.158 -49.446 -12.137 43.639 0.002 205591 1309.6 -2.811 -14.085 -20.017 -49.662 -12.746 43.690 0.002 205592 1309.2 -2.583 -12.738 -18.944 -49.721 -12.416 43.515 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.25 VOLTS 205593 1304.7 -3.746 -13.472 -18.626 -48.639 -13.000 43.485 0.002 205594 1303.3 -3.888 -13.446 -18.909 -48.502 -12.991 43.039 0.002 205595 1303.1 -3.669 -13.716 -19.746 -48.540 -12.656 42.510 0.002 205596 1305.1 -3.854 -14.291 -19.875 -48.969 -13.961 42.385 0.002 205597 1303.8 -3.635 -13.725 -19.459 -48.587 -13.137 42.853 0.002 205598 1304.0 -3.103 -13.755 -19.832 -49.201 -13.626 43.124 0.002 205599 1303.8 -3.270 -13.931 -19.995 -48.927 -13.296 42.863 0.002

Table B.13 Preliminary Processed Data for Data Set 13 —Potassium Runs at 10100F. RUN THERMOCOUTPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF ~F ~F 0F OF OF lbssq.in. ISOTHERMAL 206004 1002.9 8.793 -10.088 -13.827 -40.852 -1.468 37.113 804.0 0.163 206005 1004.4 8.751 -10.181 -13.670 -40.405 -1.864 36.916 804.4 0.164 206006 1005.7 8.856 -10.105 -13.637 -40.396 -1.687 36.864 806.8 0.169 206007 1005.0 8.873 -10.472 -13.700 -40.869 -2.919 37.641 807.5 0.170 206008 1005.5 8.974 -10.185 -13.594 -40.679 -2.443 37.270 809.1 0.171 206009 1003.2 9.008 -10.303 -13.493 -40.523 -2.645 37.333 806.5 0.168 HEATED TOP PLATE - GUARD VOLTAGE = 8.2 VOLTS 206010 1014.5 1.675 -9.725 -13.502 -40.037 -10.810 36.260 804.4 0.164 206011 1014.1 1.637 -9.713 -13.510 -40.080 -10.767 36.283 803.6 0.162 o~ HEATED TOP PLATE - GUARD VOLTAGE = 7.6 VOLTS 206013 1011.3 2.227 -10.046 -13.670 -40.675 -9.468 37.051 802.7 0.162 206014 1013.5 2.312 -10. 037 -13.632 -40.308 -9.624 36. 713 805.3 0.167 206015 1014.4 2.324 -10.059 -13.502 -40.354 -9.818 36.911 806.2 0.168 206016 1014.4 2.265 -10.143 -13.489 -40.164 -10.337 36.818 806.2 0.168 HEATED TOP PLATE - GUARD VOLTAGE = 7.3 VOLTS 206017 1011.4 2.658 -10.101 -13.413 -39.991 -9.493 36.679 804.9 0.165 206018 1010.6 2.717 -10.080 -13.358 -39.793 -9.341 36.515 804.4 0.165 206019 1014.7 2.793 -10.059 -13.371 -40.050 -9.198 36.738 809.1 0.170 HEATED TOP PLATE - GUARD VOLTAGE = 6.9 VOLTS 206020 1012.6 3.223 -10.569 -13.624 -40.472 -9.274 37.417 807.4 0.168 206021 1012.4 3.151 -10.472 -13.447 -.40.295 -9.219 37.320 807.4 0.168 206022 1012.2 3.227 -10.434 -13.556 -40.371 -9.084 37.249 807.2 0.168 206023 1012.3 3.291 -10.379 -13.531 -40.523 -9.042 37.371 807.5 0.168 206024 1012.3 3.177 -10.455 -13.569 -40.434 -9.008 37.320 806.5 0.167

Table B.14 Preliminary Processed Data for Data Set 14 —Potassium Runs at 10180F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 ~F ~F ~F'F ~F OFF ~ F lbs./sq.in. ISOTHERMAL 206025 1008.9 20.624 -14.215 -13.987 -43.708 -18.447 43.936 929.6 0.167 206026 1010.5 20.604 -14.122 -13.848 -43.185 -18.113 43.459 931.0 0.625 206027 1010.2 20.616 -14.316 -13.970 -43.776 -18.746 44.122 929.5 0.617 206028 1010.2 20.687 -14.236 -13.890 -43.818 -18.464 44.164 930.2 0.621 206029 1010.7 20.738 -14.240 -14.012 -44.257 -18.523 44.485 930.9 0.625 206030 1010.2 20.717 -14.312 -14.025 -44.691 -18.962 44.978 930.6 0.622 206031 1016.0 21.160 -14.350 -13.995 -43.831 -18.578 44.186 937.1 0.662 206032 1015.9 20.755 -14.472 -13.995 -43.957 -19.261 44.434 935.0 0.651 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6 9 VOLTS 206035 1017.4 14.924 -14.375 -13.881 -43.476 -24.645 43.970 927.6 0.604 206036 1018.6 14.928 -14.510 -13.852 -43.126 -25.059 43.784 928.2 0.610 206037 1018.1 14.839 -14.544 -13.822 -43.168 -25.219 43.890 927.6 0.604 206038 1018.1 14.877 -14.594 -13.856 -42.877 -25.189 43.615 927.8 0.605 206039 1018.3 14.873 -14.573 -13.890 -42.924 -25.130 43.607 928.1 0.609 206040 1017.6 14.746 -14.586 -13.852 -42.924 -25.160 43.658 927.0 0.601 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.5 VOLTS 206041 1023.4 15.578 -14.881 -14.172 -44.037 -24.447 44.746 934.2 0.646 206042 1023.2 15.540 -14.898 -14.033 -44.109 -24.759 44.974 933.3 0.640 206043 1023.0 15.611 -14.586 -13.751 -43.675 -24.329 44.510 934.2 0.649 206044 1023.2 15.383 -14.662 -13.738 -43.573 -24.443 44.497 933.9 0.643 206045 1023.6 15.599 -14.451 -13.670 -43.510 -24.075 44.291 935.2 0.652

Table B.15 Preliminary Processed Data for Data Set 15 —Potassium Runs at 11060F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 ~F ~F ~F ~F ~F ~F ~F ~F lbs./sq.in. ISOTHERMAL 206046 1104.5 1.063 -8.584 -14.813 -40.855 7.080 34.626 810.1 0.174 206047 1105.0 1.112 -8.559 -14.622 -41.436 6.966 35.373 812.0 0.179 206048 1104.8 1.114 -8.627 -14.733 -41.237 6.822 35.131 815.0 0.185 206049 1104.8 1.182 -8.601 -14.720 -41.745 6.902 35.626 811.9 0.179 206050 1105.5 1.228 -8.504 -14.737 -41.118 7.317 34.885 812.7 0.180 206051 1105.9 1.245 -8.669 -14.838 -41.347 6.961 35.178 813.1 0.181 206052 1105.3 1.360 -8.826 -14.788 -41.288 6.538 35.326 813.1 0.181 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.7 VOLTS 206055 1108.9 -3.936 -9.237 -14.868 -41.194 1.402 35.563 808.7 0.171 206056 1109.3 -3.923 -9.347 -14.864 -41.368 0.885 35.851 809.7 0.172 206057 1109.0 -3.944 -9.419 -14.923 -41.487 0.792 35. 983 809.6 0.172 206058 1109.1 -3.838 -9.449 -14.970 -41.741 0.792 36.220 810.3 0.174 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.0 VOLTS 206061 1110.6 -5.491 -8.762 -14.847 -41.288 -0.394 35.203 808.7 0.170 206062 1108.6 -5.381 -8.809 -14.605 -41.258 -1.067 35.462 808.7 0.170 206063 1109.3 -5.436 -8.822 -14.669 -40.851 -1.139 35.004 810.0 0.172 206064 1107.5 -5.385 -8.953 -14.805 %-40.783 -1.266 34.931 809.0 0.170 206065 1110.0 -5.343 -8.915 -14.822 -40.936 -1.152 35.029 811.7 0.178 206066 1109.5 -5.288 -8.906 -14.923 -41.224 -1.080 35.207 811.6 0.178

Table B.16 Preliminary Processed Data for Data Set 16 —Potassium Runs at 11080F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF 0F 0F OF lbs./sq.in. ISOTHERMAL 206070 1109.5 10.224 -11.381 -14.728 -43.639 -2.953 40.292 909.7 0.490 206071 1109.4 10.330 -11.444 -14.944 -43.953 -2.677 40.453 909.5 0.490 206072 1106.6 10.334 -11.618 -15.000 -44.029 -3.156 40.647 916.7 0.535 206073 1106.6 10.389 -11.529 -14.851 -43.457 -3.177 40.135 917.0 0.535 206074 1106.2 10.389 -11.521 -14.889 -44.101 -3.300 40.733 916.1 0.533 HEATED TOP PLATE - GUARD HEATER VOLTAGE ='8.0 VOLTS 206075 1110.5 3.525 -11.588 -15.008 -45.525 -9.953 42.105 907.7 0.485 206076 1111.6 3.483 -11.779 -15.021 -45.309 -10.004 41.779 909.0 0.495 206077 1110.8 3.508 -11.690 -14.974 -45.300 -9.868 42.016 909.0 0.495 206078 1111.2 3.525 -11.639 -14.957 144. 9 61 -9.724 41.643 909.3 0.496 206079 1112.2 3.529 -11.627 -14.915 -44.978 -9.822 41.690 909.8 0.499 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 9.0 VOLTS 206080 1112.1 2.351 -11.177 -14.911 -44.161 -11.177 40.427 907.6 0.490 206081 1115.3 2.567 -11.245 -14.860 -44.050 -11.669 40.435 911.2 0.510 206082 1114.3 2.588 -11.029 -14.843 -43.661 -10.919 39.847 911.0 0.510 206083 1115.9 2.754 -11.012 -14.966 -43.411 -10.677 39.457 913.2 0.520 206084 1112.9 2.300 -11.190 -15.105 -44.487 -10.898 40.572 908.2 0.491 206085 1113.1 2.173 -11.300 -15.076 -44.343 -11.165 40.567 908.1 0.491 206086 1113.2 2.292 -10.932 -14.750 -44.474 -10.940 40.656 908.8 0.495 206087 1114.0 2.369 -11.000 -14.847 -44.483 -10.894 40.636 910.0 0.500 206088 1113.2 2.402 -11.245 -14.940 -43.432 -11.173 39.737 909.6 0.499 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.5 VOLTS 206089 1110.7 6.224 -12.533 -14.966 -44.961 -7.165 42.528 914.5 0.515 206090 1111.5 6.152 -12.419 -14.881 -45.618 -7.165 43.156 915.3 0.521

Table B.17 Preliminary Processed Data for Data Set 17 —Potassium Runs at 11130F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 ~OF OF OF F F F F F ~F ~F ~F lbs./sq.in. ISOTHERMAL 206091 1105.1 19.161 -14.716 -15.262 -47.495 -12.483 46.949 1003.7 1.158 206092.1104.7 19.360 -14.262 -15.063 -46.601 -11.652 45.800 1005.7 1.176 206093 1106.3 19.533 -14.296 -14.953 -46.372 -11.927 45.715 1008.1 1.201 206094 1109.9 19.584 -14.762 -15.101 -46.432 -13.021 46.093 1011.2 1.231 206095 1109.2 19.792 -14.317 -14.932 -45.461 -12.127 44.846 1012.2 1.412 206096 1109.8 19.580 -14.711 -15.139 -46.199 -13.016 45.771 1011.2 1.232 206097 1109.4 19.656 -14.618 -15.038 -46.038 -12.707 45.618 1011.5 1.235 206098 1110.6 19.457 -14.855 -15.296 -46.478 -12.822 46.037 1011.6 1.235 206099 1109.6 19.605 -14.627 -15.076 -46.555 -12.525 46.106 1011.2 1.232 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.0 VOLTS 206101 1116.2 13.038 -14.025 -15.029 -45.326 -18.186 44.322 1005.7 1.174 206102 1117.1 13.228 -14.211 -15.186 -45.504 -18.381 44.529 1006.7 1.183 206103 1117.6 13.322 -14.203 -15.211 -45.614 -18.203 44.606 1008.0 1.200 206104 1120.3 13.758 -14.105 -15.012 -45.440 -18.542 44.533 1011.5 1.232 206105 1117.4 13.460 -14.059 -14.983 -45.266 -18.241 44.342 1008.9 1.210 206106 1118.0 13.690 -14.207 -15.114 -45.716 -18.673 44.809 1009.1 1.211 206107 1117.6 13.508 -14.266 -15.076 -45.711 -18.944 44.901 1008.1 1.200 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206108 1111.2 14.144 -14.529 -15.305 -47.496 -16.800 46.643 1002.5 1.140 206109 1111.7 14.148 -14.716 -15.296 v-47. 555 -17.279 46.975 1002.6 1.141 206110 1112.2 14.288 -14.203 -14.983 -47.262 -16.690 46.482 1004.6 1.162 206111 1114.0 14.250 -14.415 -15.055 -46.656 -17.029 46.016 1006.5 1.185 206112 1114.2 14.372 -14.343 -14.843 -46.694 -17.228 46.194 1007.0 1.190 206113 1114.6 14.411 -14.483 -15.211 -46.317 -17.237 45.589 1007.3 1.192 206114 1114.0 14.283 -14.309 -14.983 -46.889 -17.152 46.215 1006.5 1.185

Table B.l8 Preliminary Processed Data for Data Set 18 —Potassium Runs at 11900F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF F OF OF Fbs./sq.in ISOTHERMAL 206139 1185.9 3.072 -10.276 -15.872 -44.029 4.638 38.433 900.6 0.463 206140 1186.0 3.182 -10.059 -15.757 -43.719 5.034 38.021 901.0 0.467 206141 1186.2 3.314 -10.234 -15.936 -44.140 4.761 38.438 902.1 0.471 206142 1185.5 3.217 -10.302 -15.940 -43.863 4.557 38.225 900.8 0.465 206143 1186.0 3.131 -10.055 -15.795 -43.523 4.178 37.783 901.1 0.467 206144 1188.4 3.034 -10.370 -15.846 -44.038 4.229 38.563 903.2 0.476 206145 1188.2 2.910 -10.123 -15.693 -43.153 4.851 37.583 903.4 0.478 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206147 1190.7 -1.319 -10.148 -15.600 -43.263 -0.357 37.811 899.7 0.459 206148 1189.9 -1.225 -10.144 -15.544 -43.714 -0.153 38.314 899.1 0.457 206149 1190.3 -1.200 -10.280 -15.672 -43.629 -0.293 38.237 899.5 0.459 206150 1190.1 -1.225 -10.238 -15.604 -43.421 -0.353 38.055 899.3 0.458 206151 1190.8 -1.310 -10.051 -15.476 -43.727 -0.442 38.302 900.2 0.461 206152 1190.7 -1.378 -10.080 -15.468 -43.561 -0. 446 38.173 900.1 0.460

Table B.19 Preliminary Processed Data for Data Set 19 —Potassium Runs at 11920F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF F OF OF OF OF OFbs./sq.in. ISOTHERMAL 206153 1184.7 13.285 -12.923 -15.506 -45.982 -5.097 43.399 1002.4 1.141 206154 1187.1 13.285 -13.017 -15.702 -46.544 -5.225 43.859 1004.6 1.168 206155 1186.2 13.306 -13.059 -15.672 -46.868 -5.340 44.255 1003.5 1.157 206156 1186.7 12.872 -12.774 -15.200 -46.519 -5.319 44.093 1003.7 1.157 206157 1188.7 12.927 -12.714 -15.187 -46.289 -5.319 43.816 1005.0 1.171 206158 1189.5 12.459 -12.846 -15.144 -45.914 -5.957 43.616 1005.1 1.171 206159 1188.1 13.234 -12.544 -15.340 -45.791 -4.804 42.995 1004.4 1.166 206160 1187.6 12.795 -12.710 -15.272 -45.940 -5.327 43.378 1002.9 1.151 U, 206161 1187.6 12.859 -12.544 -15.251 -46.476 -5.144 43.769 1003.1 1.152 206162 1185.0 12.753 -12.340 -14.974 -45.634 -4.731 43.000 1000.3 1.128 206163 1186.4 12.548 -12.408 -15.072 -45.557 -4.880 42.893 1001.6 1.138 206164 1186.7 12.838 -12.629 -15.523 -45.591 -4.795 42.697 1002.6 1.144 206165 1189.2 13.187 -12.723 -15.523 -45.591 -5.097 42.791 1005.4 1.177 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206166 1192.2 8.600 -13.174 -15.714 -45.880 -10.404 4.3.340 1001.4 1.137 206167 1194.0 8.706 -13.280 -15.846 -46.442 -10.421 43.876 1002.9 1.151 206168 1194.7 8.740 -13.161 -15.778 -45.727 -10.255 43.110 1003.7 1.158 206169 1195.6 8.889 -13.191 -15.770 -46.136 -10.412 43.557 1004.5 1.164 206170 1196.2 8.914 -13.165 -15.676 -45.991 -10.527 43.480 1005.0 1.171 206171 1195.9 8.774 -13.200 -15.829 -46.178 -10.463 43.549 1005.2 1.172 206172 1194.8 8.770 -13.319 -15.812 -46.468 -10.791 43.975 1003.2 1.150 206173 1193.8 8.825 -13.268 -15.753 -46.051 -10.757 43.566 1002.6 1.148 206174 1193.7 8.663 -13.144 -15.697 -45.978 -10.595 43.425 1002.4 1.147

Table B.20 Preliminary Processed Data for Data Set 20 —Potassium Runs at 12O10F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 OF F OF OF OF OF OF OFbs/sq.in. ISOTHERMAL 206175 1197.9 24.553 -17.042 -15.770 -49.710 -18.855 50.982 1108.3 1.205 206176 1197.2 24.387 -16.872 -15.655 -50.123 -18.510 51.340 1107.2 1.190 206177 1195.0 24.672 -16.923 -15.880 -49.740 -18.161 50.783 1106.0 1.181 206178 1195.2 24.395 -16.663 -15.493 -49.331 -18.251 50.501 1106.7 1.189 206179 1195.5 24.970 -17.106 -16.123 -49.200 -18.034 50.183 1106.9 1.190 206180 1194.6 24.736 -17.136 -16.106 -49. 421 -18.361 50.451 1105.1 1.171 206181 1193.8 24.791 -17.051 -16.170 -49.310 -17.931 50.191 1104.9 1.170 206182 1194.5 24.961 -17.004 -16.217 -49.757 -17.778 50.544 1105.8 1.179 206183 1196.2 25.259 -16.829 -16.136 -49.357 -17.353 50.050 1109.2 1.210 206184 1196.2. 24.800 -17.097 -16.280 -49.936 -18.182 50.753 1107.1 1.190 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206185 1202.0 20.502 -16.936 -16.336 -49.825 -22.127 50.425 1106.3 1.185 206186 1202.7 20.251 -17.125 -16.323 -49.795 -22.757 50.597 1105.6 1.173 206187 1203.9 20.582 -16.931 -16.336 -49.906 -22.259 50.501 1108.5 1.203 206188 1203.8 20.527 -16.957 -16.314 -49.557 -22.365 50.200 1108.1 1.201 206189 1204.5 20.497 -16.995 -16.263 -50.042 -22.753 50.774 1108.2 1.201 206190 1203.9 20.200 -17.310 -16.429 -50.051 -23.131 50.932 1106.4 1.182 206191 1202.0 20.182 -16.991 -16.246 -49.736 -22.582 50.481 1104.3 1.161 206192 1202.4 20.238 -16.991 -16.263 -49.842 -22.659 50.570 1104.5 1.162

Table B.21 Preliminary Processed Data. for Data Set 21 —Potassium Runs at 1004F. RUN THERMOCOUPLES NULL BOILER PRESSURE,......,.,.... 3 4-3 5-3 6-3 7-3 8-3 ~F ~F ~F ~F ~F ~F ~F ~F lbs./sq.in. ISOTHERMAL 206197 999.0 8.396 -7.687 -10.616 -41.548 -3.088 38.619 801.4 0.160 206198 998.4 8.324 -7.848 -10.649 -41.662 -3.746 38.861 800.2 0.158 206199 998.2 8.392 -7.430 -10.282 -41.143 -2.831 38.291 801.3 0.160 206200 997.5 8.379 -7.599 -10.413 -41.329 -3.240 38.515 801.6 0.161 206201 996.6 8.421 -7.493 -10.413 -41.177 -2.746 38.257 802.0 0.162 206202 999.8 8.358 -7.540 -10.075 -41.316 -3.438 38.781 802.6 0.163 206203 999.6 8.451 -7.472 -10.388 -41.244 -3.008 38.328 802.7 0.163 206204 1000.3 8.367 -7.945 -10.691 -41.962 -3.215 39.216 802.3 0.162 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.2 VOLTS 206205 1006.3 2.890 -8.101 -10.784 -42.092 -9.003 39.409 799.4 0.156 206206 1005.7 2.965 -7.962 -10.670 -42.029 -9.025 39.321 798.9 0.155 206207 1004.5 2. 928 -7.881 -10.645 -41.915 -8.852 39.151 797.6 0.153 206208 1004.6 2.940 -7.772 -10.649 -41.763 -8.607 38.886 798.0 0.154 206209 1006.5 2.974 -8.000 -10.641 -41.915 -9.033 39.274 798.8 0.155 206210 1006.1 2.919 -7.839 -10.481 -41.839 -8.860 39.197 798.0 0.154 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206211 1009.1 1.898 -7.616 -10. 375 -41.603 -10.232 38.844 798.0 O. 155 206212 1008.2 1.873 -7.405 -10.295 -41.438 -9.751 38.548 797,4 0.152 206213 1009.3 1.898 -7.206 -10.223 -41.248 -9.350 38.231 798.6 0.156 206214 1010.1 1.907 -7.468 -10.405 -41.653 -9.776 38.717 7 98.5 0. 156 206215 1007.0 1.877 -7.708 -10.556 -47. 751 -10.476 38.903 797.9 0.155 206216 1006.7 1.915 -7.586 -10.489 -41.535 -10.316 38.632 797.9 0. 155 206217 1005.9 2.016 -7.375 -10.523 -41.312 -9.573 38.164 797.9 0.155 206218 1007.7 1.970 -7.421 -10.518 -41.341 -9.603 38.244 798.3 0.156

Table B.22 Preliminary Processed Data for Data Set 22 —Vacuum Runs at 9980F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF OF OnF mmHg ISOTHERMAL 206219 995.8 3.590 -7.151 -10.962 -40.316 1.181 36.505 0.003 206220 998.6 4.122 -6.755 -10.953 -40.156 2.215 35.958 0.003 206221 999.2 3.700 -6.991 -10.202 -14.350 -0.940 37.139 0. 003 206222 998.5 3.603 -6.957 -10.523 -40.105 0.438 36.539 0.003 206223 998.3 3.603 -6.751 -10.337 -40.012 0.481 36.426- 0.003 206224 998.4 3.721 -7.071 -10.704 -40.316 0.375 36.683 0.003 206225 993.6 3.544 -6.793 -10.472 -39.767 0.691 36.088 0.003 206226 993.0 3.556 -6.831 -10.253 -39.805 0.219 36.383 0.003 206227 994.5 3.780 -6.219 -10.151 -39.172 2.088 35.240 0.003 206228 998.0 3.691 - 6. 22 3 -10.126 -39.299 1.928 35.396 0.003 206229 999.5 3.763 -6.822 -10.628 -40.004 1.248 36.198 0.003 H 00 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.0 VOLTS 206230 997.9 -0.240 -7.202 -10.489 -40.126 -4.151 36.839 0.003 206231 997.1 -0.194 -6.890 -10.426 -39.970 -3.675 36.434 0.003 206232 999.6 0.113 -6.991 -10.687 -39.983 -3.240 36.287 0.003 206233 1001.0 0.147 -7.282 -10.717 -40.156 -3.915 36.721 0.003 206234 999.9 0.021 -7.345 -10.451 -40.358 -4.869 37.252 0.003 206235 998.6 -0.080 -6.890 -10.308 -39.708 -3.481 36.290 0.003 206236 997.8 0.021 -6.848 -10.240 -39.738 -3.392 36.346 0.003 206237 1003.0 0.088 -6.476 -10.265 -39.405 -1.940 35.616 0.003 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.0 VOLTS 206238 1000.4 -1.827 -6.890 -10.519 -39.852 -5.109 36.223 0.003 206239 997.3 -1.367 -6.417 -10.362 -39.531 -4.611 35.586 0.003 206240 997.7 -1'.312 -6.527 -10.459 -39.570 -4.367 35.578 0.003 206241 998.4 -1.130 -6.700 -10.869 -39.683 -4.434 35.514 0.003 206242 998.9 -0.902 -6.544 -10.687 -39.552 -4.198 35.409 0.003 206243 1001.0 -1.080 -6.746 -10.611 -39.683 -4.852 35.818 0.003 206244 1006.0 -0.498 -6.797 -10.608 -40.380 -4.747 36.227 0.003 206245 1005.5 -0.814 -6.835 -10.594 -40.008 -4.894 36.249 0.003 206246 1005.2 -0.759 -6.966 -1Q.848 -40.354 -5 004 36.472 0.003

Table B.23 Preliminary Processed Data for Data Set 23 —Vacuum Runs at 10000F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF OF OF mm Hg ISOTHERMAL 205654 990.5 -2.447 -5.219 -9.864 -38.751 5.696 34.106 0.002 205655 990.0 -2.253 -5.037 -9.877 -38.413 6.151 33. 573 0.002 205656 990.8 -2.227 -5.109 -9.873 -38.691 5.725 33.927 0.002 205657 997.0 -2.008 -4.995 -9.902 -38.308 6.059 33.401 0.002 205658 995.9 -2.071 -4.932 -10.059 -38.333 6.037 33.206 0.002 205659 995.2 -1.987 -5.059 — 10.177 -38.691 5.995 33.573 0. 002 205660 994.2 -2.417 -5.080 -10.257 -38.691 6.621 33.514 0.002 205661 994.9 -2.206 -4.354 -9.468 -38.232 7.291 33.118 0.002 205662 996.3 -1.987 -5.016 -10.303 -38.611 6.729 33.324 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.5 VOLTS 205663 1004.9 -7.708 -5.164 -10.177 -38.713 0.497 33.700 0.003 205664 1003.7 -7.708 -5.181 -10.088 -38.742 0.510 33.835 0.003 205665 1003.8 -7.738 -5.270 -10.270 -38.848 0.607 33.848 0.002 205666 1003.1 -8.063 -5.181 -9.940 -38.755 0.831 33.996 0.002 205667 1002.0 -8.177 -5.122 -9.902 -38.945 0.708 34.165 0.002 205668 1002.5 -7.911 -5.274 -10.097 -39.016 0.717 34.193 0.002 205669 1003.3 -7.729 -5.063 -10.223 -38.995 0.282 33.835 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.2 VOLTS 205670 1005.2 -8.827 -5.063 -10.367 -38.869 1.755 33.565 0.003 205671 1005.6 -8.742 -4.848 -10.270 -38.793 1.278 33.371 0.003 205672 1001.7 -9.109 -4.877 -10.151 -38.8-48 1.405 33.574 0. 002 205673 1002.2 -9.046 -5.008 -10.413 -38.818 1.282 33.397 0.002 205674 1002.6 -9.080 -4.995 -10.333 -38.784 -1.341 33.446 0.002 205675 1002.6 -9.050 -4.586 -9.645 -38.354 -1.282 33.295 0.002 205676 998.7 -9.172 -4.848 -9.936 -38.236 -1.966 33.148 0. 002 205677 998.3 -9.054 -4.835' -10.244 -38.181 -1.497 32.772 0. 002 205678 1004.4 -8.784 -5.059 -10.172 -38.751 -2.164 33.638 0.002 205679 1003.7 -8.654 -5.215 -10.594 -38.932 -1.827 33.553 0.002

Table B.24 Preliminary Processed Data for Data Set 24 —Vacuum Runs at 10020F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 O OF F OF 0F OF mHg ISOTHERMAL 206763' 995.2 -12.767 -8.476 -13.092' -34.924 4'.839 30.308 0.002 206764 994.7 -12.654 -8.219 -13.029 -34.691 5.662 29.881 0.002 206765 995.5 -12.734 -8.172 -13.012 -34.126 5.751 29.286 0.002 206766 993.3 -12.928 -8.434 -12.974 -34.383 4.839 29.843 0.002 206767 992.1 -12.772 -8.308 -12.970 -34.383 5.244 29.721 0.002 206768 999.3 -12.362 -8.101 -12.670 -34.333 5.535 29.764 0.002 206769 999.7 -12.388 -8.118 -12.662 -34.320 5.907 29.776 0.002 206770 1004.1 -12.362 -8.291 -12.578 -34.696 5.413 30.409 0.002 206771 1004.3 -12.227 -8.084 -12.565 -34.594 5.983 30.113 0.002 206772 1005.0 -12.177 -8.075 -12.464 -34.388 6.383 29.999 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.6 VOLTS 206757 1004.0 -19.873 -7.856 -12.666 -34.776 -0. 839 29.966 0.001 206758 1005.6 -20.459 -8.181 -13.181 -34.772 -0.949 29.772 0.001 206759 1007.2 -20.303 -8.274 -13.122 -35.151 -1.135 30.303 0.001 206760 1007.5 -20.037 -8.037 -13.274 -34.848 -0.383 29.611 0.001 206761 1004.3 -20.248 -8.219 -13.054 -34.772 -1.130 29.937 0.001 206762 1005.1 -20.033 -8.029 -13.080 -34.911 -0.464 29.860 0.001

Table B.25 Preliminary Processed Data for Data Set 25 —Vacuum Runs at 11910F. RUN THERMOCOUPLES NULL PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OFF FF mmHg ISOTHERMAL 206773 1189.6 -10.329 -8.923 -14.255 -38.842 4.965 33.510 0.003 206774 1185.0 -10.502 -9.600 -14.778 -39.089 3.595 33.911 0.003 206775 1185.8 - 9.995 -9.148 -14.548 -38.629 4.812 33.229 0.002 206776 1184.8 -10.234 -9.497 -15.000 -38.693 3.991 33.190 0.002 206777 1184.9 -10.157 -9.038 -14.497 -38.272 5.306 32.813 0.002 206778 1187.6 -10.204 -9.174 -14.897 -38.629 4.744 32.905 0.002 206779 1188.4 -10.012 -9.191 -15.182 -38.600 4.829 32.609 0.002 206780 1189.4 -10.365 -9.519 -14.689 -38.604 4.000 33.434 0.002 206781 1188.1 -10.255 -9.289 -15.127 -39.093 4.344 33.255 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.6 VOLTS 206782 1190.5 -14.740 -9.004 -14.817 -38.361 0.774 32.548 0.002 206783 1193.5 -14.842 -8.842 -14.285 -38.178 -1.012 32.735 0.002 206784 1193.3 -15.123 -9.259 -15.089 -39.187 -0.350 33.357 0.002 206785 1193.2 -14.863 -8.991 -14.995 -38.608 0.493 32.604 0.002 206786 1192.2 -14.600 -8.855 -14.753 -38.268 1.000 32.370 0.002 206787 1195.4 -14.663 -9.102 -14.417 -38.434 0.217 33.119 0.002 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 5.1 VOLTS 206788 1192.2 -14.012 -9.000 -13.697 -37.889 1.425 33.192 0.002 206789 1192.2 -14.204 -8.961 -14.051 -38.182 1.408 33.092 0.002 206790 1192.2 -14.174 -9.140 -14.804 -38.638 1.046 32.974 0.002 206791 1195.0 -14.038 -9.097 -14,255 -48.412 1.361 33.254 0.002 206792 1195.7 -14.068 -9.438 -14.787 -39.072 0.276 33.723 0.002 206793 1193.7 -14.140 -9.238 -14.225 -38.744 0.940 33.757 0.002 206794 1194.3 -13.995 -9.327 -14.110 -38.638 0.565 33.855 0.002 206795 1195.2 -14.114 -9.161 -13.565 -37-944 0.872 33.50

Table B.26 Preliminary Processed Data for Data Set 26 —Potassium Runs at 10160F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 F-3 OF OOF OF OF Obs./sq.in. ISOTHERMAL 206801 1011.1 18.590 -14.295 -14.278 -39.316 -12.413 39.333 905.1 0.482 206802 1009.5 18.109 -14.675 -14.430 -40.654 -14.691 40.899 902.1 0.470 206803 1008.8 18.118 -14.822 -14.472 -40.535 -14.856 40.885 901.1 0.466 206804 1015.0 18.105 -15.443 -14.991 -41.084 -14.632 41.536 906.4 0.492 206805 1014.9 18.489 -15.135 -14.864 -40.767 -14.316 41.038 907.7 0.498 206806 1014.4 18.227 -15.430 -15.054 -40.924 -14.430 41.300 906.6 0.492 00 206807 1012.1 17.316 -14.278 -14.088 -41.143 -13.594 41.333 901.2 0.466 206808 1009.3 18.312 -14.894 -14.784 -40.383 -13.978 40.493 903.5 0.478 206809 1012.7 18.333 -15.008 -14.405 -40.856 -15.763 41.457 906.0 0.490 206810 1012.1 18.451 -15.084 -14.603 -40.540 -14.928 41.021 906.6 0.492 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.95 VOLTS 206811 1022.8 11.223 -14.780 -14.523 -40.654 -21.303 40.911 898.5 0.453 206812 1018.0 12.185 -14.063 -14.004 -40.687 -21.354 40.746 899.1 0.460 206812 1017.4 12.303 -14.135 -13.962 -40.957 -21.679 41.130 899.0 0.460 206814 1019.7 11.392 -13.805 -14.059 -41.291 -20.025 41.037 895.9 0.441 206815 1018.1 11.282 -14.101 -14.210 -40.455 -20.489 40.346 894.7 0.440 206816 1017.2 11.430 -13.751 -14.118 -40.746 -20.202 40.379 895.1 0.440 206818 1017.0 11.624 -13.700 -14.004 -40.746 -20.130 40.442 895.5 0.441 206819 1021.4 11.966 -13.810 -14.261 -40.248 -19.662 39.797 901.7 0.468

Table B.27 Preliminary Processed Data for Data Set 27 —Potassium Runs at 10160F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF ~F ~F OF lF OF ~F lbs./sq.in. ISOTHERMAL 206821 1008.4 17.109 -14.324 -14.590 -40.139 -12.814 39.873 905.5 0.486 206822 1009.7 17.679 -14.805 -14.683 -40.308 -14.075 40.430 909.0 0.502 206823 1010.8 18.080 -14.784 -14.527 -40.645 -14.767 40.902 909.7 0.505 206824 1011.4 16.620 -14.493 -14.620 -40.278 -12.611 40.151 904.4 0.480 206825 1010.5 16.278 -14.476 -14.489 -39.886 -12.620 39.873 901.1 0.467 206826 1010.0 16.303 -14.455 -14.535 -39.843 -12.160 39.763 901.4 0.468 206827 1010.7 17.126 -14.717 -14.839 -40.308 -13.392 40.186 906.7 0.492 206828 1011.8 17.059 -14.869 -14.877 -40.451 -13.523 40.443 907.2 0.493 206829 1013.2 17.063 -14.662 -14.459 -39.772 -13. 362 39.975 908.9 0.502 206830 1012.3 16.603 -14.508 -14.443 -39.392 -12.578 39.457 906.4 0.491 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.0 VOLTS 206831 1019.8 11.341 -14.670 -14.852 -39.717 -18.485 39.535 903.5 0.477 206832 1019.4 11.303 -14.742 -14.856 -40.400 -19.675 40.286 902.9 0.474 206833 1020.1 11.531 -14.890 -15.004 -39.970 -19.472 39.856 905.5 0.487 206834 1015.8 12.772 -13.776 -13.772 -40.143 -20.276 40.147 906.7 0.494 206835 1018.7 13.341 -14.409 -14.645 -40.367 -21.772 40.131 911.5 0.513 206836 1017.0 13.177 -14.822 -14.932 -40.810 -22.514 40.700 908.5 0.500 206837 1016.1 13.413 -14.700 -14.936 -40.721 -21.843 40.485 909.1 0.502

Table B.28 Preliminary Processed Data for Data Set 28 —Potassium Runs at 10950F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF OF OF OF F OF bs./sq.in. ISOTHERMAL 206838 1090.5 1.360 -8.283 -13.957 -40.588 8.686 34.914 801.4 0.161 206839 1090.5 1.343 -8.313 -13.864 -40.572 8.461 35.021 801.2 0.161 206840 1089.1 1.419 -8.360 -13.805 -40.809 8.991 35.364 800.4 0.159 206841 1091.0 1.224 -8.457 -14.025 -40.025 8.872 34.457 802.5 0.163 206842 1092.1 1.385 -8.088 -13.805 -40.169 9.190 34.452 803.5 0.165 206843 1092.9 1.237 -8.682 -13.995 -40.953 8.182 35.640 803.7 0.165 206844 1088.7 1.207 -8.673 -14.665 -40.436 8.677 35.444 797.7 0.153 206845 1087.2 1.194 -8.559 -14.398 -40.940 8.834 35.101 797.4 0.152 206846 1088.1 1.004 -8.466 -14.059 -40.495 7.898 34.902 797.3 0.152 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.8 VOLTS 206847 1098.4 -3.872 -8.716 -14.004',41.199 2.211 35.911 800.7 0.160 206848 1098.6 -3.915 -8.457 -13.817 -40.851 2.322 35.491 801.4 0.161 206849 1097.0 -4.021 -8.495 -13.957 -41.038 2.190 35.576 798.9 0.156 206850 1096.8 -4.093 -8.525 -13.957 -41.156 1.940 35.724 798.8 0.156 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.6 VOLTS 206852 1097.7 -5.038 -8.351 -14.487 -39.703 1.237 33.567 798.1 0.155 206853 1097.8 -5.266 -8.326 -14.271 -40.072 0.639 34.127 797.5 0.153 206855 1094.1 -5.427 -8.241 -14.021 -41.279 1.182 35.499 791.4 0.142 206856 1096.5 -5.279 -7.953 -13.864 -40.741 1.635 34.830 794.5 0.148 206857 1097.4 -5.156 -7.902 -13.813 -40.843 1.699 34.932 796.0 0.151 206858 1098.2 -5.105 -7.665 -13.652 -40.733 1.542 34.746 797.2 0.152 206859 1098.5 -5.088 -8.161 -13.957 -4'i.1O5 1.491 35.309 797.5 0.153 206860 1096.8 -5.161 -7.966 -13.542 -39.004 1.716 33.428 796.0 0.150 206861 1096.2 -5.351 -8.093 -13.665 -38.919 1.411 33.3.47 795.0 0.149

Table B.29 Preliminary Processed Data for Data Set 29 —Potassium Runs at 10970F. RUN THERMOCOUPLES NULL BOILER PR'ESSUE 3 4-3 5-3 6-3 7-3 8-3 0F 0F F 0F F F 0F F lbs./sq~in. ISOTHERMAL 206862 1094.7 9.300 -11.483 -14.283 -41.533 -1.224 38.733 890.1 0.423 206863 1095.4 9.572 -11.516 -14.588 -41.847 -0.932 38. 775 891.7 0.429 206864 1098.0 9.398 -11.686 -14.330 -41.021 -1.733 38.377 894.9 0.440 206865 1095.8 9.194 -11.703 -14.317 -41.029 -1.779 38.415 891.7 0.429 206866 1094.5 9.338 -11.360 -14.292 -40.809 -0.716 37.877 892.1 0. 430 206867 1095.0 9.351 -11.720 -14.542 -41.'750 -1.241 3 8.928 891.7 0.429 206868 1094.9 9.351 -11.474 -14.207 -41.220 -1.169 38.487 893.0 0.433 206869 1094.1 9.461 -11.449 -14.292 -41.427 -0.936 38.584 892.0 0.430 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.42 VOLTS 206870 1101.8 2.906 -10.881 -13.906 -41.110 -7.881 38.805 887.3 0.413 206871 1099.5 3.127 -10.453 -13.830 -42.059 -7.885 38.682 885.4 0.405 U' 206872 1100.0 3.262 -10.300 -13.788 -42.067 -7.508 38.579.886.5 0.411 206873 1096.6 3.110 -10.423 -13.906 -41.737 -7.572 38.254 883.4 0.400 2-06874 1098.9 3.419 -10. 19.0 -13.970 -41.072 -6.559 37.292 886.6 0.411 206875 1102.3 3.072 -10. 529 -13.885 -41.949 -7.402 38.593 888.1 0.418 206876 1103.1 3.148 -10.605 -13.961 -42.233 -7.309 38. 877 889.0 0.420 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.0 VOLTS 206877 1100.2 3.334 -11.000 -13.927 -41.381 -7.076 38.454 885.1 0.405 206878 1099.5 3.466 -10.733 -14.042 -42.148 -6.940 38.839 884.7 0.402 206879 1098.1 3.466 -10.644 -13.953 -42.093 -6.622 38.784 883.8 0.400 206880 1098.7 3.500 -10.639 -13.944 -41.966 -6.605 38.-661 884.6 0.402 206881 1099.1 3.555 -10.593 -13.961 -42.207 -6.699 38.839 885.1 0.406 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.6 VOLTS 206882 1097.4 3.872 -10.572 -13.783 -42.618 -5.864 39.407 883.8 0.400 206883 1097.7 3.750 -10.834 -13.830 -42.779 -6.669 39.783 883.2 0.399 206884 1101.9 3.766 -11.033 -13.974 -42.033 -6.186 39.092 887.0 0.413 206885 1100.2 3.775 -10.716 -14.025 -42.461 -6.000 39.152 885.4 0.407

Table B.30 Preliminary Processed Data for Data Set 30 —Potassium Runs at 11910F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF O OF OF OF OF lbs./sq.in. ISOTHERMAL 206886 1189.6 -5.182 -7.548 -15.710 -40.842 15.970 32.680 817.3 0.191 206887 1186.3 -5.119 -7.480 -15.319 -40.765 15.523 32.926 816.1. 0.189 206888 1184.6 -5.153 -7.714 -15.417 -40.680 15.127 32.977 814.7 0.187 206889 1186.1 -5.136. -7.885 -15.408 -40.957 14.868 33.434 818.2 0.193 206890 1185.0 -4.919 -7.868 -15.434 -40.923 15.055 33.357 818.0 0.193 206891 1184.4 -5.157 -7.846 -15.285 -40.506 14.893 33.067 816.4 0.189 206892 1185.0 -4.974 -7.834 -15.310 -40.459 15.242 32.983 816.7 0.190 206893 1185.0 -5.021 -7.693 -15.021 -40.225 15.293 32.897 816.7 0.190 206894 1186.3 -5.204 -7.940 -15.131 -39.965 15.000 32.774 812.7 0.183 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 6.8 VOLTS 206895 1192.4 -9.936 -7.165 -14.497 -41.204 9.795 33.827 818.1 0. 193; 206896 1191.5 -9.974 -7.289 -14.663 -41.523 9.885 34.149 817.7 0.191 206897 1191.5 -9.582 -7.323 -14.676 -41.357 9.459 34.004 817.5 0.191 206898 1192.0 -9.510 -7.242 -14.638 -41.136 9.838 33.740 817.4 0.191 00 206899 1195.3 -9.668 -8.200 -15.651 -40.953 10.021 33.502 819.5 0.194 a' 206900 1194.1 -9.638 -8.417 -15.753 -41.204 9.655 33.868 818.5 0.193 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.75 VOLTS 206901 1195.3 -10.182 -6.838 -14.651 -40.961 9.361 33.150 818.4 0.194 206902 1191.8 -10.127 -6.842 -14.425 -41.331 8.936 33.748 816.6 0.190 206903 1196.8 -10.382 -6.902 -14.625 -41.208 9.025 33.485 820.5 0.197 206904 1196.3 -10.136 -6.902 -14.642 -41.106 8.974 33.366 820.2 0.197 206906 1193.5 -10.191 -6.961 -14.497 -41.140 8.804 33.604 818.7 0.194 206907 1193.6 -10.165 -7.008 -14.587 -41.148 8.855 33.569 818.9 0.195 206908 1193.7 -10.289 -7.234 -14.770 -41.323 8.451 33.787 819.8 0.195 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.5 VOLTS 206909 1193.3 -11.540 -6.595 -14.731 -40.268 7.808 32.132 814.5 0.186 206910 1194.3 -11.408 -6.472 -14.587 -40.978 8.025 32.863 815.3 0.187 206911 1193.2 -11.340 -6.676 -14.608 -40.931 7.761 32.999 815.1 0.187 206912 1194.7 -11.408 -6.395 -14.417 -40.885 7.497 32.863 816.2 0.189 206913 1194.5 -11.480 -6.455 -14.617 -40.523 7.497 32.361 816.2 0.189 206914 1192.5 -11.548 -6.484 -14.714 -40.408 7.791 32.183 813.5 0.184 206915 1193.9 -11.451 -6.595 -14.502 -'4t.097 7.400 33.190 815.7 0.188 206916 1193.5 -11.408 -6.438 -14.476 -40.965 7.655 32.927 816.0 0.189

Table B.31 Preliminary Processed Data for Data Set 31 —Potassium Runs at 1191'F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF F OF OF OF F bs./sq.in. ISOTHERMAL 206917 1185.7 -0.910 -9.459 -15.710 -41.497 10.595 35.246 880.4 0.389 206918 1188.9 -0.931 -9.463 -15.787 -41.778 10.446 35.454 882.9 0.397 206919 1188.6 -1.017 -10.174 -16.251 -42.059 9.978 35.982 883.2 0.399 206920 1186.8 -0.931 -9.967 -15.782 -41.561 9.697 35.476 882.0 0.394 206921 1188.5 -0.889 -8.863 -15.055 -41.740 10.570 35.548 883.4 0.399 206922 1185.9 -0.723 -9.553 -15.600 -41.821 9.782 35.774 882.1 0.394 2-06923 1183.6 -0.531 -9.302 -15.514 -41.225 10.204 35.013 882.6 0.395 206924 1183.1 -0.455 -9.468 -15.587 -41.165 9.931 35.046 881.3 0.391 206925 1186.7 -0.642 -10.182 -16.225 -41.991 9.970 35.948 883.8 0.400 206926 1199.9 -0.553 -10.059 -16.106 -41.748 10.319 35.701 885.2 0.404 206927 1201.1 -0.617 -9.774 -15.923 -41.400 10.365 35.251 885.3 0.404 00 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 8.5 VOLTS 206929 1195.2 -7.204 -8.838 -15.425 -40.400 2.693 33.813 881.8 0.393 206930 1191.8 -7.068 -8.421 -15.042 -40.736 2.025 34.115 880.0 0.385 206931 1191.7 -6.859 -8.425 -15.017 -40.791 2.089 34.199 880.2 0.386 206932 1192.3 -6.765 -8.365 -14.919 -40.782 2.442 34.228 881.2 0.390 206933 1191.9 -6.825 -8.340 -14.702 -41.204 1.710 34.842 880.7 0.389 206934 1198.1 -6.863 -8.429 -15.191 -40.808 2.680 34.046 885.9 0.409 206935 1197.5 -6.965 -8.680 -15.348 -40.659 2.536 33.991 885.5 0.408 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.55 VOLTS 206936 1194.7 -5.974 -8.765 -15.089 -41.046 4.080 34.722 883.6 0.399 206937 1190.1 -5.663 -8.582 -14.736 -41.506 3.863 35.352 880.8 0.390 206938 1190.5 -5.663 -8.-689 -14.761 -41.506 3.582 35.434 881.3 0.391 206939 1190.5 -5.706 -8.638 -14.710 -41.327 3.600 35.255 881.4 0.391 206940 1189.9 -5.880 -9.170 -15.080 -42.331 3.446 36.421 880.5 0.389 206941 1194.2 -5.855 -8.723 -14.987 -41.319 3.736 35.055 883.3 0.399 206942 1194.0 -5.889 -8.634 -14.914 -41.272 3.800 34.992 8 83. 1 0.399 206943 1193.7 -5.817 -8.689 -14.885 -41.314 3.531 35.118 883.2 0.399 206944 1194.0 -5.889 -8.817 -15.072 -41.059 3. EU8 34.804 883.2 0.399

Table B.32 Preliminary Processed Data for Data Set 32 —Potassium Runs at 10990F. RUN THERMOCOUPLES NULL BOILER PRESSURE 3 4-3 5-3 6-3 7-3 8-3 OF OF 0F 0F OF OFF bs./sq.in. ISOTHERMAL 206948 1094.8 0.241 -8.775 -14.419 -39.775 9.385' 34.131 803.3 0.164 206949 1093.4 0.152 -8.364 -14.029 -39.885 9.542 34.220 801.2 0.160 206950 1094.9 0.084 -8.559 -14.080 -39.207 9.661 33.686 802.0 0.162 206951 1094.7 0.220 -8.351 -14.029 -39.538 9.788 33.860 801.5 0.161 206952 1095.3 0.118 -8.326 -13.991 -39.665 9.444 34.000 802.5 0.163 206953 1094.9 0.275 -8.279 -13.991 -39. 77'9 9.601 34.067 802.6 0.163 HEATED TOP PLATE - GUARD HEATER VOLTAGE = 7.15 VOLTS 206954 1101.5 -5.682 -7.932 -13.915 -39.466 3.090 33.483 798.6 0.155 206955 1102.2 -5.608 -7.944 -14.012 -39.504 3.114 33.436 799.2 0.156 206956 1102.5 -5.699 -8.016 -14.042 -39.483 2.788 33.457 799.2 0.156 206957 1101.8 -5.830 -8.194 -13.690 -38.932 2.771 33.436 799.3 0.156 206958 1101.5 -5.788 -8.207 -13.728 -38.766 2.567 33.245 799.0 0.156 206959 1101.4 -5.724 -8.194 -13.733 -38.593 2.872 33.054 798.8 0.156 206960 1100.9 -5.733 -7.902 -13.813 -38.527 3.131 33.614 798.0 0.155 206961 1101.9 -5.648 -7.991 -13.911 -39.805 3.025 33.885 798.9 0.155 206962 1102.4 -5.707 -8.101 -14.000 -39.826 2.830 33.927 799.2 0.156 HEATED TOP PLAME - GUARD HEATER VOLTAGE = 6.55 VOLTS 206963 1103.3 -4.741 -8.110 -13.733 -39.991 3.584 34.368 803.5 0.165 206964 1103.6 -4.775 -8.029 -13.669 -40.105 3.411 34.465 803.9 0.166 206965 1101.1 -4.716 -8.169 -13. 614 -40.423 3.093 34.978 801.8 0.161 206966 1102.5 -4.771 -8.093 -13.525 -40.105 3.453 34.673 803.2 0.164 206967 1101.5 -4.881 -8.351 -13.644 -40U. 173 2.906 34.880 802.2 0.162 206968 1101.1 -4.868 -8.368 -13.622 -39.961 3.114 34.707 801.9 0.161

z189 APPENDIX C COMPUTER PROGRAM FORTRAN II COMPUTER PROGRAM FOR COMPUTING MEAN TEMPERATURE DIFFERENCES'STAT 1 0: 44 SA-T --- - t-0/28/-6-7 1.0 DIMENSION DTI (15), DTH(15), ANULLI(15), ANULLH(15) 19 READ, NI, (DTI(I), I 1-, NI) 20C READ, NI, (ANULLI(I), I: 1, NI) Z4 READ, NH, (DTH(I), I - 1, NH) 25 READ, NH, (ANULLH (I ), I 1, NH) 30 SUM -., 35 DO 20 I - 1, NI 40 20: SUM - SUM + ANULLI (I) 45 ANI - SUM/NI 50 SUM - 0. 55 -DO i30 I - 1, NH 60 30: SUM - SUrM + ANULLH(I) 65 ANY. - SUN/iNH'70 SUM - 0. 75 DO 40 I I- 1, NI 80 40: SUM - SUM + DTI (I) 55 ADTI SUM/NI 90 SUM - O. 95 DO 50 I - 1,4-i 100 50: SUM - SUM + DTH-(I) 105-AD.TH = SUM/NH 110 SUMA - 0. 115. DO 60 I - 1, NI 120 60: SUMA - SUMA + DTI-(I)*(ANULLI(I) - ANI)' 125 SUM8 - O. 130 DO 70 I - 1, NH 135 70: SUMS - SUMS + DTHC(I )(ANULLH(I) - ANH) 140 SUMC - O. 145 DO 80 I - 1, NI 150 80: SUMC - SUrC + (ANULLI (I) - ANI)**2 155 SUMD'- O. 160 DO 90 I -1, NH 170 90: SUMD = SUMD + (ANULLH(I) - ANH)**2 180 SXY - SUMA + SUM3 190 SXS3 -'SUMC + SUMD 200 SLOPE = SXY/SXSQ 205 SUME'-0.O 210 DO 100 I - I, NI 215 100: SUME - SUME + (DTI(I) - ADTI)**2 220 SUMF - o. 225 DO 110 I - 1, N-J 230 110: SUMF - SUMF + (DTH(I) - ADTH)**2 235 SSD - SSUMNE + SUMF - (SUMC + SUMD)*SLOPE**2 240 SIGMSQ - SSD/(NI + NH + 3) 245 DTIA - ADTI - SLOPE*A.NI 250 DTHA - ADTH - SLOPE*A.NH 255. DELT - ASS(DTIA - DTHA) 260 SI DEV - SQ9T (S ISQS ) 265 PRINT, DELT, SLOPE, STDEV, SIGMSQ 270 PRINTI, DTIA, DTHA, DELT 275 PRINT, AI, ANH, ADTI, ADTH 280 END 285 $DA TA

190 261 PRINT "POTASSIUM - 1100/900 F, FIRST RUN 206862" 291 8, 9.300, 9.572, 9.398, 9.194, 9.338,9.351, 9.351, 9*461 292 8, 38.733,938.775, 38.377, 38.415, 37.877, 38.928, 38.487, 38.584 2S2 PRINT "GUARD HEATER VOLTAGE -.7.42 VOLTS" 293 7-, 2. 906, 3.127, 3.262, 3.1 1, 3.419, 3.072i 3,1 48 294 7, 38.805, 38.682, —3S.579, 38.254, 37.292, 38.593, 38.'877 STAT I 1:03 SAT. —-10/28/67 POTASSIUM - 1100/900 F, FIRST RfN 206862 GUARD HEATER VOLTAGE - 7.42 VOLTS 6.232 -.1289.105.011 1-4.3362'. 1 042 6-.232 38.522 3,8.4403 9.3706 3. 1491 NOTATfl. N. NI NUMBER OF ISOTHERMAL RUNS DTI TEMPERATURE DIFFERENCE BETWEEN PLATES - ISOTHERMAL, F. ANULLI AVERAGE NULL,- ISOTHERMAL, F. NH NUM4BER OF HEATED.RUNS' DTH TEMPERATURE DIFFERENCE BETWEEN PLATES - HEATED, F. ANULLH. AVERAGE NULL - HEATED, FF. ANI AVERAGE NULL FOR DATA SET - ISOTHERMAL, F. ANH AVERAGE NULL FOR DATA SET - HEATED. F. SLOPE SLOPE OF LEAST SQUARED DEVIATION LINE. DELT TEMPERA.TURE DIFFERENCE, DELTA T, F. STDEV STANDARD DEVIATION FROM LEAST SQUARED DEVIATION.LINES[, F.

191 APPENDIX D MISCELLANEOUS FIGURES 100 SATURATED VAPOR PRESSURE OF POTASSIUM LOG,o P= 6.12758 812 77- 0.53299 LOG T T 1o P =ATMOSPHERES T=~R 0 I LU cn._ a: 0 600 700 800 900 1000 100 1200 1300 1400 TEMPERATURE- OF Figure D.1. Vapor Pressure of Potassium (33)

192 0.1 II0.01 C/) 0.001 0.0001 0 2 4 6 8 10 12 14 16 THERMOCOUPLE VACUUM- GAUGE EMF- Millivolts Figure D.2. Calibration for RCA 1946 Thermocouple Vacuum Gauge

193 7.0 TOP PLATE HEATER LEAD -WIRE RESISTANCE 6.0 - 0.0095 IN. DIA. NICKEL WIRE, 20.75 INCHES LONG 5.0 - 4.0 (n 3.0 cn 2.0 1.0 600 800 1000 1200 1400 1600 1800 TEMPERATURE - OF Figure D.3. Lead Wire Resistance of Top Plate Heater

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