Experimental Thermodynamics

Contents

Foreword

Preface

Contributors to this Volume

Acknowledgements


1. General Introduction

I. Introduction

II. Recommended Mathematical Symbols

III. Units and Symbols for Units


1. The International System of Units


2. Definition of SI Base Units


3. Names and Symbols for SI Base Units


4. Names and Symbols for SI Derived Units


5. Supplementary Units


6. Practical Realization of Some Important SI Units


7. Decimal Multiples and Submultiples of SI Units


8. Units Outside the International System

IV. Physical Quantities and Symbols for Physical Quantities


1. Definition


2. Basic Physical Quantities


3. Derived Physical Quantities


4. Use ofthe Words 'Specific' and 'Molar' in the Names ofPhysical Quantities


5. Symbols for Particular Cases of Physical Quantities


6. Recommended Subscripts


7. Recommended Superscripts

V. Symbols for Chemical Elements, Nuclides and Particles

VI. Values of the Fundamental Constants

VII. Thermodynamic Definitions


1. Thermodynamic System


2. Thermodynamic Equilibrium


3. Reversible and Irreversible Processes


4. Zeroth Law of Thermodynamics


5. Equation of State


6. First Law of Thermodynamics


7. Internal Energy, U


8. Enthalpy


9. Second Law of Thermodynamics-Entropy


10. Third Law of Thermodynamics


11. Free Energy


12. Heat Capacity


13. Joule-Thomson Coefficient


14. Speed of Sound

VIII. Thermodynamic Data Tables


1. Table of Atomic Weights (1971)


2. Critical Constants


3. Pressure-Volume-Temperature Relationships of Gases-Virial Coefficients Accuracy of these Tables


4. Amagat Density


5. Standard Enthalpies of Formation and Standard Entropies at 298.15 K


6. Density of Mercury


7. Density of Water

IX. Definition of Activities and Related Quantities


1. Chemical Potential and Absolute Activity


2. Pure Substances


3. Mixtures


4. Solutions

X. Accuracy and Precision


1. Definitions


2. Expression of the Uncertainties of Final Results

XI. Conversion Tables

XII. References


2. Reference Materials for Thermometric Fixed Points

I. Primary Fixed Points as Defined by the International Practical Temperature Scale of 1968


1. Definition of the IPTS-68


2. Range 13.81 K to 273.15 K


3. Range O°C to 630.74°C


4. Range 630.74°C to 1064.43°C


5. Range above 1064.43°C

II. Secondary Reference Points as Recommended by the International Committee on Weights and Measures

III. Supplementary Recommendations on Apparatus, Methods and Procedures


1. Influence of Pressure on the Freezing Point Temperature


2. Triple Point, 17.042K Point and Boiling Point of Equilibrium Hydrogen


3. Boiling Point of Neon


4. Triple Point and Boiling Point of Oxygen


5. Boiling Point of Water


6. Freezing Points of Tin and Zinc


7. Freezing Points of Silver and Gold

IV. Practical Temperature Scales over the 0.2 K to 5.2 K Range

V. Standard Reference Samples


1. Gases


2. Catalogue of Physicochemical Standard Substance


3. Further Recommendations of Calibration Materials

VI. References


3. Temperature Measurement under Pressure

I. Introduction

II. Temperature Measurement at Atmospheric Pressure


1. Temperature Measurement below 13. 81 K


2. Temperature Measurement from 13.81 K to 630.74°C


3. Temperature Measurement from 630.74°C to 1064.43°C


4. Temperature Measurement above 1064.43°C

III. Temperature Measurement under Pressure


1. Determination of Pressure Effects on Thermoelectricity


2. Temperature Measurement in a Hydrostatically Pressurized Cell


3. Temperature Measurement in Non-hydrostatic Systems


4. Effect of Pressure on the Relative Difference between Various Thermocouples


5. Optical Pyrometry at High Pressure


6. Computer Method III

IV. References


4. (Part 1). Pressure Measurements I-Mercury Absolute Manometers

I. Introduction

II. Optical Methods of Measuring the Distance between the Mercury Surfaces


1. Cathetometer


2. Lateral Shift


3. Sensing by Interference Techniques


4. Other Optical Devices

III. Electrical Methods for Sensing the Position of the Mercury Surfaces


1. Electrical Contacts


2. Capacitance Techniques

IV. Ultrasonic Sensing of the Meniscus Position

V. Determination of the Height of the Mercury Column

VI. General Considerations

VII. Conclusion

VIII. Abstract

IX. References


4. (Part 2). Pressure Measurements II-Pressure Scale and Fixed Point

I. Apparatus that Requires a Fixed Point Calibration

II. Choice of Fixed Points

III. Measurement of the Pressure at Fixed Points

IV. How to Make Use of Fixed Points in High Pressure Calibration

V. The Present Set of Fixed Points for Pressure Calibration


1. Mercury Melting Curve


2. Bismuth I-II


3. Thallium II-III


4. Barium I-II


5. Bismuth III-V


6. Fixed Points above 100 kbar

VI. Conclusions

VII. References


4. (Part 3). Pressure Measurements III-Piston Gages

List of Symbols

I. Introduction and Historical Review

II. Basic Equations and Elastic Distortion

III. Piston Gage Designs


1. Simple Piston Gage


2. Tilting Piston Gage


3. Vacuum-backed Piston Gage


4. Re-entrant Cylinder Design


5. Differential Piston


6. Controlled Clearance


7. Ball Gages


8. Grooved Pistons


9. Very High Pressure Piston Gages

IV. Calibration of Primary Standards


1. Controlled Clearance Piston Gage


2. Similarity Method

V. Calibration of Piston Gages


1. Cross-float


2. Reference Levels


3. Evaluation

VI. The Use of Piston Gages


1. Measurement of Pressure


2. Procedures and Methods

VII. Abstract

VIII. References


4. (Part 4). Pressure Measurements IV-Secondary Gage-Differential Manometers

I. Introduction

II. Mechanical Devices

III. Electrical Resistance Gages

IV. Differential Manometers

V. References


4. (Part 5). Pressure Measurements V-Instruments for Relative Pressure Measurements

I. General Considerations

II. Pressure Sensitive Elements; Sensors


1. Aneroid Capsule


2. Bellows and Springs


3. Bourdon Tube


4. Gimlet Shaped Tube


5. Piezoelectric Quartz

III. Methods of Measurement


1. Force Measurements. The Pressure Effect


2. Displacement Measurements. The Pressure Effect

IV. Special Transducers

V. Specific Designs


1. General Considerations


2. Flight-control Instruments


4. (Part 6). Pressure Measurements VI-Pressure Measurements for the Range lkPa to l00pPa

I. Introduction

II. Direct Measurement Procedures, Reference Standards


1. Precision Liquid Columns


2. Compression Manometer-McLeod Gage


3. Systematic Errors Arising from the Use of a Cold Trap


4. Viscosity Manometer


5. Knudsen Radiometer Manometer

III. Pressure Generators


1. Volumetric Pressure Divider-Static Expansion

IV. Transfer Gages. Precision

V. References


4. (Part 7). Pressure Measurements VII-Very Low Pressures and Ultra Low Pressures (below 10-6 Torr)

I. Introduction

II. General Problems of Low Pressure Measurements


1. Gages as Sinks or Sources


2. Measurement in Non-uniform Environments


3. Residual Currents


4. Relative Gage Sensitivities for Different Gases


5. Calibration of Gages

III. Pressure Measurements from 10-6 to 10- 10 Torr


1. Hot-cathode Ionization Gages


2. Cold-cathode Gages

IV. Pressure Measurements below 10- 10 Torr


1. Shielded-collector Gages


2. Bent-beam Gage


3. Hot-cathode Magnetron Gage

V. Comparison of Gages

VI. References


5. The Absolute Measurement of Volume

I. Introduction

II. Experimental Problems

III. The Volume of a Cube of Tungsten Carbide

IV. Volumes of Cubes of Fused Silica

V. Single Crystals of Pure Silicon for the Measurement of Avogadro's Number

VI. The Density of Water

VII. Summary

VIII. References


6. Measurement of p-V- T Properties of Gases and Gas Mixtures at Low Pressure 3

I. Introduction

II. General Principles of JT-V- T Measurement

III. Methods of Measuring Pressure


1. Secondary Manometers

IV. The Volume Problem

V. The Experimental Volume/Manometer Interface

VI. Temperature Measurement and Control

VII. p-V- T Methods at Constant Volume

VIII. p- V-T Methods Involving Expansion

IX. Rdative Methods

X. Effect of Gas Adsorption on p-V- T Measurements

XI. Gas Density Microbalance

XII. p-V- T Properties of Mixtures

XIII. References ..


7. Equation of State of Gases at High Pressures and Low or Moderate Temperatures

I. Introduction

II. Technical Features Common to Various Experimental Methods


1. Cryostats and Thermostats


2.. Temperature Measurement


3. High Pressure Vessels


4. Pressure Measurements


5. Determination of the Piezometer Volume

III. Various Methods of Measurement


1. The Gas Expansion Method


2. Isothermal Methods


3. The Isochore Method


4. The Weight Method


5. The Burnett Method

IV. List of the Most Important Reports

V. Comparison between Theory and Experiment


1. Virial Expansion of a Hard Sphere System


2. Perturbation Method

VI. Conclusion

VII. References


8. p-V- T Relationships in Gases at High Pressures and High Temperatures

I. Introduction

II. Techniques of Heating the Gas under Study


1. External Heating


2. Internal Heating

III. Various Methods of Measurement

()IV. Constant Temperature Methods


1. Variable Volume Techniques


2. Methods with Weighing Technique and Constant Volume Piezometer


3. Miscellaneous Techniques

V. Constant Pressure Methods

VI. Constant Volume Methods

VII. Critical Comparison of the Various Measurement Methods


1. Measurement Techniques


2. Measured Quantities

VIII. Results

IX. Equations of State


1. Law of Corresponding States


2. Empirical Equations


3. Equations Derived from Statistical Mechanics


4. Tables of Thermodynamic Properties

X. References


9. The Compression of Liquids



I. Introduction

II. Thermodynamics of Volume Changes


1. The more Important Thermodynamic Derivatives of Pressure, Volume, and Temperature


2. Relations between the Derivatives


3. Quantities that can be Determined by Measuring Volumes, Thermal Expansions and Compressions

III. Historical Introduction

IV. Some Experimental Considerations


1. Relative Expansion and Compression


2. Expansion, Compression, Expansivity and Compressibility


3. Dilatation of the Vessel


4. Seasoning of Pressure Vessels and Piezometers


5. Heat of Compression


6. Corrosive Liquids


7. Gases at High Pressures


8. External and Internal Heating of Pressure Vessels


9. Summary of the more Important Sources of Error in the Measurement of the Compression of Liquids


10. Accurate Measurements

V. Piezometric MethodS-Liquid Piston


1. Some General Considerations


2. Single-point Methods


3. Multiple-point Methods

VI. Piezometric Methods-Solid Piston

VII. Piezometric Methods-Bellows

VIII. Simple Piston-Cylinder Method

IX. Constant-Volume Vessel


1. Introduction


2. Displacement of a Solid Piston


3. Displacement of a Liquid Piston


4. Bellows Volumometer


5. Direct Weighing of Fluid Removed


6. Volumetric Measurement of the Gas at Low Pressure


7. Volumetric Measurement of Liquid at Low Pressure

X. Weight Methods


1. Direct Weighing Methods


2. Hydrostatic Weighing

XI. Ultracentrifuge Method

XII. Negative Pressures

XIII. Adiabatic Compression

XIV. Isochoric Thermal Pressure Coefficient


1. Piezometric Methods


2. Constant-volume Vessel with Direct Pressure Measurement


3. Constant-volume Vessel with Indirect Pressure Measurement

XV. Calorimetric Methods

XVI. Miscellaneous Methods


1. Methods Based on Radioactivity


2. Variable-volume Vessel

XVII. References


10. Determination of 1bermodynamic Properties from tbe Experimental p-V-T Relations

I. Computational Methods-Introduction

II. The Equation of State

III. Estimation of the Parameters of an Equation of State


1. Linear Least Squares


2. The Round Off Problem


3. Least Squares with Constraints


4. Non-linear Parameter Estimation


5. The Simultaneous Use of Several Types of Property Data in Least Squares Parameter Estimation

IV. Statistical Aspects of Least Squares Estimation

V. Miscellaneous Techniques for Improving the Accuracy of Thermodynamic Properties Calculated from an Equation of State


1. Thermodynamic Equilibrium Conditions as Simultaneous Data


2. Constrained Boundary Conditions

VI. Thermodynamic Property Equations

VII. Mathematical Formulas Useful in Thermodynamic Calculations


1. Derivative Chain Rule


2. Implicit Solutions of Equations of State


3. Joining Independent p-V- T Surfaces


4. A Solution of M Equations for M Unknowns

VIII. Abstract

IX. References


11. Thermodynamic Properties and the Velocity of Sound

List of Symbols

Introduction

I. Thermodynamic Relations


1. Adiabatic Properties


2. Sound Velocity

II. Absorption and Dispersion


1. Translational Relaxation


2. Rotational and Vibrational Relaxation


3. Critical Dispersion


4. Other Relaxation Phenomena

III. Sound Velocity and the Equation of State


1. Ideal Gas


2. Virial Equation of State


3. Van der Waals Equation of State


4. BWR Equation of State

IV. Sound Velocity in Mixtures


1. Ideal Mixture


2. Non-ideal Mixtures

V. Experimental Methods


1. Interferometer Methods


2. Pulse Methods

VI. Sound Velocity in Gases


1. General Behavior


2. The Absolute Value of W in the Low Pressure Limit


3. The Initial Slope (δW²/δp)T


4. High Density Data


5. Generalized Behavior of Sound Velocity in Gases. Corresponding States Treatment

VII. Sound Velocity in Pure Liquids


1. General Behavior


2. Liquids Coexisting with Their Saturated Vapor


3. Single Phase High Density Fluids


4. Critical Region


5. Generalized Sound Velocity Behavior in Dense Fluids

VIII. Sound Velocity in Liquid Mixtures


1. Homogeneous Mixtures


2. Mixtures Showing Phase Separation

IX. Acknowledgements

X. References


12. Relation of the Dielectric Constant and the Refractive Index to Thermodynamic Properties

I. Introduction

II. Theoretical


1. Lorentz Model


2. Onsager-Bottcher Theory


3. Statistical-mechanical Calculations


4. Phenomenological Shell Model


5. Variation of Polarizability with Density


6. Generalization of Theory to Optical Frequencies

III. Experimental Determinations of Dielectric Properties


1. Methods for Determining Refractive Index


2. Results of Refractive Index Measurements


3. Methods for Determining Dielectric Constants


4. Results of Dielectric Constant Measurements and Comparison with Refractive Index Data

IV. Magneto-optical Properties

V. Conclusions

VI. References


13. Vapor Pressures

I. Introduction

II. Static Measurements

III. The Isoteniscope and Related Methods

IV. Static Measurements at Elevated Temperatures and Pressures

V. The Critical Point

VI. Effect of the Presence of Mercury

VII. Vapor Pressures of Liquefied Gases

VIII. Effect of Thermal Transpiration

IX. Comparative Static Measurements

X. Static Measurements at Very Low Pressures

XI. Use of Radioactive Tracers

XII. Ebulliometric Measurements

XIII. Ebulliometric Measurements at ·Pressures below 2 kPa

XIV. Method of Ramsay and Young

XV. Dynamic Measurements without a Buffer Gas

XVI. The Quasi-static Method

XVII. Measurement of the Force Exerted by the Vapor

XVIII. Evaporation Methods for Low Pressures

XIX. Gas-saturation Method

XX. Differential Thermal Analysis

XXI. Gas Chromatography

XXII. Mass Spectrometry

XXIII. Vapor Pressures of Mixtures

XXIV. References


14. Thermodynamic Properties near the Critical State

I. Introduction

II. Theoretical Background


1. The Origin of Critical Anomalies


2. Power Laws


3. Symmetry


4. Homogeneity and Scaling


5. Beyond Simple Scaling

III. Special Experimental Difficulties


1. Divergences and Their Consequences


2. Gravity


3. Equilibration

IV. Refractive Index Measurements


1. Principle


2. The Use of Optical Techniques for Bulk Density Determination


3. Local Density Determination Using Refractive Index


4. Density Gradient Determination

V. Dielectric Constant Measurements


1. General


2. peT Measurements


3. Density Profiles by Dielectric Constant Determination

VI. Conventional pVT and Vapor Pressure Measurements


1. pVT Measurements


2. The Vapor Pressure

VII. Calorimetry


1. Experimental Problems in Cv Determination


2. Reducing the Heat Capacity of the Container


3. Long Relaxation Times


4. Correcting for Gravity


5. Increasing the Temperature Resolution


6. Checking for Consistency


7. Tests of Scaling

VIII. Coexistence Curves


1. General


2. Gravity


3. The Method of Meniscus Disappearance


4. Young's Method of the Twin Cells


5. Coexistence Curves from Isothermal and Isochoric Intercepts


6. Coexistence Curves by Dielectric Constant and Refractive Index Techniques


7. The Use of Floats


8. Power Law Analysis of Coexistence Curves


9. The Diameter of the Coexistence Curve

IX. Scattering


1. Introduction


2. Intensity of Scattered Light


3. Angular Dependence of the Intensity of Scattered Light


4. Light Scattering and Small-angle X-Ray Scattering


5. The Experimental Situation in Critical Opalescence


6. The Spectrum of Scattered Light

X. Sound


1. Sound, Ultrasound and Hypersound


2. Gravity Effects in Sound Velocity Measurements


3. Sound Dispersion and Attenuation

XI. Concluding Remarks

XII. Acknowledgements

XIII. References


15. Solubility

I. Introduction

II. General Considerations

III. Concentration and Activity Coefficient Scales

IV. Solubility of Gases in Liquids


1. Manometric-volumetric Methods


2. Chemical-analytical Methods


3. Miscellaneous Methods

V. Solubility of Liquids in Liquids


1. Volume Reading


2. Cloud Point


3. Miscellaneous Methods

VI. Solubility of Solids in Liquids


1. Saturation Method


2. Cloud Point


3. Chemical and Instrumental Analysis

VII. References


16. (Part 1). Phase Equilibria (General Procedure) I-Phase Equilibria of Two-component Systems and Multicomponent Systems

List of Symbols

I. Introduction

II. Thermodynamics of Mixtures

III. Liquid Mixtures

IV. Empirical Representation of Liquid-Vapor Equilibrium Data

V. Tests for Thermodynamic Consistency of Liquid-Vapor Equilibrium Data

VI. Experimental Methods of Determining Liquid-Vapor Equilibrium Data


1. Dynamic Methods


2. Static Methods

VII. Static Measurements with Analyses of Both Phases

VIII. The McBain Balance Method

IX. Dewpoint and Bubble-point Measurements

X. The Isopiestic Method

XI. Differential Methods

XII. Light-scattering Measurements

XIII. References


16. (Part 2). Phase EquiHbria (General Proceuree) II-Phase EquiHbria of Liquid and Gaseous Mixtures at High Pressures

I. Introduction

II. Basic Phase-Theoretical Aspects

III. Discussion of General Procedures


1. The Analytical Method


2. The Synthetic Method


3. Miscellaneous Methods

IV. Description of Special Equipments


1. Mercury-operated Apparatus of Krichevskii and Tsiklis


2. Apparatus of Tsiklis and Maslennikova


3. Apparatus of Tödheide and Franck


4. Optical Cell Used by de Swaan Arons and Diepen


5. Optical Cell Developed by Oeder and Schneider


6. Optical Cell Developed by Alwani and Schneider


7. Optical Cell Developed by Buback and Franck


8. Apparatus Developed by Michels et al.

V. Conclusions

VI. References


17. (Part 1). Liquid-Solid Phase Equilibria I-Melting Points and Volume Changes upon Melting

I. Introduction

II. Methods used for Melting Point Determination at Normal Pressure


1. Visual Methods


2. Microscopical Methods


3. Quenching Methods


4. Pyrometric Methods for Use above 2000°C


5. Calorimetric Methods


6. Thermal Arrest Methods


7. Special Methods Used in Isolated Cases

III. Differential Thermal Analysis at Normal Pressure


1. Historical


2. Basic Method


3. Critical Assessment of DTA

IV. Methods Used for Melting Point Determination at High Pressure


1. Historical


2. Methods of Measuring Melting Points at High Pressures in Apparatus Using Hydrostatic Pressure Media


3. Methods of Measuring Melting Points at High Pressures in Apparatus Using Quasi-hydrostatic Pressure Media


4. Methods of Measuring Melting Points at High Pressures in Opposedanvil Apparatus


5. Methods of Measuring Melting Points at High Pressures in Multipleanvil Apparatus


6. Conclusion

V. Methods for Determining Volume Changes on Melting

VI. Abstract

VII. References


17. (Part 2). Liquid-Solid Phase Equilibria II-Cryoscopy

List of Symbols

I. General Considerations


1. Cryoscopic Law for Ideal, Non-ionic Solutions


2. Cryoscopic Law for Non-ideal and Non-ionic Solvents


3. Cryoscopic Law for Aqueous Electrolytes


4. Cryoscopic Law for Electrolyte Solutions in Salt Media


5. The Methods of Cryoscopy

II. Kinetic Cryoscopy Equipments


1. Apparatus Used from - 100°C to 200°C


2. Temperature Measurement


3. Table of Organic and Inorganic Solvents


4. Salt Hydrate and Aqueous Eutectic Cryoscopy


5. Molten Salts Cryoscopy

III. Adiabatic Cryoscopy Equipments


1. Aqueous Solution Equipment


2. Non-aqueous Solvents Equipment


3. Concentration Measurements


4. Pseudo-equilibrium Methods

IV. A Few Applications of Cryoscopy


1. Data Derived from Zero Concentration Extrapolation, (θ/m)o


2. Data Derived from the (θ/m) versus m Cryoscopic Graph


3. Data Derived from the Schroder Curve

V. References


18. EMF Measurements in Molten Salts

I. Introduction and Scope

II. Cell EMF and Thermodynamic Properties


1. Introduction


2. Classification of EMF Cells


3. Sign Convention for EMF and Cell Diagram


4. Thermodynamic Expressions for Cell EMFs


5. Principal Error Sources

III. Experimental


1. Reporting Data and Results


2. Apparatus


3. Electrodes

IV. Special Applications


1. Phase Diagrams


2. Association Equilibria of Dilute Solutes


3. Miscellaneous

V. Acknowledgement

VI. References


19. (Part 1). Thermodynamic Properties of Fluid Metals I-Mediun and Low Pressures

I. Introduction

II. Thermal Properties. Specific Heat


1. The Direct Heating Method


2. The Drop-calorimeter


3. The Exploding Wire Method

III. Density Measurements


1. Direct Methods


2. Indirect Methods

IV. Vapor Pressures

V. References


19. (Part 2). Thermodynamic Properties of Fluid Metals II-High Temperatures and High Pressures

I. Introduction

II. Experimental Methods


1. Density


2. Vapor Pressures

III. Results


1. Density


2. Vapor Pressure Curves and Critical Data

IV. References


20. Interphase Surface Tension

I. Introduction

II. Static Methods of Determination of the Interphase Surface Tension


1. Method of Capillary Rise or Depression


2. Method of the Shape of a Sessile Drop or a Gas Bubble

III. Semistatic Methods of Determination of the Interphase Surface Tension


1. Method of the Weight and Volume of a Bubble


2. Ring or Plate Rupture Method


3. Method of Maximal Pressure in a Gas Bubble or a Drop


4. Improved Gas Devices with One Calibrated Tube


5. Improved Gas Devices with Two Calibrated Tubes


6. Gravitational Devices

IV. References


21. Adsorption

I. Introduction

II. Vacuum Systems

III. Pressure Measurements


1. Gages


2. Sources of Error and Their Correction

IV. Adsorption Isotherms


1. Cleaning the Adsorbent Surfaces


2. Equilibration


3. Volumetric Methods


4. Gravimetric Methods


5. Flow Methods

V. Adsorption Cryostats

VI. Acknowledgement

VII. References


22. Chemical Relaxation in Liquid Systems

I. Introduction

II. Chemical Relaxation Techniques


1. Jump Methods


2. Stationary Methods

III. The Information Obtainable from Chemical Relaxation Measurements

IV. Some Applications of Chemical Relaxation Techniques


1. The Neutralization Reaction H+ + K/K Η20


2. The Formation of Metal Ion Complexes: Mᵐ+ + Lⁿ- ML(ᵐ-ⁿ)+


3. The Mechanism of Cooperative Ligand Binding on an Allosteric Enzyme


4. Ultrasonic Absorption in Water-Dioxane Mixtures

V. Summary

VI. References


23. Thermodynamic Properties from Shock Waves

I. Introduction

II. Theoretical Aspects


1. The Basic Relations


2. Properties of the Hugoniot Curve ; Stability of Shock Waves


3. Reflection of Shock Waves and Rarefaction Waves

III. Experimental Techniques


1. Shock Wave Generators


2. Methods of Measurement

IV. Equation of State for Liquids at Very High Pressures


1. Experimental Results


2. Theoretical Models of the Equation of State

V. References


24. Electrical Discharge Techniques for Measurements of Thermodynamic Properties of Fluids at High Temperatures

List of Symbols

I. Introduction

II. General Method

III. Capacitor Discharge Systems


1. Description of Systems


2. Design Considerations


3. Measurement of Experimental Quantities


4. Examples of Thermodynamic Measurements


5. Summary of Pertinent Literature since 1964

IV. A Millisecond-resolution System


1. Description of the System


2. An Example of Thermodynamic Measurements at and above Melting Points

V. Discussion

VI. Appendix

VII. References


25. The Ballistic Compression and High Temperature Properties of Dense Gases

I. Introduction

II. The Ballistic Piston Compressor


1. General Description


2. Operation


3. Instrumentation

III. Physical Properties Studies


1. The Equation of State


2. Optical Studies


3. Other Studies 1215

IV. Summary

V. References


26. Thermodynamic Properties of Fluids below 20 K

I. Introduction

II. Temperature Scales and Thermometry below 20 K


1. The Basis for Thermodynamic Thermometry below 20 K


2. Primary Thermometry from 1 to 20 K


3. Primary Thermometry below 1 K


4. Temperature Scales in Use below 20 K


5. Secondary Thermometry below 20 K

III. Refrigeration Techniques below 0.3 K


1. The ³He-4He Dilution Refrigerator


2. Nuclear Cooling


3. Cooling by Adiabatic Freezing in Liquid ³He


4. Heat Transfer and Isolation at ULT

IV. Preparation of Helium and Hydrogen Samples

V. Calorimetry of Fluids below 20 K


1. Liquid 4He near the Melting Curve


2. Liquid 4He near the A-Point


3. Liquid 3He at ULT and at Pressures up to the Melting Curve


4. Latent Heats of Vaporization of Hydrogen and 4He


5. Liquid ³He-4He Mixtures

VI. pVT Measurements below 20 K


1. Molar Volume


2. pVT Properties at Melting


3. Osmotic Pressure of ³He-4He Solutions

VIII. References


27. Author Index


28. Subject Index