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Chapter Ⅰ Gas Liquefaction and the Equation of State1

Equation of State for a Gas1

Entropy and Enthalpy4

Production of Low Temperatures with Gases5

Claude Expander5

Entropy Changes and Temperature Drop6

Joule-Thomson Cooling—Linde Process8

Engineering Applications9

Physical Constants of Various Gases11

Chapter Ⅱ Experimental Methods of Low-temperature Physics12

Compressors12

Gasholders13

Helium Liquefiers15

Storage Containers for Liquid Helium20

Liquid Hydrogen by Condensation21

Cryostats for Experiments21

Temperature Measurements25

Vapor Pressure of Liquid Helium25

Vapor Pressure of Liquid Hydrogen27

Equipment for Vapor-pressure Measurements27

Constant-volume Gas Thermometer28

Resistance Thermometer29

Thermocouples30

Heat Flow into Cryostats30

Chapter Ⅲ Theoretical Considerations of the Equation of State32

Classical Quantum Statistics32

Lennard-Jones Potential34

Second Virial Coefficient inClassical Statistics36

Third Virial Coefficient in Classical Statistics39

De Boer Theory of the Equation of State41

Calculations of the Molecular Constants σ and e46

Quantum-mechanical Partition Function48

Transformation of the Slater Sum49

Slater Sums in Some Simple Examples50

Second Virial Coefficient for an Ideal Quantum Gas53

Kirkwood Expansion of the Slater Sum55

Second Virial Coefficient at Low Temperatures56

Equation of State of Compressed Gases and Liquids58

Chapter Ⅳ Liquid Helium—Thermal Properties60

Liquid Helium Ⅰ and Liquid Helium Ⅱ61

Diagram of State p vs.T61

Specific Heat of Liquid Helium61

Entropy of Liquid Helium62

Zero-point Energy64

Latent Heat of Vaporization65

Density and Dielectric Constant of Liquid Helium66

Viscosity of Liquid Helium68

Thermal Properties of He3 Isotope70

Chapter Ⅴ Liquid Helium—Dynamic Properties74

Flow Phenomena in Capillaries74

Film Flow in Liquid Helium Ⅱ75

Mechano-caloric Effect77

Entropy of Helium Ⅱ—Flow Studies by P. Kapitza78

Hydrodynamic Studies—Fountain Effect79

Heat Conductivity82

Velocity and Attenuation of Sound in Liquid Helium84

Second Sound or Thermal Waves in Liquid Helium Ⅱ86

Second-sound Velocity at Very Low Temperatures88

Thermal Rayleigh Disk in Helium Ⅱ89

Mixtures of He？and He4 in Vapor and Liquid Phase93

Chapter Ⅵ Theories of Liquid Helium97

Quantum Theories of F. London97

Thermodynamics of the Two-fluid Model for Liquid Helium Ⅱ103

Tisza’s Phenomenological Theory of the Dynamic Properties of He Ⅱ104

Second-sound-wave Equation105

Transmission Line Analogy107

The Theory of L. Landau108

Chapter Ⅶ Superconductivity110

Resistance Studies111

Crystal Structure and Volume112

Isotope Effect113

Consequences of Infinite Conductivity113

Magnetic Critical Field114

Meissner Effect115

Thermal Properties of Superconductors117

Specific Heat and Entropy117

Magneto-caloric Effect in Superconductors121

Electrodynamic Studies121

Gyro-magnetic Effect121

Torsion Pendulum Studies—Infinite Conductivity and Superconductivity123

Skin Depth of Penetration of a Magnetic Field125

Thermal Conductivity of Superconductors126

Thermoelectric Effect in Superconductors126

Effect of Strain on a Superconductor127

High-frequency Measurements on Superconductors127

The Theories of Superconductivity131

Theory of H.London and F.London131

Quantum Theories of Superconductivity134

Two-electron Fluid Model136

Chapter Ⅷ Magnetism at Low Temperatures138

Some Fundamental Concepts of Magnetization138

Electronic Magnetic Moment—Orbital Motion139

Larmor Precession139

Diamagnetism141

Electron Spin Magnetic Moment141

Spin-orbit Coupling142

Statistical Mechanics of Paramagnetism143

Low Temperatures and High Magnetic Fields—Saturation144

Brillouin Function145

Measurement of Magnetic Susceptibility and Moments145

Balance Method145

Induction Coils for Magnetic Susceptibility at Low Temperatures147

Demagnetization Factor148

Some Typical Experimental Results148

Ideal Salts—Curie Law148

Antiferromagnetism150

Magnetic Cooling151

Thermodynamics and Statistical Mechanics of the Method151

Experimental Methods in Magnetic Cooling154

Remarks on the Magnetization Process155

Demagnetization156

Determination of Temperature156

Experimental Results157

Iron Ammonium Alum157

Chromium Potassium Alum161

Theoretical Analysis161

Nuclear Alignment163

Magnetic Resonance164

Nuclear Magnetic Induction167

Theoretical Analysis of Magnetic Induction167

Particular Solution170

Some General Remarks about Magnetic Induction and Absorption172

Experimental Results173

Solid Hydrogen173

Studies on Solids at Low Temperature175

Paramagnetic Resonance Absorption by Electron Systems176

Diamagnetism of Free Electrons180

de Haas-van Alphen Effect180

Theory of Diamagnetism of Free Electrons181

Chapter Ⅸ Thermal Energy in the Solid State at Low Temperatures186

Lattice Vibrations186

The Difference Cp—Cv for Solids191

Electronic Specific Heat at Low Temperatures in Metals192

Some Characteristic Experimental Results on Metals194

Copper194

Silver and Gold196

Iron，Cobalt，and Nickel196

Palladium and Platinum197

Specific Heat of Superconductors197

Tin197

Tantalum198

Experimental Results on Metals with Anomalous Specific Heats199

Tungsten199

Lithium200

Beryllium201

Rare-earth Elements：Lanthanum，Cerium，Neodymium，and Praseodymium201

Chromium and Manganese202

Germanium and Hafnium202

Specific Heat of Solids with Several Types of Atoms202

Rotation of Atoms and Molecules in the Solid State205

Theory of Cooperative Phenomena207

Specific Heats Showing λ Transitions210

Experimental Methods211

Heat Conductivity in Solids214

Chapter Ⅹ Dielectric Properties at Low Temperatures220

Some Fundamental Concepts220

Barium Titanate222

Strontium Titanate225

Ferro-electric Tartrates226

Solid Hydrogen Bromide227

Theory of Barium Titanate228

Appendix229

Agreed Vapor Pressure of Liquid Helium229

Deviations with Kistemaker’s Temperature Scale234

Vapor Pressure of Liquid Hydrogen234

Vapor Pressure of Liquid Oxygen235

Vapor Pressure of Mixture of He3 and He4236

Physical Constants238

Index239