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CHAPTER ONE Introduction1

1．1 Introduction to Thermodynamics1

1．2 Large-Scale or Macroscopic View1

1．3 Molecular or Microscopic View2

1．4 Systems and Their Surroundings3

1．5 Walls and Boundaries4

Rigid Walls4

Cylinder and Piston4

Diathermic Walls4

Adiabatic Walls4

Semipermeable Walls4

Isolating Walls5

1．6 Thermodynamic Equilibrium5

1．7 Thermal Equilibrium and the Zeroth Law5

1．8 Temperature as a Property of a System8

1．9 The Equation of State and the Temperature Scale9

1．10 Intensive and Extensive Properties11

1．11 Thermodynamic States of a System:Degrees of Freedom13

1．12 The Two-Phase System16

1．13 Other Systems18

Thin Uniform Filament under Tension19

Systems with Surface Tension19

Charged Soap Bubble19

1．14 Quasistatic Processes and Reversibility20

PROBLEMS22

CHAPTER TWO Temperature24

2．1 Measurement of Temperature24

2．2 General Temperature Scales25

2．3 Various Celsius Thermometers27

2．4 Criteria for Good Thermometers28

2．5 Gas Thermometers29

The Constant-Volume Thermometer30

The Constant-Pressure Thermometer30

2．6 The Thermodynamic Celsius Scale31

2．7 Boyle＇s Law and the Ideal Gas Celsius Scale35

2．8 Empirical Behavior of Gases34

2．9 The Absolute Gas Scale36

2．10 Correction of the Constant-Volume Gas Thermometer38

2．11 Correction of the Constant-Pressure Thermometer40

2．12 Numerical Magnitudes of Corrections44

2．13 Primary and Secondary Thermometers45

2．14 The Platinum Resistance Thermometer47

2．15 The Thermocouple49

2．16 New Basis for the Thermodynamic Scale50

PROBLEMS51

CHAPTER THREE The Equation of State53

3．1 The Ideal Gas53

3．2 The Universal Gas Constant55

3．3 Units56

Volume56

Pressure56

Pressure-Volume(pV)57

3．4 The P-V-T Surface57

3．5 The Reciprocal and the Reciprocity Theorems60

3．6 Thermodynamic Coefficients61

3．7 The P-V-T Relation for a Pure Substance62

3．8 The Kamerlingh Onnes Equation66

3．9 Van der Waals＇Equation68

3．10 Berthelot＇s Equation72

3．11 Dieterici＇s Equation74

3．12 The Beattie-Bridgeman Equation75

3．13 The Equation of State in Virial Form75

3．14 Solid and Liquid States77

PROBLEMS79

CHAPTER FOUR The First Law of Thermodynamics82

4．1 Measurement of Heat82

4．2 Heat Capacity and the Unit of Heat83

4．3 Method of Mixtures85

4．4 Mechanical Nature of Heat87

4．5 Mechanical Equivalent of Heat89

Direct Mechanical Determinations90

Electrical Methods90

4．6 The System as a Reservoir of Energy93

4．7 Formulation of the First Law of Thermodynamics95

4．8 Relative and Absolute Internal Energy97

4．9 The First Law for Differential Processes98

4．10 Work in Quasistatic Processes100

4．11 Heat Absorbed in Quasistatic Processes102

4．12 The First Law in Differential and Integral Forms103

4．13 Cyclic Processes and Perpetual Motion104

4．14 Mechanics and the First Law106

PROBLEMS107

CHAPTER FIVE Work and Heat in Various Systems109

5．1 Introduction109

5．2 Systems under Uniform Hydrostatic Pressure109

5．3 Other Mechanical Systems112

Thin Uniform Filament under Stretching Force112

Systems with Surface Tension112

5．4 Electrical Systems112

5．5 Magnetic Systems114

5．6 The General Case117

5．7 Heat Capacities of a Pure Substance118

5．8 Heat Capacities with the Variables T and p119

5．9 Heat Capacities with the Variables T and V120

5．10 Heat Absorbed along Certain Curves121

5．11 Relations among the Heat Capacities;Specific Heats123

5．12 Heat Capacities for Other Systems124

5．13 Internal Energy of a Gas126

5．14 Internal Energy of a Gas from Experiment127

5．15 Heat Capacities of an Ideal Gas131

5．16 Heat Capacities of Real Gases132

5．17 Slope of the Adiabatic Curve133

5．18 Equation of the Adiabatic for the Ideal Gas135

PROBLEMS137

CHAPTER SIX Heat Capacities of Gases140

6．1 Experimental Measurements of Cv,Cp,and γ140

6．2 Joly＇s Steam Calorimeter for Cv141

6．3 Eucken＇s Low-Temperature Gas Calorimeter for Cv142

6．4 Explosion Method for Cv142

6．5 Method of Mixtures of Holborn and Henning for Cp144

6．6 Continuous-Flow Method for Cp144

6．7 γ by Adiabatic Expansion145

6．8 Rüchhardt＇s Method for γ147

6．9 Rinkel＇s Modified Method for γ159

6．10 Experimental Values of Cv and γ159

6．11 Kinetic Theory of the Ideal Gas151

6．12 Equipartition of Energy152

6．13 Degrees of Freedom of Molecules154

6．14 Molecular Vibration154

6．15 Quantization of Energy159

6．16 Empirical Formula for Variation of Cp with T163

PROBLEMS164

CHAPTER SEVEN Solids,Liquids,and Change of Phase165

7．1 Measurement of the Heat Capacities of Solids165

7．2 The Nernst-Lindemann Vacuum Calorimeter166

7．3 The Adiabatic Vacuum Calorimeter168

7．4 Equilibrium Method169

7．5 The Law of Dulong and Petit171

7．6 Temperature Variation of Cv172

7．7 Theoretical Interpretation of Cv for Solids176

7．8 Heat Capacities of Liquids178

7．9 Change of Phase179

7．10 Enthalpy180

7．11 Enthalpy and Internal Energy182

7．12 Heat of Sublimation of a Monatomic Solid184

7．13 Enthalpy and Internal Energy for Simple Substances186

7．14 Heat of Reaction and Enthalpy Tables189

7．15 Kirchhoff＇s Heat Capacity Formulas193

7．16 The First Law with Mass Flow194

The Constant-Flow Calorimeter196

The Porous Plug and the Throttle Valve196

The Ideal Nozzle197

The Steam Turbine197

PROBLEMS198

CHAPTER EIGHT Heat Engines and the Second Law200

8．1 Heat Engines200

8．2 Thermal Efficiency201

8．3 Idealized Engine Cycles203

Reversible Cycles204

Single Pure Substance as Working Substance204

Ideal Gas204

Infinite Reservoirs204

8．4 The Gasoline Engine205

8．5 The Air Standard Otto Cycle206

8．6 The Air Standard Diesel Cycle207

8．7 Carnot＇s Principle209

8．8 Carnot＇s Theorem211

8．9 Clausius＇Statement of the Second Law213

8．10 The Second Law According to Kelvin and Planck214

8．11 Criteria for Equivalence215

8．12 The Carnot Refrigerator216

8．13 Kelvin＇s Thermodynamic Heating217

8．14 Various Carnot Cycles220

Two-Phase System220

Stretched Elastic Wire221

Surface Film221

8．15 The Kelvin Temperature Scale222

PROBLEMS225

CHAPTER NINE Entropy and the Second Law228

9．1 Entropy and Necessary Waste228

9．2 The Clausius Sum for a Closed Cycle229

9．3 The Clausius Sum as an Integral231

9．4 Entropy as a Property of a System233

9．5 The Principle of the Increase of Entropy235

9．6 Free Expansion of an Ideal Gas237

9．7 Mixing of Gases239

9．8 Dissipation of Mechanical and Electrical Energy241

9．9 Temperature Equalization242

9．10 Uses of Entropy244

9．11 Temperature-Entropy Diagram244

9．12 dS as a Perfect Differential245

9．13 Heat Capacities as Entropy Derivatives247

9．14 Entropy of an Ideal Gas249

9．15 General Laboratory Equations for dU,dH,and dS251

9．16 Thermodynamic Potentials253

Internal Energy253

Enthalpy253

Entropy253

9．17 The Potentials of Helmholtz and Gibbs254

Helmholtz＇s Potential254

Gibbs＇Potential255

9．18 The Clausius Equations256

9．19 The Principle of Carathéodory257

9．20 Natural,Unnatural,and Reversible Processes259

PROBLEMS261

CHAPTER TEN The Steam Engine and the Refrigerator264

10．1 Introduction264

10．2 The Rankine Cycle264

10．3 Efficiency of the Rankine Cycle266

10．4 Steam Tables267

10．5 Use of Steam Tables270

10．6 The Steam Dome in the p-v Plane271

10．7 The T-s,h-s,and p-s Diagrams273

10．8 Improvements in the Utilization of Steam275

The Newcomen Atmospheric Engine276

James Watt＇s Contributions276

Multiple-Expansion Engines276

The Uniflow Engine277

10．9 The Steam Turbine277

10．10 Superpressure Turbines279

10．11 The Refrigerator282

10．12 Common Refrigerants285

10．13 The Heat Pump287

10．14 The Electrolux Refrigerator289

REFERENCES290

PROBLEMS290

CHAPTER ELEVEN Thermodynamic Methods292

11．1 Introduction292

11．2 Thermodynamic Methods292

The Cyclic Method293

Analytic Methods295

11．3 The Clausius-Clapeyron Equation(Cyclic Method)297

11．4 The Clausius-Clapeyron Equation in General299

11．5 Maxwell＇s Relations(Cross Derivative Method)302

11．6 Maxwell＇s Relations and Multiphase Systems303

11．7 Specific Heats of Saturated Phases304

11．8 Gibbs＇Potential307

11．9 Relation of the Triple Point to the Ice Point208

Solubility Effect309

Direct Pressure Effect310

11．10 The Six General Relations of Maxwell311

11．11 The Three Independent or Basic Derivatives312

11．12 Derivatives in Terms of the Basic Three315

11．13 Jacobians317

11．14 The Reciprocity Theorem for Jaeobians319

11．15 Maxwell＇s Relations in Jacobian Form321

11．16 General Derivatives by Jacobians323

11．17 The Fundamental Jacobian323

PROBLEMS325

CHAPTER TWELVE Applications of the General Relations328

12．1 Introduction328

12．2 Internal Energy,Enthalpy,and Entropy for Condensed Phases330

12．3 Thermodynamic Functions for Ideal Gases332

12．4 The van tier Waals Gas335

12．5 The Adiabatic Law for a van der Waals Gas336

12．6 Internal Energy,Enthalpy,and Entropy for Real Gases338

12．7 The Joule-Kelvin Effect344

12．8 The Inversion Curve345

12．9 Joule-Kelvin Cooling347

12．10 The Maximum Inversion Temperature349

12．11 Integration of the Clausius-Clapeyron Equation352

12．12 The Ideal Gas Approximation352

12．13 The General Vapor Pressure Equation of Kirchhoff356

12．14 Kirchhoff＇s Formula for Latent Heat of Sublimation357

12．15 The Vapor Pressure Formula for a Solid(Ideal Vapor)359

12．16 Latent Heat of Sublimation of a Monatomie Solid360

12．17 Vapor Pressure of a Monatomic Solid362

12．18 Entropy and the Vapor Pressure Constant364

PROBLEMS366

CHAPTER THIRTEEN Applications to Various Systems370

13．1 The n-Variable Thermodynamic System370

13．2 Restricted and Unrestricted Systems372

13．3 Tensed Filament or Uniform Rod374

Temperature Change on Stretching(Adiabatic)375

Heating a Stiff Rod at Constant Length375

13．4 Reversible Electric Cell376

13．5 The Cavity Radiator and Black Body Radiation381

Radiancy of a Surface or Cavity381

The Cavity Radiator382

Properties of surfaces383

13．6 Radiation Density and Radiancy384

Directional Radiancy384

Parallel Beam Radiancy385

Relation of R to R？386

Relation of Rc to the Energy Density386

13．7 Pressure of Radiation388

13．8 The Stefan-Boltzmann Total Radiation Law389

13．9 Surface Tension391

13．10 Stressed Dielectrics in an Electric Field394

13．11 Behavior of Entropy and Helmholtz＇s and Gibbs＇Potentials on Approach to Equilibrium397

Adiabatic Processes398

Isothermal Processes399

13．12 Conditions for Stable Equilibrium399

13．13 The Electrochemical Potential400

13．14 Multicomponent Systems401

13．15 Heterogeneous Equilibrium and the Phase Rule402

Gibbs＇Phase Rule403

13．16 Chemical Systems of Two Components405

13．17 The Thermocouple406

13．18 Kelvin＇s Treatment of the Thermoeouple408

PROBLEMS410

CHAPTER FOURTEEN The Physics of Low Temperatures413

14．1 Production of Low Temperatures413

14．2 Helium Liquefiers414

14．3 Measurement of Low Temperatures415

14．4 The Liquid Helium Vapor Pressure Formula416

14．5 Phase Relations Of Helium419

14．6 The Order of a Transition421

14．7 The λ Transition in Helium424

14．8 Dynamic Properties of Helium425

The Phenomenon of Surface Flow425

Abnormal Flow in Capillaries426

The Mechanocaloric and Fountain Effects427

14．9 The Two-Fluid Theory of HeII429

14．10 Superconductivity431

14．11 Superconductors in a Magnetic Field433

14．12 Magnetic Cooling by Adiabatic Demagnetization435

Isothermal Magnetization437

Adiabatic Change of Magnetic Field437

14．13 Magnetic Temperatures439

14．14 The Lowest Temperature in the World441

14．15 The Third Law of Thermodynamics442

REFERENCES446

PROBLEMS446

CHAPTER FIFTEEN Entropy and Probability448

15．1 Order,Disorder,and the Second Law448

15．2 Mathematical Probability449

15．3 Distribution of Marked Objects451

15．4 Microstates and the Disorder Number of a Macrostate455

15．5 The Disorder Number for a Macrostate of a Physical System457

15．6 Entropy and the Disorder Number460

15．7 Conditions for Maximum Entropy462

15．8 Volume Distribution for Maximum Entropy464

15．9 Velocity Distribution for Maximum Entropy465

15．10 Evaluation of the Parameter α＇467

15．11 Evaluation of the Parameters κ and β471

15．12 Various Forms of the Velocity Distribution Law474

15．13 The Speed Distribution Law477

15．14 Mean and Root-Mean-Square Speeds479

15．15 The Equipartition Theorem and the Equation of State of an Ideal Monatomic Gas481

15．16 Mass Flux483

PROBLEMS487

CHAPTER SIXTEEN Classical Statistical Mechanics490

16．1 Introduction490

16．2 Configuration-Velocity Space491

16．3 Hamiltonian Coordinates and Phase Space494

Free Point Mass in Space495

Symmetric Rotor with a Fixed Axis496

Mass Point Moving in Space about the Origin496

The Rotating Vibrator497

16．4 μ Space and Γ Space502

16．5 Liouville＇s Theorem and Equal a Priori Probabilities in Γ Space505

16．6 The Equilibrium Distribution in μ Space506

16．7 The General Partition Function in μ Space508

16．8 The Ideal Monatomic Gas510

16．9 The Ideal Gas in a Uniform Gravitational Field512

16．10 The Boltzmann Equipartition Theorem516

16．11 Fluctuations in Entropy518

16．12 Entropy and Gibbs＇Mixing Paradox521

16．13 Thermodynamic Functions in Terms of the Partition Function523

16．14 Summary of Useful General Formulas525

PROBLEMS526

CHAPTER SEVENTEEN Advent of the Quantum Theory529

17．1 Cell Size and Planck＇s Constant529

17．2 The Sackur-Tetrode Vapor Pressure Formula530

17．3 Basic Weaknesses of the Classical Argument532

17．4 Indistinguishability of Identical Particles533

17．5 The Combinatory Formula for Identical Objects536

17．6 The Bose-Einstein Distribution Law537

17．7 The Boltzmann Approximation539

17．8 Diatomic Molecule in a 1∑ State542

17．9 Quantization of Vibration and Rotation544

17．10 Rotation and Rotation-Vibration Bands546

17．11 The Partition Function for a Diatomic Gas550

17．12 The Partition Function and Internal Energy for Vibration552

17．13 Vibratory Heat Capacity556

17．14 The Partition Function and Internal Energy for Rotation558

17．15 The Vapor Pressure Constant for a Diatomic Gas562

PROBLEMS565

CHAPTER EIGHTEEN Quantum Statistics566

18．1 Photons and Matter Waves566

18．2 Wave Amplitudes and Probability569

18．3 The Wave Equation569

18．4 Particle in a Box572

18．5 The Linear Vibrator577

18．6 The Rigid Rotor in Space582

18．7 The Quantum Partition Function for Translation584

18．8 Angular Momentum and Statistical Weights586

18．9 Statistical Weights for Atoms588

18．10 Statistical Weights of Diatomic Molecular States593

18．11 Electronic Heat Capacities595

18．12 Formation of a Molecule from Atoms600

18．13 Nuclear Symmetry and Nuclear Weights604

18．14 1∑ States of Homonuclear Molecules605

18．15 Rotational Behavior of Homonuclear Molecules608

18．16 Spectroscopic and Calorimetric Entropies611

REFERENCES616

PROBLEMS616

CHAPTER NINETEEN Applications to Various Systems618

19．1 Bose-Einstein and Fermi-Dirac Statistics618

19．2 The Ideal Paramagnetic Solid620

Small x623

Large x624

19．3 Black Body Radiation and the Photon Gas626

19．4 Planck＇s Radiation Law628

19．5 Gibbs＇Ensembles633

19．6 The System Partition Function637

19．7 The Imperfect Monatormic Gas640

19．8 The van der Waals Approximation641

19．9 The van der Waals Equation645

19．10 The Einstein Model of a Monatomic Solid648

19．11 The Debye Model of a Solid650

19．12 The Debye Formula for Internal Energy653

19．13 The Debye Function655

19．14 Extension of the Theory for Solids657

19．15 Fermi-Dirac Statistics660

19．16 The Electron Gas661

19．17 Approximation to the Value of the Parameter B663

19．18 Significance of the Fermi Level664

REFERENCES666

PROBLEMS666

Appendixes669

APPENDIX 2．1 Smoothed Second Virial Coefficients(B1 Values)for Thermometric Gases669

APPENDIX 4．1 Specific Heat,cp,and Specific Enthalpy,h,of Water at Atmospheric Pressure670

APPENDIX 11．1 The Reciprocity Theorem for Jacobians671

APPENDIX 13．1 Forms of Maxwell＇s Relations for n=3672

APPENDIX 15．1 Stirling＇s Formula673

APPENDIX 16．1 Liouville＇s Theorem675

APPENDIX 18．1 Solution of the Hermitian Equation676

APPENDIX 18．2 Solution of the Associated Legendre Equation678

APPENDIX 19．1 Evaluation of the Improper Integral in Sec．19．4680

APPENDIX 19．2 The Method of Darwin and Fowler681

NOTATION LIST684

USEFUL CONSTANTS689

INDEX690