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CHAPTER ONE Introduction 1

1．1 Introduction to Thermodynamics 1

1．2 Large-Scale or Macroscopic View 1

1．3 Molecular or Microscopic View 2

1．4 Systems and Their Surroundings 3

1．5 Walls and Boundaries 4

Rigid Walls 4

Cylinder and Piston 4

Diathermic Walls 4

Adiabatic Walls 4

Semipermeable Walls 4

Isolating Walls 5

1．6 Thermodynamic Equilibrium 5

1．7 Thermal Equilibrium and the Zeroth Law 5

1．8 Temperature as a Property of a System 8

1．9 The Equation of State and the Temperature Scale 9

1．10 Intensive and Extensive Properties 11

1．11 Thermodynamic States of a System:Degrees of Freedom 13

1．12 The Two-Phase System 16

1．13 Other Systems 18

Thin Uniform Filament under Tension 19

Systems with Surface Tension 19

Charged Soap Bubble 19

1．14 Quasistatic Processes and Reversibility 20

PROBLEMS 22

CHAPTER TWO Temperature 24

2．1 Measurement of Temperature 24

2．2 General Temperature Scales 25

2．3 Various Celsius Thermometers 27

2．4 Criteria for Good Thermometers 28

2．5 Gas Thermometers 29

The Constant-Volume Thermometer 30

The Constant-Pressure Thermometer 30

2．6 The Thermodynamic Celsius Scale 31

2．7 Boyle＇s Law and the Ideal Gas Celsius Scale 35

2．8 Empirical Behavior of Gases 34

2．9 The Absolute Gas Scale 36

2．10 Correction of the Constant-Volume Gas Thermometer 38

2．11 Correction of the Constant-Pressure Thermometer 40

2．12 Numerical Magnitudes of Corrections 44

2．13 Primary and Secondary Thermometers 45

2．14 The Platinum Resistance Thermometer 47

2．15 The Thermocouple 49

2．16 New Basis for the Thermodynamic Scale 50

PROBLEMS 51

CHAPTER THREE The Equation of State 53

3．1 The Ideal Gas 53

3．2 The Universal Gas Constant 55

3．3 Units 56

Volume 56

Pressure 56

Pressure-Volume(pV) 57

3．4 The P-V-T Surface 57

3．5 The Reciprocal and the Reciprocity Theorems 60

3．6 Thermodynamic Coefficients 61

3．7 The P-V-T Relation for a Pure Substance 62

3．8 The Kamerlingh Onnes Equation 66

3．9 Van der Waals＇Equation 68

3．10 Berthelot＇s Equation 72

3．11 Dieterici＇s Equation 74

3．12 The Beattie-Bridgeman Equation 75

3．13 The Equation of State in Virial Form 75

3．14 Solid and Liquid States 77

PROBLEMS 79

CHAPTER FOUR The First Law of Thermodynamics 82

4．1 Measurement of Heat 82

4．2 Heat Capacity and the Unit of Heat 83

4．3 Method of Mixtures 85

4．4 Mechanical Nature of Heat 87

4．5 Mechanical Equivalent of Heat 89

Direct Mechanical Determinations 90

Electrical Methods 90

4．6 The System as a Reservoir of Energy 93

4．7 Formulation of the First Law of Thermodynamics 95

4．8 Relative and Absolute Internal Energy 97

4．9 The First Law for Differential Processes 98

4．10 Work in Quasistatic Processes 100

4．11 Heat Absorbed in Quasistatic Processes 102

4．12 The First Law in Differential and Integral Forms 103

4．13 Cyclic Processes and Perpetual Motion 104

4．14 Mechanics and the First Law 106

PROBLEMS 107

CHAPTER FIVE Work and Heat in Various Systems 109

5．1 Introduction 109

5．2 Systems under Uniform Hydrostatic Pressure 109

5．3 Other Mechanical Systems 112

Thin Uniform Filament under Stretching Force 112

Systems with Surface Tension 112

5．4 Electrical Systems 112

5．5 Magnetic Systems 114

5．6 The General Case 117

5．7 Heat Capacities of a Pure Substance 118

5．8 Heat Capacities with the Variables T and p 119

5．9 Heat Capacities with the Variables T and V 120

5．10 Heat Absorbed along Certain Curves 121

5．11 Relations among the Heat Capacities;Specific Heats 123

5．12 Heat Capacities for Other Systems 124

5．13 Internal Energy of a Gas 126

5．14 Internal Energy of a Gas from Experiment 127

5．15 Heat Capacities of an Ideal Gas 131

5．16 Heat Capacities of Real Gases 132

5．17 Slope of the Adiabatic Curve 133

5．18 Equation of the Adiabatic for the Ideal Gas 135

PROBLEMS 137

CHAPTER SIX Heat Capacities of Gases 140

6．1 Experimental Measurements of Cv,Cp,and γ 140

6．2 Joly＇s Steam Calorimeter for Cv 141

6．3 Eucken＇s Low-Temperature Gas Calorimeter for Cv 142

6．4 Explosion Method for Cv 142

6．5 Method of Mixtures of Holborn and Henning for Cp 144

6．6 Continuous-Flow Method for Cp 144

6．7 γ by Adiabatic Expansion 145

6．8 Rüchhardt＇s Method for γ 147

6．9 Rinkel＇s Modified Method for γ 159

6．10 Experimental Values of Cv and γ 159

6．11 Kinetic Theory of the Ideal Gas 151

6．12 Equipartition of Energy 152

6．13 Degrees of Freedom of Molecules 154

6．14 Molecular Vibration 154

6．15 Quantization of Energy 159

6．16 Empirical Formula for Variation of Cp with T 163

PROBLEMS 164

CHAPTER SEVEN Solids,Liquids,and Change of Phase 165

7．1 Measurement of the Heat Capacities of Solids 165

7．2 The Nernst-Lindemann Vacuum Calorimeter 166

7．3 The Adiabatic Vacuum Calorimeter 168

7．4 Equilibrium Method 169

7．5 The Law of Dulong and Petit 171

7．6 Temperature Variation of Cv 172

7．7 Theoretical Interpretation of Cv for Solids 176

7．8 Heat Capacities of Liquids 178

7．9 Change of Phase 179

7．10 Enthalpy 180

7．11 Enthalpy and Internal Energy 182

7．12 Heat of Sublimation of a Monatomic Solid 184

7．13 Enthalpy and Internal Energy for Simple Substances 186

7．14 Heat of Reaction and Enthalpy Tables 189

7．15 Kirchhoff＇s Heat Capacity Formulas 193

7．16 The First Law with Mass Flow 194

The Constant-Flow Calorimeter 196

The Porous Plug and the Throttle Valve 196

The Ideal Nozzle 197

The Steam Turbine 197

PROBLEMS 198

CHAPTER EIGHT Heat Engines and the Second Law 200

8．1 Heat Engines 200

8．2 Thermal Efficiency 201

8．3 Idealized Engine Cycles 203

Reversible Cycles 204

Single Pure Substance as Working Substance 204

Ideal Gas 204

Infinite Reservoirs 204

8．4 The Gasoline Engine 205

8．5 The Air Standard Otto Cycle 206

8．6 The Air Standard Diesel Cycle 207

8．7 Carnot＇s Principle 209

8．8 Carnot＇s Theorem 211

8．9 Clausius＇Statement of the Second Law 213

8．10 The Second Law According to Kelvin and Planck 214

8．11 Criteria for Equivalence 215

8．12 The Carnot Refrigerator 216

8．13 Kelvin＇s Thermodynamic Heating 217

8．14 Various Carnot Cycles 220

Two-Phase System 220

Stretched Elastic Wire 221

Surface Film 221

8．15 The Kelvin Temperature Scale 222

PROBLEMS 225

CHAPTER NINE Entropy and the Second Law 228

9．1 Entropy and Necessary Waste 228

9．2 The Clausius Sum for a Closed Cycle 229

9．3 The Clausius Sum as an Integral 231

9．4 Entropy as a Property of a System 233

9．5 The Principle of the Increase of Entropy 235

9．6 Free Expansion of an Ideal Gas 237

9．7 Mixing of Gases 239

9．8 Dissipation of Mechanical and Electrical Energy 241

9．9 Temperature Equalization 242

9．10 Uses of Entropy 244

9．11 Temperature-Entropy Diagram 244

9．12 dS as a Perfect Differential 245

9．13 Heat Capacities as Entropy Derivatives 247

9．14 Entropy of an Ideal Gas 249

9．15 General Laboratory Equations for dU,dH,and dS 251

9．16 Thermodynamic Potentials 253

Internal Energy 253

Enthalpy 253

Entropy 253

9．17 The Potentials of Helmholtz and Gibbs 254

Helmholtz＇s Potential 254

Gibbs＇Potential 255

9．18 The Clausius Equations 256

9．19 The Principle of Carathéodory 257

9．20 Natural,Unnatural,and Reversible Processes 259

PROBLEMS 261

CHAPTER TEN The Steam Engine and the Refrigerator 264

10．1 Introduction 264

10．2 The Rankine Cycle 264

10．3 Efficiency of the Rankine Cycle 266

10．4 Steam Tables 267

10．5 Use of Steam Tables 270

10．6 The Steam Dome in the p-v Plane 271

10．7 The T-s,h-s,and p-s Diagrams 273

10．8 Improvements in the Utilization of Steam 275

The Newcomen Atmospheric Engine 276

James Watt＇s Contributions 276

Multiple-Expansion Engines 276

The Uniflow Engine 277

10．9 The Steam Turbine 277

10．10 Superpressure Turbines 279

10．11 The Refrigerator 282

10．12 Common Refrigerants 285

10．13 The Heat Pump 287

10．14 The Electrolux Refrigerator 289

REFERENCES 290

PROBLEMS 290

CHAPTER ELEVEN Thermodynamic Methods 292

11．1 Introduction 292

11．2 Thermodynamic Methods 292

The Cyclic Method 293

Analytic Methods 295

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

11．4 The Clausius-Clapeyron Equation in General 299

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

11．6 Maxwell＇s Relations and Multiphase Systems 303

11．7 Specific Heats of Saturated Phases 304

11．8 Gibbs＇Potential 307

11．9 Relation of the Triple Point to the Ice Point 208

Solubility Effect 309

Direct Pressure Effect 310

11．10 The Six General Relations of Maxwell 311

11．11 The Three Independent or Basic Derivatives 312

11．12 Derivatives in Terms of the Basic Three 315

11．13 Jacobians 317

11．14 The Reciprocity Theorem for Jaeobians 319

11．15 Maxwell＇s Relations in Jacobian Form 321

11．16 General Derivatives by Jacobians 323

11．17 The Fundamental Jacobian 323

PROBLEMS 325

CHAPTER TWELVE Applications of the General Relations 328

12．1 Introduction 328

12．2 Internal Energy,Enthalpy,and Entropy for Condensed Phases 330

12．3 Thermodynamic Functions for Ideal Gases 332

12．4 The van tier Waals Gas 335

12．5 The Adiabatic Law for a van der Waals Gas 336

12．6 Internal Energy,Enthalpy,and Entropy for Real Gases 338

12．7 The Joule-Kelvin Effect 344

12．8 The Inversion Curve 345

12．9 Joule-Kelvin Cooling 347

12．10 The Maximum Inversion Temperature 349

12．11 Integration of the Clausius-Clapeyron Equation 352

12．12 The Ideal Gas Approximation 352

12．13 The General Vapor Pressure Equation of Kirchhoff 356

12．14 Kirchhoff＇s Formula for Latent Heat of Sublimation 357

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

12．16 Latent Heat of Sublimation of a Monatomie Solid 360

12．17 Vapor Pressure of a Monatomic Solid 362

12．18 Entropy and the Vapor Pressure Constant 364

PROBLEMS 366

CHAPTER THIRTEEN Applications to Various Systems 370

13．1 The n-Variable Thermodynamic System 370

13．2 Restricted and Unrestricted Systems 372

13．3 Tensed Filament or Uniform Rod 374

Temperature Change on Stretching(Adiabatic) 375

Heating a Stiff Rod at Constant Length 375

13．4 Reversible Electric Cell 376

13．5 The Cavity Radiator and Black Body Radiation 381

Radiancy of a Surface or Cavity 381

The Cavity Radiator 382

Properties of surfaces 383

13．6 Radiation Density and Radiancy 384

Directional Radiancy 384

Parallel Beam Radiancy 385

Relation of R to R？ 386

Relation of Rc to the Energy Density 386

13．7 Pressure of Radiation 388

13．8 The Stefan-Boltzmann Total Radiation Law 389

13．9 Surface Tension 391

13．10 Stressed Dielectrics in an Electric Field 394

13．11 Behavior of Entropy and Helmholtz＇s and Gibbs＇Potentials on Approach to Equilibrium 397

Adiabatic Processes 398

Isothermal Processes 399

13．12 Conditions for Stable Equilibrium 399

13．13 The Electrochemical Potential 400

13．14 Multicomponent Systems 401

13．15 Heterogeneous Equilibrium and the Phase Rule 402

Gibbs＇Phase Rule 403

13．16 Chemical Systems of Two Components 405

13．17 The Thermocouple 406

13．18 Kelvin＇s Treatment of the Thermoeouple 408

PROBLEMS 410

CHAPTER FOURTEEN The Physics of Low Temperatures 413

14．1 Production of Low Temperatures 413

14．2 Helium Liquefiers 414

14．3 Measurement of Low Temperatures 415

14．4 The Liquid Helium Vapor Pressure Formula 416

14．5 Phase Relations Of Helium 419

14．6 The Order of a Transition 421

14．7 The λ Transition in Helium 424

14．8 Dynamic Properties of Helium 425

The Phenomenon of Surface Flow 425

Abnormal Flow in Capillaries 426

The Mechanocaloric and Fountain Effects 427

14．9 The Two-Fluid Theory of HeII 429

14．10 Superconductivity 431

14．11 Superconductors in a Magnetic Field 433

14．12 Magnetic Cooling by Adiabatic Demagnetization 435

Isothermal Magnetization 437

Adiabatic Change of Magnetic Field 437

14．13 Magnetic Temperatures 439

14．14 The Lowest Temperature in the World 441

14．15 The Third Law of Thermodynamics 442

REFERENCES 446

PROBLEMS 446

CHAPTER FIFTEEN Entropy and Probability 448

15．1 Order,Disorder,and the Second Law 448

15．2 Mathematical Probability 449

15．3 Distribution of Marked Objects 451

15．4 Microstates and the Disorder Number of a Macrostate 455

15．5 The Disorder Number for a Macrostate of a Physical System 457

15．6 Entropy and the Disorder Number 460

15．7 Conditions for Maximum Entropy 462

15．8 Volume Distribution for Maximum Entropy 464

15．9 Velocity Distribution for Maximum Entropy 465

15．10 Evaluation of the Parameter α＇ 467

15．11 Evaluation of the Parameters κ and β 471

15．12 Various Forms of the Velocity Distribution Law 474

15．13 The Speed Distribution Law 477

15．14 Mean and Root-Mean-Square Speeds 479

15．15 The Equipartition Theorem and the Equation of State of an Ideal Monatomic Gas 481

15．16 Mass Flux 483

PROBLEMS 487

CHAPTER SIXTEEN Classical Statistical Mechanics 490

16．1 Introduction 490

16．2 Configuration-Velocity Space 491

16．3 Hamiltonian Coordinates and Phase Space 494

Free Point Mass in Space 495

Symmetric Rotor with a Fixed Axis 496

Mass Point Moving in Space about the Origin 496

The Rotating Vibrator 497

16．4 μ Space and Γ Space 502

16．5 Liouville＇s Theorem and Equal a Priori Probabilities in Γ Space 505

16．6 The Equilibrium Distribution in μ Space 506

16．7 The General Partition Function in μ Space 508

16．8 The Ideal Monatomic Gas 510

16．9 The Ideal Gas in a Uniform Gravitational Field 512

16．10 The Boltzmann Equipartition Theorem 516

16．11 Fluctuations in Entropy 518

16．12 Entropy and Gibbs＇Mixing Paradox 521

16．13 Thermodynamic Functions in Terms of the Partition Function 523

16．14 Summary of Useful General Formulas 525

PROBLEMS 526

CHAPTER SEVENTEEN Advent of the Quantum Theory 529

17．1 Cell Size and Planck＇s Constant 529

17．2 The Sackur-Tetrode Vapor Pressure Formula 530

17．3 Basic Weaknesses of the Classical Argument 532

17．4 Indistinguishability of Identical Particles 533

17．5 The Combinatory Formula for Identical Objects 536

17．6 The Bose-Einstein Distribution Law 537

17．7 The Boltzmann Approximation 539

17．8 Diatomic Molecule in a 1∑ State 542

17．9 Quantization of Vibration and Rotation 544

17．10 Rotation and Rotation-Vibration Bands 546

17．11 The Partition Function for a Diatomic Gas 550

17．12 The Partition Function and Internal Energy for Vibration 552

17．13 Vibratory Heat Capacity 556

17．14 The Partition Function and Internal Energy for Rotation 558

17．15 The Vapor Pressure Constant for a Diatomic Gas 562

PROBLEMS 565

CHAPTER EIGHTEEN Quantum Statistics 566

18．1 Photons and Matter Waves 566

18．2 Wave Amplitudes and Probability 569

18．3 The Wave Equation 569

18．4 Particle in a Box 572

18．5 The Linear Vibrator 577

18．6 The Rigid Rotor in Space 582

18．7 The Quantum Partition Function for Translation 584

18．8 Angular Momentum and Statistical Weights 586

18．9 Statistical Weights for Atoms 588

18．10 Statistical Weights of Diatomic Molecular States 593

18．11 Electronic Heat Capacities 595

18．12 Formation of a Molecule from Atoms 600

18．13 Nuclear Symmetry and Nuclear Weights 604

18．14 1∑ States of Homonuclear Molecules 605

18．15 Rotational Behavior of Homonuclear Molecules 608

18．16 Spectroscopic and Calorimetric Entropies 611

REFERENCES 616

PROBLEMS 616

CHAPTER NINETEEN Applications to Various Systems 618

19．1 Bose-Einstein and Fermi-Dirac Statistics 618

19．2 The Ideal Paramagnetic Solid 620

Small x 623

Large x 624

19．3 Black Body Radiation and the Photon Gas 626

19．4 Planck＇s Radiation Law 628

19．5 Gibbs＇Ensembles 633

19．6 The System Partition Function 637

19．7 The Imperfect Monatormic Gas 640

19．8 The van der Waals Approximation 641

19．9 The van der Waals Equation 645

19．10 The Einstein Model of a Monatomic Solid 648

19．11 The Debye Model of a Solid 650

19．12 The Debye Formula for Internal Energy 653

19．13 The Debye Function 655

19．14 Extension of the Theory for Solids 657

19．15 Fermi-Dirac Statistics 660

19．16 The Electron Gas 661

19．17 Approximation to the Value of the Parameter B 663

19．18 Significance of the Fermi Level 664

REFERENCES 666

PROBLEMS 666

Appendixes 669

APPENDIX 2．1 Smoothed Second Virial Coefficients(B1 Values)for Thermometric Gases 669

APPENDIX 4．1 Specific Heat,cp,and Specific Enthalpy,h,of Water at Atmospheric Pressure 670

APPENDIX 11．1 The Reciprocity Theorem for Jacobians 671

APPENDIX 13．1 Forms of Maxwell＇s Relations for n=3 672

APPENDIX 15．1 Stirling＇s Formula 673

APPENDIX 16．1 Liouville＇s Theorem 675

APPENDIX 18．1 Solution of the Hermitian Equation 676

APPENDIX 18．2 Solution of the Associated Legendre Equation 678

APPENDIX 19．1 Evaluation of the Improper Integral in Sec．19．4 680

APPENDIX 19．2 The Method of Darwin and Fowler 681

NOTATION LIST 684

USEFUL CONSTANTS 689

INDEX 690