Introductory Statistical Thermodynamics

Introductory Statistical Thermodynamics......Page 3
Copyright......Page 4
Preface......Page 5
Introduction......Page 8
Systems of Identical Particles......Page 10
Quantum Description of Particles *)......Page 11
Problems with Solutions *)......Page 14
Hamiltonian of Translational Motion......Page 15
Solution of the Schrödinger Equation *)......Page 16
Normalization of the Wave Function *)......Page 19
Quantized Energy of Translational Motion......Page 20
Problems with Solutions *)......Page 21
Hamiltonian of Vibrations......Page 23
Solution of the Schrödinger Equation *)......Page 24
Quantized Energy of Vibrations......Page 25
Hermite Polynomials *)......Page 26
Normalization of the Wave Function *)......Page 27
Problems with Solutions *)......Page 29
Kinetic Energy and Hamiltonian Operator......Page 32
Angular Momentum Operator *)......Page 33
Solution of the Schrödinger Equation *)......Page 35
Quantized Energy of Rotations......Page 40
Legendre Polynomials *)......Page 41
Normalization of the Wave Function *)......Page 45
Spin Angular Momentum *)......Page 49
Problems with Solutions *)......Page 50
Introduction and Definitions......Page 52
Calculation of the Number of Accessible States......Page 53
Classical Number of Accessible States......Page 55
Number of Accessible States for Bosons......Page 56
Number of Accessible States for Fermions......Page 57
Problems with Solutions......Page 58
Equilibrium Conditions......Page 60
Occupation Numbers of Energy Levels......Page 62
Concept of Temperature......Page 64
Problems with Solutions......Page 66
Free Energy and the Partition Function......Page 71
Internal Energy: Caloric-State Equation......Page 74
Pressure: Thermal-State Equation......Page 76
Classification of Thermodynamic Variables......Page 79
Problems with Solutions......Page 80
Changes of States. Heat and Work......Page 86
First Law of Thermodynamics......Page 88
Third Law of Thermodynamics......Page 89
Open Systems......Page 90
Isobaric Expansion......Page 92
Isothermal Expansion......Page 93
Caloric Properties of Systems......Page 95
Specific Heat at Constant Volume cV......Page 96
Relation between Specific Heats......Page 97
Relations between Thermodynamic Coefficients......Page 100
Problems with Solutions......Page 103
Chemical Potential......Page 117
Thermodynamic Potential......Page 119
Latent Heat......Page 122
Clausius–Clapeyron Formula......Page 123
Problems with Solutions......Page 125
Continuous Energy Spectrum......Page 135
Continuous Partition Function......Page 137
Partition Function of Ideal Monatomic Gases......Page 139
Maxwell–Boltzmann Speed Distribution......Page 140
Average Speed of Gas Particles......Page 141
Root-Mean-Square Speed of Gas Particles......Page 142
Equipartition Theorem......Page 144
Caloric-State Equation......Page 146
Thermal-State Equation......Page 147
Universal and Particular Gas Constants......Page 148
Caloric and Thermal Coefficients......Page 150
General Maxwell–Boltzmann Distribution......Page 151
Harmonic and Anharmonic Oscillators......Page 161
Classical Limit of Quantum Partition Function......Page 165
Problems with Solutions......Page 170
Ideal Diatomic Gases......Page 182
Rotations of Gas Particles......Page 185
Vibrations of Gas Particles......Page 187
Problems with Solutions......Page 192
Partition Function for Nonideal Gases......Page 197
Free Energy of Nonideal Gases......Page 198
Free Energy of Particle Interactions......Page 200
van der Waals Equation......Page 203
Caloric-State Equation for Nonideal Gases......Page 204
Specific Heats for Nonideal Gases......Page 205
Problems with Solutions......Page 207
Isobaric Process......Page 223
Isochoric Process......Page 225
Isothermal Process......Page 226
Adiabatic Process......Page 228
Polytropic Process......Page 230
Cyclic Processes: Carnot Cycle......Page 232
Problems with Solutions......Page 236
The Case of Bosons......Page 251
The Case of Fermions......Page 252
Quantum Equilibrium Distribution......Page 253
Helmholtz Thermodynamic Potential......Page 257
Thermodynamics of Quantum Systems......Page 258
Evaluation of Integrals *)......Page 261
Problems with Solutions......Page 264
Electron Gases in Metals......Page 279
Ground State of Electron Gases in Metals......Page 280
Electron Gases in Metals at Finite Temperatures......Page 281
Chemical Potential at Finite Temperatures......Page 286
Thermodynamics of Electron Gases......Page 287
Problems with Solutions......Page 289
Planck Distribution......Page 292
Thermodynamics of Photon Gas in Equilibrium......Page 295
Problems with Solutions......Page 299
Lattice Vibrations and Phonons......Page 303
Vibration Modes......Page 304
Internal Energy of Lattice Vibrations......Page 311
Bose–Einstein Condensation......Page 322
Problems with Solutions......Page 326
Ultrarelativistic Fermion Gas......Page 338
Ultrarelativistic Fermion Gas for T/TF << 1......Page 342
Ultrarelativistic Fermion Gas for T/TF >> 1......Page 345
Thermodynamics of the Expanding Universe......Page 346
Internal Energy of Elementary Particle Species......Page 347
Entropy per Volume Element......Page 348
Problems with Solutions......Page 350
Physical Constants......Page 353
Bibliography......Page 354
B......Page 355
C......Page 356
D......Page 357
E......Page 358
F......Page 359
G......Page 360
H......Page 361
I......Page 362
J......Page 363
L......Page 364
M......Page 365
O......Page 366
P......Page 367
Q......Page 369
R......Page 370
S......Page 371
T......Page 372
V......Page 374
W......Page 375
Z......Page 376