Thermal Physics: Concepts and Practice

Thermal Physics: Concepts and Practice......Page 3
Tilte......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
1.1 The beginning......Page 17
1.2 Thermodynamic vocabulary......Page 19
1.3.1 Thermodynamic variables defined......Page 20
Interaction energy......Page 21
1.4 Quantum mechanics, the\"mother of theories\'\'......Page 22
1.4.2 A brief review......Page 23
1.5 Probabilities in quantum mechanics......Page 25
1.5.1 Expectation values......Page 26
1.6 Closing comments......Page 27
2.1 The density operator: pure states......Page 28
2.1.1 Traces, expectations and information......Page 29
2.2 Mixed states......Page 31
2.2.1 Example......Page 32
2.2.3 Macroscopic consequences......Page 33
2.2.4 Thermodynamic state functions(?)......Page 35
2.3 Thermal density operator p top and entropy......Page 36
Example 2.1......Page 37
Example 2.2......Page 38
Problems and exercises......Page 39
3.1.1 Work, W......Page 41
3.1.4 Internal energy, U......Page 43
3.3 Equations of state......Page 44
Quasi-static reversible work......Page 46
Irreversible work......Page 48
Quasi-static irreversible work......Page 50
A loaded rubber band......Page 51
A compressed metal rod......Page 53
3.4.1 Heat transfer at constant volume......Page 54
3.4.2 Heat transfer at constant pressure......Page 55
Ideal monatomic gas......Page 56
A steel wire......Page 57
A rapidly expanding gas......Page 59
The filling problem: atmospheric gas filling an evacuated vessel......Page 60
Problems and exercises......Page 63
4.1 Thermodynamic differentials......Page 65
4.2.1 Exactness......Page 66
4.2.3 Entropy: a thermal introduction......Page 67
4.3 Euler\'s homogeneous function theorem......Page 70
4.4 A cyclic chain rule......Page 71
Free expansion: the cyclic chain rule......Page 72
Exactness and line integration......Page 75
Example 1......Page 76
Example 2......Page 77
Example 3......Page 79
4.6 Thermal engines......Page 81
4.6.1 Carnot\'s thermal engine......Page 82
4.6.2 The Carnot cycle – entropy......Page 85
Problems and exercises......Page 86
5.1.1 Internal energy U......Page 89
5.1.2 Enthalpy H......Page 91
5.1.3 Helmholtz potential F......Page 92
5.1.4 Gibbs potential G......Page 94
5.2 Enthalpy and throttling......Page 95
5.3 Entropy and heat capacity......Page 97
5.3.1 Relationship between Cp and CV......Page 98
Problems and exercises......Page 99
6.1 Entropy: ticket to the Emerald City......Page 101
6.2 The bridge......Page 102
6.3 Thermodynamic hamiltonians......Page 103
6.4 Microcanonical (Boltzmann) theory......Page 105
6.5 Gibbs\' canonical theory......Page 109
6.6 Canonical thermodynamics......Page 110
Example 1......Page 112
Example 2......Page 113
Example 3......Page 114
Example 5......Page 116
Example 6......Page 117
Problems and exercises......Page 119
7.1 Introduction......Page 122
7.2 Ideal gas law......Page 123
7.3 Quasi-classical model......Page 124
7.4 Ideal gas partition function......Page 125
7.5 Thermodynamics of the ideal gas......Page 127
7.6 Gibbs\' entropy paradox......Page 129
7.7 Entropy of mixing......Page 130
Problems and exercises......Page 131
8.2 Schottky model......Page 133
8.3 Two-level systems and negative temperature......Page 136
Problems and exercises......Page 138
9.1 Heat capacity of solids......Page 139
9.3 Einstein model in one dimension......Page 140
9.3.1 Partition function for one-dimensional Einstein model......Page 142
9.3.2 Phonons and the one-dimensional oscillator......Page 143
9.4.1 Partition function for the three-dimensional Einstein model......Page 144
9.4.2 Thermodynamics of the three-dimensional Einstein model......Page 145
9.5 Debye model......Page 147
Problems and exercises......Page 149
10.1 Naive one-dimensional elastomer......Page 152
10.2 Elongation as an extensive observable......Page 154
10.2.1 Naive elastomer model......Page 155
10.3.1 Elongation......Page 156
10.3.2 Entropy......Page 157
10.4 \"Hot rubber bands\'\': a thermodynamic analysis......Page 159
10.4.1 Abruptly relaxed rubber band......Page 161
10.5 A non-ideal elastomer......Page 162
10.6 Three-dimensional elastomer thermodynamics......Page 165
Problems and exercises......Page 167
Paramagnetism......Page 170
“Permanent” magnetism......Page 171
11.2 Magnetic work......Page 172
11.3 Microscopic models and uniform fields......Page 176
11.4 Local paramagnetism......Page 177
11.5 Simple paramagnetism......Page 178
11.6 Local paramagnet thermodynamics......Page 180
11.7 Magnetization fluctuations......Page 183
11.7.1 Example: Adiabatic (isentropic) demagnetization......Page 184
11.8 A model for ferromagnetism......Page 185
11.9 A mean field approximation......Page 186
11.10 Spontaneous magnetization......Page 188
11.11 Critical exponents......Page 189
11.13 Closing comment......Page 190
12.1 Variable particle number......Page 191
12.3.1 Formalities......Page 192
12.3.2 Grand thermodynamics......Page 194
12.3.3 Grand potential......Page 195
12.3.4 G, gr and Euler\'s theorem......Page 197
12.4 A \"grand\'\' example: the ideal gas......Page 198
12.4.1 Ideal gas thermodynamic properties......Page 199
12.5 Van der Waals\' equation......Page 200
12.6 A star is born......Page 202
12.6.1 Thermodynamic model......Page 203
12.6.2 Collapse criterion......Page 205
Problems and exercises......Page 207
13.1 Introduction......Page 208
Ideal gas in the Earth’s gravitational field......Page 209
Charged ideal gas between capacitor plates......Page 210
Ideal gas in a rotating cylinder......Page 211
13.3 Thermodynamics of chemical equilibrium......Page 212
13.4 A law of mass action......Page 214
13.5 Thermodynamics of phase equilibrium......Page 216
13.6 Gibbs–Duhem relation......Page 217
13.7 Multiphase equilibrium......Page 218
13.8 The Clausius–Clapeyron equation......Page 219
13.9 Surface adsorption: Langmuir\'s model......Page 220
13.10 Dissociative adsorption......Page 223
13.11 Crystalline bistability......Page 224
Problems and exercises......Page 226
14.1 Introduction......Page 228
14.2 Electromagnetic eigen-energies......Page 229
14.3 Thermodynamics of electromagnetism......Page 230
14.3.2 Average photon number......Page 231
14.4 Radiation field thermodynamics......Page 232
14.5 Stefan–Boltzmann, Planck, Rayleigh–Jeans laws......Page 233
14.6 Wien\'s law......Page 236
14.8 Stefan–Boltzmann radiation law......Page 237
14.9 Radiation momentum density......Page 240
Problems and exercises......Page 241
15.2 Ideal gas eigen-energies......Page 244
15.3 Grand partition function......Page 245
15.4 Electron spin......Page 246
15.5 Fermi–Dirac thermodynamics......Page 247
15.6 Independent fermion model......Page 249
15.7 The chemical potential (T≠ 0)......Page 250
15.8 Internal energy (T ≠ 0)......Page 252
15.9 Pauli paramagnetic susceptibility......Page 253
15.10 Electron gas model......Page 254
15.11.1 White dwarf thermodynamics......Page 257
Problems and exercises......Page 259
16.1 Introduction......Page 262
16.2 Ideal Bose gas......Page 263
16.3 Bose–Einstein thermodynamics......Page 264
16.4 The ideal BE gas and the BE condensation......Page 265
16.4.1 The condensate......Page 268
Problems and exercises......Page 269
17.1 Introduction......Page 271
17.3 Moving frame thermodynamic potential Ώ......Page 273
17.3.1 Moving frame blackbody thermodynamics......Page 275
17.4 Radiation energy flux......Page 277
Problems and exercises......Page 278
A.1 0 <  Tr(t P op) 2 < 1......Page 279
B.1 Properties of  F......Page 280
B.2 The \"bias\'\' function......Page 281
B.3 A thermal Lagrangian......Page 282
C.2 The proof......Page 284
D Appendix D Occupation numbers and the partition function......Page 285
Example 1......Page 287
Example 2......Page 289
F.1 Objectives......Page 291
F.2 Results and analysis......Page 293
G.2 Thermodynamic potentials and magnetic fields......Page 294
G.3 Work and uniform fields......Page 295
G.4 Thermodynamics with internal fields......Page 299
H.2 Electromagnetic waves......Page 301
H.2.1 Solution in free space – periodic boundary conditions......Page 302
Properties of wave solutions......Page 303
H.3 Electromagnetic vector potential......Page 304
H.4 Quantized electromagnetic hamiltonian......Page 306
I.2 Expansion method: βμ >> 1......Page 309
J.1 BE integrals: μ = 0......Page 312
J.2 BE integrals: μ < 0......Page 313
Index......Page 315