Preface ...................................................... xvii
Introduction .................................................... 1
I SIMPLE MATERIALS ............................................. 7
1 Constitutive functions ....................................... 7
1.1 The fundamental thermodynamical quantities ............. 7
1.2 Other thermodynamical quantities ....................... 9
1.3 Rules for the relations among the thermodynamical
quantities ............................................. 9
1.4 Formalization of the basic rules ...................... 10
1.5 Simple materials ...................................... 10
1.6 Entropic property ..................................... 11
1.7 A special kind of material with entropic property ..... 12
1.8 The Nernst property ................................... 13
1.9 Exercises ............................................. 14
2 Some special simple materials ............................... 16
2.1 Ideal gases ........................................... 16
2.2 van der Waals materials ............................... 17
2.3 The Clausius materials ................................ 18
2.4 The Berthelot materials ............................... 19
2.5 The Kammerlingh Onnes materials ....................... 20
2.6 Concluding remarks .................................... 20
2.7 Exercises ............................................. 21
3 Change coefficients ......................................... 22
3.1 Convention about notations ............................ 22
3.2 Processes of special type ............................. 22
3.3 Other processes with constraints ...................... 23
3.4 Thermal expansion coefficients ........................ 23
3.5 Compressibility factors ............................... 24
3.6 Strain coefficients ................................... 25
3.7 Specific heats ........................................ 25
3.8 Latent heats .......................................... 26
3.9 Normal dilation ....................................... 26
3.10 Practical importance of the change coefficients ....... 27
3.11 Change coefficients of ideal gases .................... 28
3.12 Transition heat ....................................... 28
3.13 Exercises ............................................. 29
4 State curves ................................................ 30
4.1 Introductory remarks .................................. 30
4.2 Adiabats .............................................. 31
4.3 State curves of ideal gases ........................... 32
4.4 State curves of van der Waals materials ............... 34
4.5 Exercises ............................................. 37
5 Canonical variables ......................................... 38
5.1 Fundamental relations ................................. 38
5.2 Canonical form of simple materials .................... 40
5.3 Entropic property in the canonical variables .......... 40
5.4 Canonical form of ideal gases and van der Waals
materials ............................................. 41
5.5 Exercises ............................................. 42
6 Phases ...................................................... 42
6.1 Introductory remarks .................................. 42
6.2 Definition of phases .................................. 44
6.3 Phases of the van der Waals material .................. 44
6.4 Phases in the canonical variables ..................... 45
6.5 Characterization of phases by temperature and
pressure .............................................. 45
6.6 Change of variables ................................... 47
6.7 A useful formalism .................................... 47
6.8 Exercises ............................................. 48
7 Phase connections ........................................... 49
7.1 Introductory remarks .................................. 49
7.2 Zeroth-order phase connections ........................ 49
7.3 Second-order phase connections ........................ 50
7.4 λ transitions ......................................... 50
7.5 On the classification of second-order phase
connections ........................................... 52
7.6 First-order phase connections ......................... 52
7.7 Clausius-Clapeyron equation ........................... 53
7.8 Critical points ....................................... 54
7.9 First-order phase connections of the van der Waals
material .............................................. 54
7.10 Exercises ............................................. 56
8 Bodies ...................................................... 56
8.1 The notion of a body ................................... 56
8.2 The entire quantities ................................. 57
8.3 Entire canonical variables ............................ 58
8.4 Entropic property in the entire canonical variables ... 60
8.5 A useful formalism .................................... 61
8.6 Legendre transforms ................................... 61
8.7 Exercises ............................................. 62
II SYSTEM OF SIMPLE BODIES: A SURVEY ........................... 63
9 Dynamics of processes ....................................... 63
9.1 Introductory remarks .................................. 63
9.2 The dynamical equation ................................ 64
9.3 About working and transferring ........................ 64
9.4 A few words about the first law ....................... 65
9.5 The specific dynamical quantities ..................... 66
9.6 System of bodies ...................................... 66
9.7 Independence of interactions .......................... 67
10 Properties of dynamical quantities .......................... 67
10.1 Convention about notations ............................ 67
10.2 Exact form of the dynamical quantities ................ 68
10.3 Mutuality ............................................. 68
10.4 'The non-compensated heat' ............................ 69
10.5 Indirect heat conduction .............................. 70
10.6 Convention about the dynamical quantities ............. 71
10.7 Forbidden interactions ................................ 71
10.8 Equilibrium properties ................................ 72
10.9 The dissipation inequality ............................ 73
10.10 A few words about the second law ...................... 74
11 Thermodynamical forces ...................................... 75
11.1 Introductory remarks .................................. 75
11.2 The notion of thermodynamical forces .................. 75
11.3 Pseudolinear dynamical quantitities ................... 77
11.4 The pair conductance matrices ......................... 78
11.5 Non-uniqueness of pair conductance matrices ........... 79
11.6 Mechanically strong springing ......................... 80
11.7 The dissipation inequality in the pseudolinear case ... 80
11.8 Symmetry properties of the canonical conductance
matrix ................................................ 81
11.9 Concluding remarks .................................... 81
11.10 Exercises ............................................. 82
III SIMPLE SYSTEMS WITHOUT PARTICLE CHANGE ................... 83
12 One body in a given environment ............................. 83
12.1 Introductory remarks .................................. 83
12.2 General formulae ...................................... 83
12.3 Processes without constraint .......................... 87
12.4 Isochoric processes ................................... 89
12.5 Adiabatic processes ................................... 91
12.6 Isothermal processes .................................. 94
12.7 Isobaric processes .................................... 96
12.8 Non-zero heat source .................................. 99
12.9 Elastic hull .......................................... 99
12.10 Zeroth-order and second-order phase transitions ...... 100
12.11 Extremum properties .................................. 101
12.12 Remarks on the intensive constraints ................. 102
12.13 Control instead of constraint ........................ 106
12.14 Heat engines ......................................... 107
12.15 Thermal efficiency with maximal power ................ 110
12.16 Remarks on the second law ............................ 111
12.17 Exercises ............................................ 112
13 Two bodies in a given environment .......................... 114
13.1 Introductory remarks ................................. 114
13.2 General formulae ..................................... 115
13.3 System without constraint ............................ 118
13.4 Fixed total volume ................................... 120
13.5 Fixed total volume and joint heat insulation ......... 122
13.6 Fixed total volume and individual heat insulations ... 124
13.7 Fixed individual volumes ............................. 127
13.8 Fixed individual volumes and joint heat insulation ... 129
13.9 Individual heat insulations .......................... 130
13.10 Joint heat insulation ................................ 132
13.11 Constant temperature ................................. 132
13.12 Constant temperature and fixed total volume .......... 134
13.13 Constant pressure .................................... 135
13.14 Constant pressure and joint heat insulation .......... 136
13.15 Extremum properties .................................. 137
13.16 On the second law again .............................. 139
13.17 Exercises ............................................ 141
IV SYSTEM OF SIMPLE BODIES; GENERAL TREATMENT ................ 144
14 Description of systems ..................................... 144
14.1 Exact definition of systems .......................... 144
14.2 Consequences of the equilibrium property and the
dissipation inequalities ............................. 148
14.3 Equilibrium .......................................... 149
14.4 Exercises ............................................ 150
15 Summarizing formulae ....................................... 150
15.1 General notations .................................... 150
15.2 The dynamical equation ............................... 152
15.3 Constraints .......................................... 153
15.4 The pseudolinear case ................................ 157
15.5 The dissipation inequalities ......................... 160
15.6 Asymptotic stability of equilibrium .................. 160
15.7 Application to special systems ....................... 162
15.8 Strict asymptotic stability of equilibria ............ 163
15.9 Entropy maximum and entropy production ............... 165
15.10 Exercises ............................................ 166
16 Remarks on some usual notions .............................. 166
16.1 The Onsager theory ................................... 166
16.2 The Prigogine principle .............................. 169
16.3 Some thermodynamical aspects of interactions ......... 171
16.4 Entropy and intrinsic stability ...................... 173
16.5 Exercises ............................................ 175
V SIMPLE SYSTEMS WITH PARTICLE INTERCHANGE .................... 176
17 On diffusions and phase transitions ........................ 176
18 Diffusion between a body and an environment ................ 176
18.1 General formulae ..................................... 176
18.2 Processes without constraint ......................... 180
18.3 Fixed volume ......................................... 180
18.4 Constant temperature ................................. 181
18.5 Constant pressure .................................... 183
18.6 Heat insulation ...................................... 184
18.7 Semipermeable wall, fixed volume ..................... 185
18.8 Exercises ............................................ 187
19 Diffusion between two bodies and an environment ............ 187
19.1 General formulae ..................................... 187
19.2 System without constraint ............................ 189
19.3 Fixed total volume ................................... 190
19.4 Fixed total particle number .......................... 191
19.5 Fixed total volume and particle number ............... 193
19.6 Fixed total volume, particle number and internal
energy ............................................... 194
19.7 Fixed individual volumes, total particle number
and joint heat insulation ............................ 195
19.8 Constant temperature, fixed total volume and
particle number ...................................... 198
19.9 Constant pressure, fixed total particle number ....... 199
19.10 Fixed total particle number and joint heat
insulation ........................................... 201
19.11 Fixed total particle number, joint heat insulation
and mechanical separation ............................ 201
19.12 Cooling of gases ..................................... 202
19.13 Exercises ............................................ 206
20 First-order phase transitions .............................. 207
20.1 General formulae ..................................... 207
20.2 Phase transition in a given environment .............. 208
20.3 Phase transition insulated from the environment ...... 210
20.4 Supercooling, superheating ........................... 211
20.5 Exercise ............................................. 214
VI COMPOSITE MATERIALS (MIXTURES, SOLUTIONS) .................. 215
21 Constitutive functions ..................................... 215
21.1 Concentrations ....................................... 215
21.2 Definition of composite materials .................... 215
21.3 Convention about notations ........................... 217
21.4 Canonical variables .................................. 217
21.5 Entropic property .................................... 218
21.6 A useful formalism ................................... 219
21.7 Change coefficients .................................. 220
21.8 Exercises ............................................ 220
22 Ideal mixtures ............................................. 221
22.1 Definition of an ideal mixture ....................... 221
22.2 The purity conditions ................................ 222
22.3 The intrinsic stability conditions ................... 223
22.4 Ideal mixture of entropic materials .................. 224
22.5 Ideal mixture of ideal gases ......................... 225
22.6 Ideal mixture of identical materials ................. 226
22.7 The Gibbs paradox .................................... 227
22.8 Exercises ............................................ 228
23 Non-ideal mixtures ......................................... 229
23.1 Partial pressures, Henry law ......................... 229
23.2 Fugacities, Lewis-Randall rule ....................... 230
24 Some phenomena connected with mixing ....................... 231
24.1 Experimental facts ................................... 231
24.2 Change of quantities in mixing ....................... 231
24.3 Mixing heat .......................................... 232
24.4 Freezing-point decrease .............................. 233
24.5 Osmosis .............................................. 233
24.6 Saturation ........................................... 234
24.7 Exercises ............................................ 235
25 Phases, phase connections .................................. 235
25.1 Phases ............................................... 235
25.2 Phase connections .................................... 236
25.3 Phase surfaces ....................................... 237
25.4 Phase connections of different mixtures .............. 238
25.5 Exercises ............................................ 239
26 Mixture families ........................................... 239
26.1 Definition of a mixture family ....................... 239
26.2 Canonical variables .................................. 242
26.3 Entropic mixture families ............................ 243
26.4 Exercises ............................................ 243
27 Bodies ..................................................... 243
27.1 Definition of a body ................................. 243
27.2 The entire quantities ................................ 244
27.3 The entire canonical variables ....................... 245
27.4 Entropic property in the entire canonical
variables ............................................ 247
27.5 A useful formalism ................................... 247
27.6 Exercises ............................................ 248
28 Thermo dynamical forces .................................... 248
28.1 Problems of definition ............................... 248
28.2 Solution of the problems ............................. 248
29 System of bodies ........................................... 249
29.1 Definition of a system ............................... 249
29.2 Summarizing formulae ................................. 252
30 A body in a given environment .............................. 253
30.1 The framework of description ......................... 253
30.2 System without constraint ............................ 254
30.3 Selective converting, fixed volume ................... 255
30.4 Selective converting ................................. 256
30.5 Exercises ............................................ 256
31 Two bodies in a given environment .......................... 256
31.1 The framework of description ......................... 256
31.2 Fixed total energy and total volume .................. 257
31.3 Selective converting, fixed total energy and fixed
individual volumes ................................... 258
31.4 Selective converting ................................. 259
31.5 Supersaturated solutions ............................. 260
31.6 Exercises ............................................ 260
VII CHEMICAL REACTIONS ....................................... 262
32 Characteristics of chemical reactions ...................... 262
32.1 Introductory remarks ................................. 262
32.2 Stoichiometric coefficients .......................... 262
32.3 Chemical affinity .................................... 263
32.4 The degree of reaction ............................... 263
32.5 Entropic body ........................................ 264
32.6 Exercises ............................................ 265
33 Dynamics of chemical reactions ............................. 265
33.1 The dynamical equation ............................... 265
33.2 Thermodynamical forces ............................... 265
33.3 The role of affinity ................................. 266
33.4 Catalysators ......................................... 267
33.5 The law of mass action ............................... 268
33.6 Exercises ............................................ 268
34 Reaction heats ............................................. 269
34.1 Energy change of an isolated body .................... 269
34.2 Energy change of a body at constant volume and
temperature .......................................... 269
34.3 Energy change of a body at constant temperature and
pressure ............................................. 270
35 Description of chemical reactions .......................... 270
35.1 Introductory remarks ................................. 270
35.2 Definition of a chemical reaction .................... 271
35.3 Consequences of the equilibrium property and the
dissipation inequality ............................... 272
35.4 Summarizing formulae ................................. 273
36 Special chemical reactions ................................. 274
36.1 Reactions without constraint ......................... 274
36.2 Fixed volume ......................................... 275
36.3 Constant temperature ................................. 275
36.4 Constant pressure .................................... 276
36.5 Heat insulation ...................................... 276
36.6 Exercises ............................................ 277
VIII EXTENDED ORDINARY THERMODYNAMICS ........................ 278
37 Thermo-mechanical interaction .............................. 278
37.1 Problems of the description .......................... 278
37.2 A new dynamical equation ............................. 279
37.3 Exercises ............................................ 280
38 Extended thermodynamical processes ......................... 281
38.1 Introductory remarks ................................. 281
38.2 The extended thermodynamical material ................ 282
38.3 Description of processes ............................. 283
38.4 Exercises ............................................ 283
39 A body in a given environment .............................. 283
39.1 The dynamical quantitities ........................... 283
39.2 The equilibrium properties ........................... 284
39.3 The dissipation inequalities ......................... 284
39.4 The dynamical equation ............................... 285
39.5 Processes without constraint ......................... 285
39.6 Isothermal processes ................................. 287
39.7 Adiabatic processes .................................. 288
39.8 Isobaric processes ................................... 289
39.9 Limiting case of the extended dynamical equation ..... 290
39.10 Exercises ............................................ 291
40 Bounds of extended thermodynamics .......................... 291
IX ELECTROMAGNETIC PHENOMENA IN THERMODYNAMICS ................ 293
41 Introductory remarks ....................................... 293
42 Electrically chargeable bodies ............................. 295
42.1 The potential of a charged body ...................... 295
42.2 The pressure of a charged body ....................... 297
42.3 The internal energy of a charged body ................ 298
42.4 Extensive and intensive quantities ................... 298
42.5 Definition of a chargeable body ...................... 298
42.6 Canonical variables .................................. 300
42.7 Entropic property .................................... 300
42.8 Conventional chargeable body ......................... 301
42.9 Remarks on the entropic property ..................... 301
42.10 Two customary conditions ............................. 303
42.11 Exercises ............................................ 303
43 Processes of electrically chargeable bodies ................ 304
43.1 Dynamical equation, dynamical quantitities ........... 304
43.2 Equilibrium properties, thermodynamical force ........ 305
43.3 Dissipation inequality ............................... 306
43.4 Concluding remarks ................................... 307
44 Some special systems ....................................... 307
44.1 General formulae ..................................... 307
44.2 Fixed volume ......................................... 308
44.3 Constant pressure .................................... 309
44.4 Constant temperature ................................. 310
44.5 Direct currents ...................................... 311
44.6 Exercises ............................................ 311
45 Some important thermoelectric effects ...................... 311
45.1 Basic assumptions .................................... 311
45.2 The Seebeck effect ................................... 312
45.3 The Peltier effect ................................... 312
45.4 The Thomson effect ................................... 312
45.5 Concluding remarks ................................... 313
45.6 Exercise ............................................. 313
46 Extended chargeable bodies ................................. 314
46.1 Definition of an extended chargeable body ............ 314
46.2 Dynamical equation, dissipation inequalities ......... 314
46.3 Quasi-stationary currents ............................ 315
46.4 Constant exterior potential .......................... 316
46.5 Periodic exterior potential .......................... 317
46.6 Exercises ............................................ 320
47 Bodies consisting of ions .................................. 320
48 Electrically polarizable bodies ............................ 321
48.1 Electric field of a polarized body ................... 321
48.2 Polarization in an exterior field .................... 322
48.3 Fundamental assumptions .............................. 322
48.4 The Clausius-Mosotti formula ......................... 323
48.5 The notion of induced polarization ................... 324
48.6 Definition of a polarizable body ..................... 325
48.7 Canonical variables .................................. 326
48.8 Entropic property .................................... 327
48.9 Conventional polarizable body ........................ 327
48.10 Two customary conditions ............................. 328
48.11 Exercises ............................................ 328
49 Induced polarization ....................................... 329
49.1 Dielectric bodies .................................... 329
49.2 Langevin-Weiss induced polarization .................. 330
49.3 Properties of the Langevin function .................. 331
49.4 Exercises ............................................ 331
50 Further observations ....................................... 331
50.1 Equilibrium relations ................................ 331
50.2 Remarks on usual treatments .......................... 332
50.3 Vectorial quantities ................................. 333
50.4 Exercises ............................................ 333
51 Processes of a polarizable body ............................ 334
51.1 Dynamical equation, dynamical quantitities ........... 334
51.2 Equilibrium properties, thermodynamical force ........ 334
51.3 Dissipation inequality ............................... 336
51.4 Electrostriction ..................................... 336
52 Some special systems ....................................... 337
52.1 General formulae ..................................... 337
52.2 Fixed volume ......................................... 337
52.3 Constant pressure .................................... 338
52.4 Constant temperature ................................. 339
52.5 Exercises ............................................ 340
53 Extended polarizable bodies ................................ 340
53.1 Definition of an extended polarizable body ........... 340
53.2 Dynamical equation, dissipation inequalities ......... 341
53.3 Processes of special systems ......................... 341
53.4 Constant or periodic exterior field .................. 342
53.5 Complex susceptance .................................. 343
53.6 Exercises ............................................ 343
54 Magnetizable bodies ........................................ 343
54.1 Magnetic field of a magnetized body .................. 343
54.2 Magnetization in an exterior field ................... 344
54.3 Fundamental assumptions .............................. 345
54.4 The Clausius-Mosotti formula ......................... 345
54.5 Definition of a magnetizable body .................... 346
54.6 Canonical variables, entropic property ............... 348
54.7 Conventional magnetizable body ....................... 348
54.8 Two customary conditions ............................. 349
54.9 Exercises ............................................ 349
55 Induced magnetization ...................................... 349
55.1 Diamagnetic and paramagnetic bodies .................. 349
55.2 Langevin-Weiss induced magnetization ................. 350
55.3 Approximate solution of the Langevin-Weiss
equation ............................................. 351
55.4 Examination of the Langevin-Weiss equation ........... 352
55.5 Exercises ............................................ 354
56 Processes of a magnetizable body ........................... 354
56.1 Dynamical equation, dynamical quantitities ........... 354
56.2 Equilibrium properties, thermodynamical force ........ 355
56.3 Dissipation inequality ............................... 356
56.4 Magnetic cooling ..................................... 356
56.5 On the negative temperature .......................... 357
57 Some special systems ....................................... 359
57.1 General formulae ..................................... 359
57.2 Fixed volume ......................................... 359
57.3 Hysteresis ........................................... 360
57.4 Theory and experience ................................ 361
57.5 Exercises ............................................ 362
Tables ........................................................ 363
Appendix ...................................................... 374
Subject index ................................................. 388
|
