General and statistical thermodynamics:
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
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| Schriftenreihe: | Graduate texts in physics
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| Beschreibung: | XXIX, 677 S. graph. Darst. |
| ISBN: | 9783642214806 3642214800 9783642214813 |
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IMAGE 1
CONTENTS
INTRODUCTION AND ZEROTH LAW 1
1. 1 SOME DEFINITIONS 1
1.1.1 A THERMODYNAMIC SYSTEM 1
1.1.2 ADIABATIC ENCLOSURE 2
1.1.3 ADIABATICALLY ISOLATED SYSTEM 2
1.1.4 ADIABATICALLY ENCLOSED SYSTEM 2
1.1.5 CONDUCTING WALLS 2
1.1.6 DIATHERMAL WALLS 2
1.1.7 ISOBARIC PROCESS 3
1.1.8 ISOCHORIC PROCESS 3
1.1.9 THERMAL EQUILIBRIUM 3
1.1.10 QUASI-STATIC PROCESS 3
1.1.11 REVERSIBLE AND IRREVERSIBLE PROCESSES 4
1.2 THERMODYNAMICS: LARGE NUMBERS 4
1.2.1 REMARK: MOST PROBABLE STATE 4
1.3 ZEROTH LAW OF THERMODYNAMICS 4
1.3.1 EMPIRICAL TEMPERATURE 5
1.3.2 TAKINGSTOCK 7
1.3.3 ISOTHERMAL PROCESS 8
1.3.4 EQUATION OF STATE 8
1.3.5 REMARK 8
1.4 USEFUL, SIMPLE MATHEMATICAL PROCEDURES 8
1.5 EXACT DIFFERENTIAL 9
1.5.1 EXERCISE I-A 9
1.5.2 NOTATION 11
1.5.3 EXERCISE I-B 13
1.5.4 INEXACT DIFFERENTIAL 13
1.5.5 STATE FUNCTION AND STATE VARIABLES 14
1.5.6 CYCLIC IDENTITY 14
1.5.7 EXERCISE H-A 16
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011458160
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.6 JACOBIANS: A SIMPLE TECHNIQUE 16
1.6.1 EXERCISE IL-B 17
1.6.2 JACOBIAN EMPLOYED 18
1.7 USEFUL IDENTITIES 19
1.7.1 CYCLIC IDENTITY: RE-DERIVED 19
1.7.2 SIMPLE IDENTITY 20
1.7.3 MIXED IDENTITY 20
PERFECT GAS 23
2.1 MODEL OF A PERFECT GAS 23
2.1.1 PRESSURE 24
2.2 TEMPERATURE: A STATISTICAL APPROACH 26
2.2.1 BOLTZMANN-MAXWELL-GIBBS DISTRIBUTION: PERFECT GAS WITH CLASSICAL
STATISTICS 26
2.2.2 ENERGY IN THE PERFECT GAS 28
2.3 EQUATION OF STATE 30
2.4 INTENSIVE AND EXTENSIVE PROPERTIES 30
2.4.1 EXTENSIVE 30
2.4.2 INTENSIVE 31
2.5 TEMPERATURE: THERMODYNAMIC APPROACH 31
2.5.1 ATTAINMENT OF THERMODYNAMIC EQUILIBRIUM BY A PERFECT GAS 33
2.6 DIATOMS 34
2.6.1 MONATOMIC AND DIATOMIC PERFECT GASES 34
2.7 MIXTURE OF PERFECT GASES: TEMPERATURE AND PRESSURE 35
2.7.1 DALTON'S LAW OF PARTIAL PRESSURES 36
2.8 PERFECT GAS ATMOSPHERE 38
2.8.1 THE BAROMETRIC EQUATION FOR ISOTHERMAL ATMOSPHERE 38
2.8.2 A RELATED CALCULATION 40
2.8.3 HEIGHT BELOW WHICH A SPECIFIED PERCENTAGE OF MOLECULES ARE FOUND
41
2.8.4 ENERGY OF ISOTHERMAL ATMOSPHERE 42
2.8.5 BAROMETRIC EQUATION FOR ATMOSPHERE WITH HEIGHT DEPENDENT
TEMPERATURE 44
2.9 PERFECT GAS OF EXTREMELY RELATIVISTIC PARTICLES 46
2.10 EXAMPLES I-VII 47
2.10.1 I: PARTIAL PRESSURE OF MIXTURES 47
2.10.2 II: DISSOCIATING TRI-ATOMIC OZONE 48
2.10.3 III: ENERGY CHANGE IN LEAKY CONTAINER 49
2.10.4 IV: MIXTURE OF CARBON AND OXYGEN 50
2.10.5 V : CARBON ON BURNING 51
2.10.6 VI : PRESSURE, VOLUME AND TEMPERATURE 52
2.10.7 VII: ADDITION TO EXAMPLE VI 53
IMAGE 3
CONTENTS
2.11 EXERCISES 55
2.11.1 I: WHERE 90% MOLECULES ARE FOUND IN ATMOSPHERE WITH DECREASING
TEMPERATURE 55 2.11.2 II: TOTAL ENERGY OF A COLUMN IN ATMOSPHERE WITH
DECREASING
TEMPERATURE 55
THE FIRST LAW 57
3.1 HEAT ENERGY, WORK AND INTERNAL ENERGY 58
3.1.1 CALORIC THEORY OF HEAT 58
3.1.2 LATER IDEAS 58
3.1.3 PERPETUAL MACHINES OF THE FIRST KIND 62
3.2 SPECIFIC HEAT ENERGY 63
3.3 NOTATION 63
3.4 SOME APPLICATIONS 64
3.4.1 T AND V INDEPENDENT 65
3.5 EXAMPLES 68
3.5.1 I: HEAT ENERGY NEEDED FOR RAISING TEMPERATURE 68 3.5.2 II: WORK
DONE AND INCREASE IN INTERNAL ENERGY DUE TO CHANGES IN PRESSURE, VOLUME,
AND TEMPERATURE 69
3.5.3 HI: WORK DONE BY EXPANDING VAN DER WAALS GAS 71 3.5.4 IV: METAL
VERSUS GAS: WORK DONE AND VOLUME CHANGE 72
3.5.5 V: EQUATION OF STATE: GIVEN PRESSURE AND TEMPERATURE CHANGE 73
3.5.6 VI: SPREADING GAS: AMONG THREE COMPARTMENTS 74 3.6 T AND P
INDEPENDENT 77
3.7 P AND V INDEPENDENT 80
3.8 ENTHALPY 81
3.8.1 ENTHALPY: STATE FUNCTION 82
3.8.2 ENTHALPY AND THE FIRST LAW 83
3.9 EXAMPLES 85
3.9.1 VII: PROVE C P - C V = - A P (F )
= M), ** 85
3.9.2 VIII: INTERNAL ENERGY FROM LATENT HEAT ENERGY OF VAPORIZATION 86
3.10 HESS' RULES FOR CHEMO-THERMAL REACTIONS 88
3.11 EXAMPLES 89
3.11.1 IX-OXIDATIONOFCOTOCO 2 89
3.11.2 X: LATENT HEAT OF VAPORIZATION OF WATER 90
3.12 ADIABATICS FOR THE IDEAL GAS 91
3.12.1 XI: WORK DONE IN ADIABATIC EXPANSION AND ISOTHERMAL COMPRESSION
OF IDEAL GAS 93
IMAGE 4
XVI CONTENTS
3.12.2 XII: NON-QUASI-STATIC FREE ADIABATIC EXPANSION OF IDEAL GAS 95
3.12.3 XIII: QUASI-STATIC ADIABATIC COMPRESSION OF IDEAL GAS 96
3.12.4 XIV: ISOBARIC, ISOTHERMAL, OR ADIABATIC EXPANSION OF DIATOMIC
IDEAL GAS 96
3.12.5 XV: CONDUCTING AND NON-CONDUCTING CYLINDERS IN CONTACT 98
3.13 IDEAL GAS POLYTROPICS 99
3.14 EXAMPLES XVI-XXI : SOME INTER-RELATIONSHIPS 101
3.14.1 XVI: ALTERNATE PROOF OF C* (F) H = - (F-J), 1 01
3.14.2 XVII: SHOW THAT C ( J |) = ( J |) 1 01
3.14.3 XVIII: SHOW THAT C, (&)", = ( F^ 102
3.14.4 XIX: SHOW THAT C P = {^) P + PVA P 102
3.14.5 XX: SHOW THAT (§) V = C V + V ( ^) 102
3.14.6 XXI: SHOW THAT ( ) = ( & ), ( & ), **** 103
3.15 CONSTRUCTION OF EQUATION OF STATE FROM THE BULK AND ELASTIC MODULI:
EXAMPLES XXII-XXXI 103
3.15.1 XXII: XT AND A P AND EQUATION OF STATE 104
3.15.2 XXIII: ALTERNATE SOLUTION FOR EXAMPLE XXII 106 3.15.3 XXIV 108
3.15.4 XXV 109
3.15.5 XXVI: ALTERNATE SOLUTION OF XXV I LL
3.15.6 XXVII 112
3.15.7 XXVIII 114
3.15.8 XXIX: ALTERNATE SOLUTION OF XXVIII 116
3.15.9 XXX 117
3.15.10 XXXI: EQUATION OF STATE FOR CONSTANT X ANDA 119
3.16 NEWTON'S LAW OF COOLING 120
3.16.1 XXXII: RELATED TO NEWTON'S LAW OF COOLING 121 3.17 INTERNAL
ENERGY IN NON-INTERACTING MONATOMIC GASESIS= \P V 122
3.17.1 XXXIII: THE VOLUME DEPENDENCE OF SINGLE PARTICLE ENERGY LEVELS
122
4 THESECONDLAW 125
4.1 HEAT ENGINES: INTRODUCTORY REMARKS 126
4.1.1 NON-EXISTENCE OF PERPETUAL MACHINES OF THE SECOND KIND 126
4.2 A PERFECT CARNOT ENGINE 128
4.2.1 IDEAL GAS CARNOT ENGINE 128
IMAGE 5
CONTENTS
4.3 KELVIN'S DESCRIPTION OF THE ABSOLUTE TEMPERATURE SCALE 131 4.3.1
EFFICIENCY OF A PERFECT CARNOT ENGINE 132
4.3.2 IDEAL GAS CARNOT ENGINE: REVISITED 133
4.4 CARNOT VERSION OF THE SECOND LAW 135
4.4.1 EXERCISE I: WORK ALONG THE TWO ADIABATIC LEGS 135 4.5 ENTROPY 136
4.5.1 INFINITESIMAL CARNOT CYCLES 136
4.5.2 EVEN IF THE ENTROPY CHANGE OCCURS VIA IRREVERSIBLE PROCESSES, ONE
CAN USE REVERSIBLE PATHS FOR ITS COMPUTATION 138
4.5.3 PERFECT CARNOT ENGINE WITH ARBITRARY WORKING SUBSTANCE 139
4.6 STATEMENTS OF THE SECOND LAW 141
4.6.1 THE CARNOT STATEMENT 141
4.6.2 THE CLAUSIUS STATEMENT 142
4.6.3 SECOND LAW: CARNOT VERSION LEADS TO THE CLAUSIUS VERSION 142
4.7 ENTROPY INCREASE IN SPONTANEOUS PROCESSES 142
4.8 KELVIN-PLANCK: THE SECOND LAW 145
4.8.1 KELVIN-PLANCK: ENTROPY ALWAYS INCREASES IN IRREVERSIBLE-ADIABATIC
PROCESSES 146
4.9 NON-CARNOT HEAT CYCLE CLAUSIUS INEQUALITY: THE INTEGRAL FORM 148
4.9.1 CLAUSIUS INEQUALITY: THE DIFFERENTIAL FORM 150 4.9.2 HEAT TRANSFER
ALWAYS INCREASES TOTAL ENTROPY 151 4.9.3 FIRST-SECOND LAW: THE CLAUSIUS
VERSION 152
4.10 ENTROPY CHANGE AND THERMAL CONTACT: EXAMPLES I-III 153 4.10.1 I: AN
OBJECT AND A RESERVOIR 153
4.10.2 II: TWO FINITE MASSES: ENTROPY CHANGE 155
4.10.3 III: RESERVOIR AND MASS WITH TEMPERATURE- DEPENDENT SPECIFIC HEAT
157
4.11 CARNOT CYCLES: ENTROPY AND WORK. EXAMPLES IV-XVI 159 4.11.1 IV:
CHANGES ALONG CARNOT PATHS 159
4.11.2 V: AN OBJECT AND A RESERVOIR 161
4.11.3 VI: ALTERNATE SOLUTION FOR V 163
4.11.4 VII: MAXIMUM WORK DONE AND CHANGE IN ENTROPY 167
4.11.5 VIII: BETWEEN TWO FINITE MASSES 168
4.11.6 IX: ALTERNATE SOLUTION FOR VIII 169
4.11.7 X: BETWEEN THREE FINITE MASSES 171
4.11.8 XI: ALTERNATE SOLUTION FOR X 172
4.11.9 EXERCISE II: RE-DO XI FOR N OBJECTS 174
4.11.10 XII: CARNOT ENGINE AND THREE RESERVOIRS 174 4.11.11 XIII:
ALTERNATE SOLUTION FOR XII 176
4.11.12 XIV: TWO MASSES AND RESERVOIR 178
IMAGE 6
CONTENTS
4.11.13 XV: ALTERNATE SOLUTION FOR XIV 179
4.11.14 XVI: CARNOT ENGINE OPERATING BETWEEN TWO FINITE SOURCES WITH
TEMPERATURE DEPENDENT SPECIFIC HEAT 183
4.12 CARNOT REFRIGERATORS AND AIR-CONDITIONERS 185
4.12.1 XVII: WORK NEEDED FOR COOLING AN OBJECT WITH CONSTANT SPECIFIC
HEAT 187
4.12.2 XVIII: COOLING WITH TEMPERATURE DEPENDENT SPECIFIC HEAT: ENTROPY
CHANGE AND WORK INPUT 188
4.13 CARNOT HEAT ENERGY PUMP 190
4.13.1 EXERCISE III 192
4.13.2 XIX: ENTROPY INCREASE ON REMOVING TEMPERATURE GRADIENT 192
4.13.3 XX: MAXIMUM WORK AVAILABLE IN XIX 195
4.13.4 EXERCISELV 197
4.14 IDEAL GAS STIRLING CYCLE 197
4.15 IDEALIZED VERSION OF SOME REALISTIC ENGINES 199
4.16 THE DIESEL CYCLE 199
4.16.1 XXI: DIESEL ENGINE 201
4.17 IDEAL GAS OTTO CYCLE 202
4.18 IDEAL GAS JOULE CYCLE 206
4.18.1 XXII: JOULE ENGINE 208
4.19 NEGATIVE TEMPERATURE: CURSORY REMARK 209
FIRST AND SECOND LAWS COMBINED 211
5.1 FIRST AND SECOND LAWS 212
5.1.1 THE CLAUSIUS VERSION: DIFFERENTIAL FORM 212
5.2 T ANDT INDEPENDENT 213
5.2.1 PROOF OF RELATIONSHIP: (FI), = ' ( T 1 ) ~P 2 14 5.3 FIRST T.DS
EQUATION ." 215
5.3.1 DEPENDENCE OF C V ON V 217
5.3.2 ALTERNATE PROOF: (F*), = T (&} -P 218
5.4 MIXING OF IDEAL GAS: EXAMPLES I-IV .". 219
5.4.1 I: ISOTHERMAL, DIFFERENT PRESSURES, SAME NUMBER OF ATOMS 219
5.4.2 II: ISOTHERMAL, DIFFERENT PRESSURES, DIFFERENT NUMBER OF ATOMS 222
5.4.3 III: DIFFERENT PRESSURE, DIFFERENT TEMPERATURE, AND DIFFERENT
NUMBER OF ATOMS 225
5.4.4 .V: ) (
5.5 / AND P INDEPENDENT 230
5.5.1 PROVE EQUATION: ( | ) ( -V = - I ( F ) P 230
IMAGE 7
CONTENTS
5.6 SECOND TAS EQUATION 231
5.6.1 DEPENDENCE OF C P ON P 232
5.6.2 ALTERNATE PROOF: ( F |) - V = -T (Q) P 233
5.7 FIRST AND SECOND TAS TOGETHER 234
5.8 P AND V INDEPENDENT 235
5.9 THIRD TAS EQUATION 236
5.9.1 ISENTROPIC PROCESSES 236
5.10 VELOCITY OF SOUND: NEWTON'S TREATMENT 237
5.11 EXAMPLES 238
5.11.1 V: GAS IN CONTACT WITH RESERVOIR: CHANGE IN U AND S 238
5.12 EXAMPLES VI-XV 239
5.12.1 VI: AW, AC/, AS FOR/ = (A/2B)T 2 + (1/BV) 239 5.12.2 VII: AW,
AC/, AS FOR PV = RT(L + B 2 /V + B 3 /V 2 + --- + B N /V" +L ) 240
5.12.3 VIII: SHOW (F^ = 1 - (^-) 241
5.12.4 IX: SHOW C P (%) H = T - A P T 2 242
5.12.5 X:SHOW(^) = (!) S -(F^ 243
5.12.6 XI: ISOTHERMALLY STRETCHED IDEAL RUBBER 244 5.12.7 XII: ENERGY
AND ENTROPY CHANGE IN VAN DER WAAL'S GAS 246
5.12.8 XIII: EQUATION OF STATE OF A METAL ROD 247
5.12.9 XIV: ENTROPY CHANGE IN EXTENDABLE CORD 248 5.12.10 XV: A "TRICK"
QUESTION ABOUT THE CARNOT ENGINE . 250 5.13 EXERCISES: I-VI 251
5.13.1 EXERCISEL 251
5.13.2 EXERCISELL 252
5.13.3 EXERCISE III: EXERCISE II BY JACOBIANS 252
5.13.4 EXERCISELV 252
5.13.5 EXERCISE V 253
5.13.6 EXERCISE: VI 253
VAN DER WAALS THEORY OF IMPERFECT GASES 255
6.1 FINITE SIZED MOLECULES WITH INTERACTION 256
6.2 VOLUME REDUCTION DUE TO MOLECULAR HARD CORE 256
6.3 PRESSURE CHANGE DUE TO LONG RANGE ATTRACTION 257
6.3.1 EQUATION OF STATE FOR A MIXTURE 260
6.3.2 EQUATION OF STATE IN REDUCED FORM 260
6.4 THE VIRIAL EXPANSION 261
6.5 THE CRITICAL POINT 262
6.6 CRITICAL CONSTANTS P C , V C ,T C 264
6.7 THE REDUCED EQUATION OF STATE 264
IMAGE 8
CONTENTS
6.8 THE CRITICAL REGION 266
6.8.1 EXAMPLE I: PRESSURE VERSUS VOLUME FOR THE CRITICAL ISOTHERM 267
6.8.2 II: ISOTHERMAL COMPRESSIBILITY ALONG THE CRITICAL ISOCHORE JUST
ABOVE T C 268
6.9 BEHAVIOR BELOW T C 269
6.10 THE MAXWELL CONSTRUCTION 269
6.10.1 (PO,V O ) ISOTHERMS 269
6.10.2 THERMODYNAMIC JUSTIFICATION FOR THE MAXWELL PRESCRIPTION: FIRST
ANALYSIS 270
6.10.3 EXERCISE I: SHOW THAT FIG. 6.2B FOLLOWS THE MAXWELL PRESCRIPTION
271
6.10.4 THERMODYNAMIC JUSTIFICATION: ALTERNATE ANALYSIS . 272 6.10.5
EXERCISELL 274
6.10.6 COMMENTS: METASTABLE REGIONS 274
6.10.7 (P O , V O ) ISOTHERMS FOR VAN DER WAALS GAS 274
6.10.8 THE SPINODAL CURVE: BOUNDARY OF THE METASTABLE-UNSTABLE REGIONS
AU VAN DER WAALS 275
6.11 MOLAR SPECIFIC VOLUMES AND DENSITIES 276
6.12 TEMPERATURE JUST BELOW THE CRITICAL POINT 277
6.12.1 III: DIFFERENCE IN CRITICAL DENSITIES 277
6.12.2 IV: THE SATURATION PRESSURE 279
6.12.3 V: ISOTHERMAL COMPRESSIBILITY JUST BELOW T C 280
6.13 THE LEVER RULE 281
6.14 SMOOTH TRANSITION FROM LIQUID TO GAS AND VICE VERSA 282 6.14.1
EXERCISE III: QUESTION FOR SKEPTICS 282
6.15 THE PRINCIPLE OF CORRESPONDING STATES 282
6.15.1 X O AS FUNCTION OF P O FOR VARIOUS FLUIDS 283
6.15.2 X O AS FUNCTION OF P O FOR VAN DER WAALS GAS 285
6.15.3 THE REDUCED SECOND VIRIAL COEFFICIENT 285
6.15.4 MOLAR DENSITIES OF THE CO-EXISTING PHASES AND THE PCS 287
6.16 EXAMPLES VI-XI 288
6.16.1 VI: INTERNAL ENERGY AND VOLUME DEPENDENCE OF C V 288
6.16.2 REDUCED VAPOR PRESSURE IN THE CO-EXISTENT REGIME AND THE PCS 289
6.16.3 REDUCED VAPOR PRESSURE FOR A VAN DER WAALS GAS 290
6.16.4 VII: TEMPERATURE CHANGE ON MIXING OF VAN DER WAALS GASES 290
6.16.5 VIII: SPECIFIC HEATS, ENTHALPY, 77 AND SS FOR VAN DER WAALS GAS
293
IMAGE 9
CONTENTS
6.17
6.16.6 IX: WORK DONE AND CHANGE IN INTERNAL ENERGY AND ENTROPY IN VAN
DER WAALS GAS 296 6.16.7 EXAMPLE X: ADIABATIC EQUATION OF STATE FOR VAN
DER WAALS GAS IN THE REGION
ABOVE THE CRITICAL POINT 297
6.16.8 XI: U, H, S, C P - C V , AND ADIABATIC EQUATION OF STATE 298
DIETERICI'S EQUATION OF STATE 300
6.17.1 XII: BEHAVIOR OF DIETERICI GAS 300
6.17.2 DIETERICI ISOTHERMS 302
INTERNAL ENERGY AND ENTHALPY: MEASUREMENT AND RELATED EXAMPLES 303
7.1 GAY-LUSSAC-JOULE COEFFICIENT 303
7.1.1 INTRODUCTORY REMARK 303
7.1.2 MEASUREMENT 304
7.1.3 DERIVATION 305
7.1.4 EXAMPLE I: FOR A PERFECT GAS 306
7.1.5 II: FOR A NEARLY PERFECT GAS 306
7.1.6 III: FOR A VAN DER WAALS GAS 307
7.1.7 DESCRIPTION 308
7.1.8 CONSTANT ENTHALPY 308
7.1.9 CONSTANT ENTHALPY CURVES AND GASEOUS COOLING 310 7.2 JOULE-KELVIN
EFFECT: DERIVATION 312
7.2.1 IV: JK COEFFICIENT FOR A PERFECT GAS 313
7.2.2 V: JK COEFFICIENT FOR A NEARLY PERFECT GAS 313
7.3 JK COEFFICIENT FOR A VAN DER WAALS GAS 314
7.4 JK COEFFICIENT: INVERSION POINT FOR A VAN DER WAALS GAS 315
7.4.1 JK COEFFICIENT: POSITIVE AND NEGATIVE REGIONS 315 7.5 UPPER AND
LOWER INVERSION TEMPERATURES 317
7.6 EXAMPLES VI-VIII 318
7.6.1 VI: ADIABATIC-FREE EXPANSION OF VAN DER WAALS GAS 318
7.6.2 EXAMPLE VII: FOR HYDROGEN, ESTIMATE OF INVERSION TEMPERATURE FROM
THE EQUATION OF STATE 320
7.6.3 ALTERNATE SOLUTION OF VII 320
7.6.4 VIII: ENTHALPY MINIMUM FOR A GAS WITH THREE VINAL COEFFICIENTS 321
7.7 FROM EMPIRICAL TO THERMODYNAMIC 322
7.7.1 THERMODYNAMIC TEMPERATURE SCALE VIA JGL COEFFICIENT 324
7.7.2 THERMODYNAMIC SCALE VIA J-K COEFFICIENT 326
7.7.3 TEMPERATURE OF THE ICE-POINT: AN ESTIMATE 328
IMAGE 10
CONTENTS
7.7.4 TEMPERATURE: THE IDEAL GAS THERMODYNAMIC SCALE 328
7.8 IX-XV: SOME INTERESTING RELATIONSHIPS 330
7.8.1 IX: PROVE (&)* - ( J& = ( #) 3 3
7.8.2 EXAMPLE X: PROVE
(*),-(FC).=-TE) 331
7.8.3 XI: PROVE V F(%), = C P 332
7.8.4 XII: PROVE ^ (F*) F = C* 333
7.8.5 XIII: PROVE (F )* = C*(L - SS ET P / X T) 333
7.8.6 XIV: PROVE ( D ^ I ^ - ^ ) - 1 334
7.8.7 XV: PROVE ( ) * =/ AND ( ), = -/ 335
7.9 NEGATIVE TEMPERATURE: CURSORY REMARKS 335
FUNDAMENTAL EQUATION AND THE EQUATIONS OF STATE 337
8.1 THE EULER EQUATION 338
8.1.1 CHEMICAL POTENTIAL 338
8.1.2 MULTIPLE-COMPONENT SYSTEMS 341
8.1.3 SINGLE-COMPONENT SYSTEMS 341
8.2 EQUATIONS OF STATE 342
8.2.1 CALLEN'S REMARKS 342
8.2.2 THE ENERGY REPRESENTATION 343
8.2.3 THE ENTROPY REPRESENTATION 343
8.2.4 KNOWN EQUATIONS OF STATE: TWO EQUATIONS FOR IDEAL GAS 344
8.2.5 WHERE IS THE THIRD EQUATION OF STATE? 344
8.3 GIBBS-DUHEM RELATION: ENERGY REPRESENTATION 345
8.4 GIBBS-DUHEM RELATION: ENTROPY REPRESENTATION 345
8.5 FUNDAMENTAL EQUATION FOR IDEAL GAS 346
8.6 THREE EQUATIONS OF STATE IN ENTROPY REPRESENTATION: IDEAL GAS 348
8.7 IDEAL GAS: ENERGY REPRESENTATION 349
8.7.1 FUNDAMENTAL EQUATION 349
8.8 THREE EQUATIONS OF STATE IN ENERGY REPRESENTATION: IDEAL GAS. 349
8.8.1 EXERCISEL 350
8.8.2 EXAMPLE I 350
8.8.3 EXAMPLE II 351
8.9 REMARK 352
ZEROTH LAW REVISITED; MOTIVE FORCES; THERMODYNAMIC STABILITY 353 9.1
ZEROTH LAW REVISITED 354
9.1.1 SUB-SYSTEMS IN MUTUAL EQUILIBRIUM 354
9.2 DIRECTION OF THERMODYNAMIC MOTIVE FORCES 357
9.2.1 THE ENTROPY EXTREMUM 357
9.2.2 HEAT ENERGY FLOW 357
IMAGE 11
CONTENTS XXIII
9.2.3 MOLECULAR FLOW 359
9.2.4 ISOTHERMAL COMPRESSION 360
9.2.5 THE ENERGY EXTREMUM: MINIMUM ENERGY 361
9.2.6 RECONFIRMATION OF THE ZEROTH LAW 363
9.2.7 MOTIVE FORCES: THE ENERGY FORMALISM 364
9.2.8 ISOBARIC ENTROPY FLOW 364
9.2.9 ISOTHERMAL-ISOBARIC MOLECULAR FLOW 365
9.2.10 ISOTHERMAL COMPRESSION 365
9.3 THERMODYNAMIC STABILITY 366
9.3.1 LE CHATELIER'S PRINCIPLE 366
9.4 STABLE THERMODYNAMIC EQUILIBRIUM 367
9.4.1 INTRINSIC STABILITY: C V AND XT 0 367
9.4.2 ANALYSIS: SECOND REQUIREMENT 370
9.4.3 INTRINSIC STABILITY: CHEMICAL POTENTIAL 371
9.4.4 INTRINSIC STABILITY: C P AND XS 0 371
9.4.5 EXERCISE 372
9.4.6 SUMMARY 372
10 ENERGY AND ENTROPY EXTREMA; LEGENDRE TRANSFORMATIONS; THERMODYNAMIC
POTENTIALS; CLAUSIUS-CLAPEYRON EQUATION; GIBBS PHASE RULE 373
1 0. 1 SYSTEMS CONSTITUTED OF SINGLE VARIETY OF MOLECULES 374 10.1.1
MINIMUM INTERNAL ENERGY IN ADIABATICALLY ISOLATED SYSTEMS 374
10.1.2 EQUALITY OF SPECIFIC INTERNAL ENERGY OF DIFFERENT PHASES 374
10.2 MAXIMUM ENTROPY IN ADIABATICALLY ISOLATED SYSTEMS 375 10.2.1
COMMENT 375
10.2.2 RELATIVE SIZE OF PHASES AND ENTROPY MAXIMUM 376 10.2.3 EQUALITY
OF SPECIFIC ENTROPY 376
10.2.4 REMARK 377
10.3 LEGENDRE TRANSFORMATIONS 377
10.3.1 SIMPLE SYSTEM 378
10.4 HELMHOLTZ FREE ENERGY 379
10.4.1 SYSTEM AS FUNCTION OF VOLUME AND TEMPERATURE 379
10.4.2 MAXIMUM AVAILABLE WORK 380
10.4.3 ISOTHERMAL CHANGE OF STATE 381
10.4.4 DECREASE OF HELMHOLTZ FREE ENERGY FOR CONSTANT EXTENSIVE
VARIABLES 381
10.4.5 EXTREMUM PRINCIPLE FOR HELMHOLTZ FREE ENERGY 382 10.4.6 RELATIVE
SIZE OF PHASES AND HELMHOLTZ POTENTIAL MINIMUM 383
10.4.7 SPECIFIC HELMHOLTZ FREE ENERGY IS EQUAL FOR DIFFERENT PHASES 383
IMAGE 12
XXIV CONTENTS
10.5 GIBB'S FREE ENERGY 384
10.5.1 MAXIMUM AVAILABLE WORK: ISOTHERMAL- ISOBARIC CHANGE OF STATE 385
10.5.2 DECREASE IN GIBBS FREE ENERGY AT CONSTANT MOLE-NUMBERS AND
CONSTANT X 386 10.5.3 EXTREMUM PRINCIPLE FOR GIBBS FREE ENERGY 387
10.5.4 RELATIVE SIZE OF PHASES AND GIBBS
POTENTIAL MINIMUM 387
10.5.5 EQUALITY OF SPECIFIC GIBBS FREE ENERGY OF DIFFERENT PHASES 388
10.6 THE ENTHALPY: REMARKS 389
10.6.1 HEAT OF TRANSFORMATION 390
10.7 THERMODYNAMIC POTENTIALS: S, F, G AND H 391
10.7.1 CHARACTERISTIC EQUATIONS 392
10.7.2 HELMHOLTZ POTENTIAL HELPS DETERMINE INTERNAL ENERGY 392
10.7.3 GIBBS POTENTIAL HELPS DETERMINE ENTHALPY 393 10.8 THE MAXWELL
RELATIONS 393
10.8.1 EXERCISES 395
10.9 META-STABLE EQUILIBRIUM 395
10.10 THE CLAUSIUS-CLAPEYRON DIFFERENTIAL EQUATION 396
10.10.1 SOLVING CLAUSIUS-CLAPEYRON DIFFERENTIAL EQUATION. 399 10.10.2
TRIPLE AND THE ICE-POINTS OF WATER: WHY THE SEPARATION? 400
10.11 GIBBS PHASE RULE 402
10.11.1 MULTI-PHASE MULTI-CONSTITUENT SYSTEMS 402 10.11.2 PHASE
EQUILIBRIUM RELATIONSHIPS 403
10.11.3 THE PHASE RULE 405
10.11.4 THE VARIANCE 405
10.11.5 PHASE RULE FOR SYSTEMS WITH CHEMICAL REACTIONS. 406
11 STATISTICAL THERMODYNAMICS: THIRD LAW 409
11.1 PARTITION FUNCTION: CLASSICAL SYSTEMS IN A-DIMENSIONS 410
11.1.1 THE CANONICAL ENSEMBLE 410
11.2 NON-INTERACTING CLASSICAL SYSTEMS: MONATOMIC PERFECT GAS IN
THREE-DIMENSIONS 413
11.2.1 THE PARTITION FUNCTION 413
11.2.2 MONATOMIC PERFECT GAS: THERMODYNAMIC POTENTIALS 415
11.3 MONATOMIC PERFECT GASES: CHANGES DUE TO MIXING 416 11.3.1 EXAMPLE
I: ISOTHERMAL MIXING OF IDEAL GAS: DIFFERENT PRESSURES BUT SAME GAS AND
SAME NUMBER OF ATOMS 416
11.3.2 EXERCISEL 417
IMAGE 13
CONTENTS
11.4
11.5
11.3.3 II: ISOTHERMAL MIXING OF MONATOMIC IDEAL GAS: DIFFERENT PRESSURES
AND DIFFERENT NUMBER OF ATOMS 417
11.3.4 EXERCISELL 419
11.3.5 III: MIXING OF IDEAL GAS WITH DIFFERENT TEMPERATURE, PRESSURE,
AND NUMBER OF ATOMS 419 11.3.6 EXERCISE HI 420
DIFFERENT MONATOMIC IDEAL GASES MIXED 421
11.4.1 THERMODYNAMIC POTENTIALS 422
11.4.2 GIBBSPARADOX 422
11.4.3 EXERCISELV 423
PERFECT GAS OF CLASSICAL DIATOMS 423
11.5.1 FREE INTERATOMIC BOND 423
11.5.2 NON-INTERACTING ATOMS IN FREE DIATOMS 424
11.5.3 THERMODYNAMICS OF N FREE-DIATOMS 424
11.5.4 EXPERIMENTAL OBSERVATION 425
11.5.5 MOTION OF AND ABOUT CENTER OF MASS 426
11.5.6 TRANSLATIONAL MOTION OF CENTER OF MASS 428
11.5.7 MOTION ABOUT CENTER OF MASS 429
11.5.8 SINGLE CLASSICAL DIATOM WITH STIFF BOND: ROTATIONAL KINETIC
ENERGY 432
11.5.9 STATISTICAL THERMODYNAMICS OF NJ CLASSICAL DIATOMS WITH STIFF
BONDS 434
11.5.10 FREE BONDS 434
11.5.11 REMARK 434
11.5.12 CHARACTERISTIC TEMPERATURES FOR ROTATION AND VIBRATION OF
DIATOMS 436
11.5.13 CLASSICAL DIATOMS: HIGH TEMPERATURE 436
11.5.14 END OF STIFFNESS: BOND LENGTH VIBRATION 437 11.6 ANHARMONIC
SIMPLE OSCILLATORS 439
11.6.1 EXERCISEV 441
11.7 CLASSICAL DIPOLE PAIRS: AVERAGE ENERGY AND AVERAGE FORCE 441 11.7.1
DISTRIBUTION FACTOR AND THERMAL AVERAGE 442 11.7.2 AVERAGE FORCE BETWEEN
A PAIR 444
11.8 LANGEVIN PARAMAGNETISM: CLASSICAL PICTURE 445
11.8.1 STATISTICAL AVERAGE 445
11.8.2 HIGH TEMPERATURE 446
11.8.3 LOW TEMPERATURE 447
11.9 EXTREMELY RELATIVISTIC MONATOMIC IDEAL GAS 448
11.10 GAS WITH INTERACTION 450
.10.1 THE HAMILTONIAN 450
.10.2 PARTITION FUNCTION : MAYER'S CLUSTER EXPANSION 450 .10.3 HARD CORE
INTERACTION 453
.10.4 EXERCISE VI 454
.10.5 LENNARD-JONES POTENTIAL 454
.10.6 THE REPULSIVE POTENTIAL 455
IMAGE 14
CONTENTS
11.11 QUASI-CLASSICAL QUANTUM SYSTEMS 456
11.11.1 QUANTUM MECHANICS: CURSORY REMARKS 456
11.11.2 CANONICAL PARTITION FUNCTION 457
11.11.3 QUANTUM PARTICLE 458
11.11.4 CLASSICAL-CO-QUANTUM GAS 461
11.11.5 NON-INTERACTING PARTICLES: "CLASSICAL-CO- QUANTUM" VS. QUANTUM
STATISTICS 461
11.12 QUASI-CLASSICAL STATISTICAL THERMODYNAMICS OF RIGID QUANTUM
DIATOMS 462
11.13 HETERO-NUCLEAR DIATOMS: ROTATIONAL MOTION 463
11.13.1 QUANTUM PARTITION FUNCTION 464
11.13.2 ANALYTICAL TREATMENT 464
11.13.3 LOW AND HIGH TEMPERATURE: THERMODYNAMIC POTENTIALS 466
11.14 HOMO-NUCLEAR DIATOMS: ROTATIONAL MOTION 467
11.14.1 VERY HIGH TEMPERATURE 468
11.14.2 VERY LOW TEMPERATURE 469
11.14.3 INTERMEDIATE TEMPERATURE 469
11.15 DIATOMS WITH VIBRATIONAL MOTION 469
11.15.1 QUASI-CLASSICAL QUANTUM STATISTICAL TREATMENT 470 11.15.2 HIGH
TEMPERATURE 471
11.15.3 LOW TEMPERATURE 473
11.15.4 LANGEVIN PARAMAGNET: QUASI-CLASSICAL QUANTUM STATISTICAL PICTURE
474
11.15.5 PARTITION FUNCTION AND HELMHOLTZ POTENTIAL 475 11.15.6 ENTROPY
476
11.15.7 THE INTERNAL ENERGY 477
11.15.8 LOW TEMPERATURE 480
11.15.9 SPECIFIC HEAT 481
11.15.10 PRODUCTION OF VERY LOW TEMPERATURES: ADIABATIC DEMAGNETIZATION
OF PARAMAGNETS 483
11.16 NERNST'S HEAT THEOREM: THIRD LAW 485
11.16.1 THIRD LAW: UNATTAINABILITY OF ZERO TEMPERATURE 486 11.17
NEGATIVE TEMPERATURES 489
11.18 GRAND CANONICAL ENSEMBLE 494
11.18.1 CLASSICAL SYSTEMS 494
11.19 STATISTICS OF QUANTUM STATES 499
11.20 NON-INTERACTING FERMI-DIRAC SYSTEM 500
11.20.1 PARTITION FUNCTION FOR A SINGLE STATE 500
11.20.2 PARTITION FUNCTION: FOR FERMI-DIRAC SYSTEM 500 11.21
NON-INTERACTING BOSE-EINSTEIN SYSTEM 501
11.21.1 PARTITION FUNCTION FOR A SINGLE STATE 501
11.21.2 FOR PERFECT B-E SYSTEM THE CHEMICAL POTENTIAL IS ALWAYS NEGATIVE
501
IMAGE 15
CONTENTS
11.25
.22.2 .22.3 .22.4
.22.5 .22.6 .22.7 11.22.8 11.22.9 11.22.10
11.22.11
11.22.12
11.21.3 PARTITION FUNCTION: FOR BOSE-EINSTEIN SYSTEM 502 11.21.4
FERMI-DIRAC AND BOSE-EINSTEIN SYSTEMS 503 11.21.5 PRESSURE, INTERNAL
ENERGY, AND CHEMICAL POTENTIAL . 504 11.22 PERFECT F-D SYSTEM 505
11.22.1 LOW DENSITY AND HIGH TEMPERATURE: WEAKLY DEGENERATE F-D SYSTEM
507
REMARK 511
EXERCISE VII 511
HIGHLY OR PARTIALLY DEGENERATE F-D GAS 512 ZERO TEMPERATURE : COMPLETE
DEGENERACY 516 FINITE BUT LOW TEMPERATURE: PARTIAL DEGENERACY 520
THERMODYNAMIC POTENTIALS 521
PAULI PARAMAGNETISM 523
HAND-WAVING ARGUMENT: THE SPECIFIC HEAT 531 HAND-WAVING ARGUMENT: THE
PAULI PARAMAGNETISM AT ZERO TEMPERATURE 532
HAND-WAVING ARGUMENT: THE PAULI PARAMAGNETISM AT FINITE TEMPERATURE 533
LANDAU DIAMAGNETISM 534
11.23 THE RICHARDSON EFFECT: THERMIONIC EMISSION 536
11.23.1 QUASI-CLASSICAL STATISTICS: RICHARDSON EFFECT 538 11.24
BOSE-EINSTEIN GAS 539
11.24.1 THE GRAND POTENTIAL 539
11.24.2 PERFECT B-E GAS IN THREE DIMENSIONS 540
11.24.3 OCCURRENCE OF BOSE-EINSTEIN CONDENSATION: TEMPERATURE T T C
542
11.24.4 PRESSURE AND THE INTERNAL ENERGY 542
11.24.5 DEGENERATE IDEAL B-E GAS 544
1.24.6 SPECIFIC HEAT IN THE DEGENERATE REGIME 545 1.24.7 STATE FUNCTIONS
IN THE DEGENERATE REGIME 546 NON-DEGENERATE B-E GAS 546
1.25.1 EQUATION OF STATE 546
1.25.2 NON-DEGENERATE B-E GAS: SPECIFIC HEAT 548 1.25.3 BOSE-EINSTEIN
CONDENSATION IN A-DIMENSIONS 549
11.26 BLACK BODY RADIATION 552
11.26.1 THERMODYNAMIC CONSIDERATION 552
11.26.2 QUANTUM STATISTICAL TREATMENT 555
11.26.3 CALCULATION OF ENERGY AND PRESSURE 555
11.27 PHONONS 558
11.27.1 PHONONS IN A CONTINUUM 558
11.27.2 EXERCISE VIII 560
11.27.3 PHONONS IN LATTICES 560
11.27.4 THE EINSTEIN APPROXIMATION 564
11.27.5 THE DEBYE APPROXIMATION 564
IMAGE 16
XXVIII CONTENTS
11.28 DEBYE TEMPERATURE 0 D 568
11.28.1 THERMODYNAMIC POTENTIALS 568
A THERMODYNAMICS, LARGE NUMBERS AND THE MOST PROBABLE STATE 571 A.I
MODEL 571
A.2 BINOMIAL EXPANSION 572
A.2.1 TWO SITES: A TRIVIAL EXAMPLE 573
A.3 LARGE NUMBER OF CALLS 574
A.3.1 EXERCISE: 1 575
A.3.2 LARGE NUMBER OF CALLS: CONTINUED 576
A.3.3 REMARK: A GAUSSIAN DISTRIBUTION 576
A.3.4 GAUSSIAN APPROXIMATION FOR REGION AROUND HALF-CONCENTRATION 576
A.3.5 EXERCISE: II 577
A.3.6 GAUSSIAN APPROXIMATION: CONTINUED 577
A.3.7 PLOT OF THE GAUSSIAN DISTRIBUTION 578
A.4 MOMENTS OF THE DISTRIBUTION FUNCTION: REMARKS 579
A.5 MOMENTS OF THE GAUSSIAN DISTRIBUTION FUNCTION 580
A.5.1 UN-NORMALIZED MOMENTS 580
A.5.2 NORMALIZED MOMENTS OF THE GAUSSIAN DISTRIBUTION FUNCTION 581
A.5.3 NORMALIZED MOMENTS OF THE EXACT DISTRIBUTION FUNCTION FOR GENERAL
OCCUPANCY 582 A.5.4 EXACT, SECOND NORMALIZED MOMENT 583
A.5.5 EXACT, THIRD - SIXTH NORMALIZED MOMENTS 584 A.5.6 EXERCISE: III
585
A.5.7 THE FOURTH MOMENT 585
A.5.8 CALCULATION OF THE FIFTH AND THE SIXTH NORMALIZED MOMENTS 586
A.5.9 CONCLUDING REMARK 588
A.5.10 SUMMARY 589
B PERFECT GAS REVISITED 59 1
B. 1 MONATOMIC PERFECT GAS 591
B.I.I PRESSURE 591
B.I.2 CLASSICAL STATISTICS: BOLTZMANN-MAXWELL- GIBBS DISTRIBUTION 595
B.1.3 ENERGY IN A MONATOMIC PERFECT GAS 597
C SECOND LAW: CARNOT VERSION LEADS TO CLAUSIUS VERSION 601 C.I A CARNOT
AND AN ORDINARY ENGINE IN TANDEM 601
D POSITIVITY OF THE ENTROPY INCREASE: (4.73) 605
D.I ANALYSIS 605
E MIXTURE OF VAN DER WAALS GASES 609
E.I ANALYSIS 609
IMAGE 17
CONTENTS XXIX
F POSITIVE-DEFINITE HOMOGENEOUS QUADRATIC FORM 615
F.I ANALYSIS 615
F.2 POSITIVE DEFINITENESS OF 3 X 3 QUADRATIC FORM 616
F.2.1 A HELPFUL SURPRISE 617
G THERMODYNAMIC STABILITY: THREE VARIABLES 619
G. 1 ENERGY MINIMUM PROCEDURE: INTRINSIC STABILITY 620
G.I.I THIRD REQUIREMENT FOR INTRINSIC STABILITY 622
G.2 EXAMPLES 623
G.2.1 EXAMPLE I 623
G.2.2 EXAMPLE II 625
H MASSIEU TRANSFORMS: THE ENTROPY REPRESENTATION 627
H. 1 MASSIEU POTENTIAL: M{V, U) 627
H.I.I MASSIEU POTENTIAL: M {V, }} 628
H.1.2 REMARK 629
H.1.3 MASSIEU POTENTIAL: M{F,} 629
H.1.4 MASSIEU POTENTIAL: M{F,}} 629
I INTEGRAL (11.83) 631
1.0.5 AVERAGE FORCE BETWEEN A PAIR 636
J INDISTINGUISHABLE, NON-INTERACTING QUANTUM PARTICLES 637 J. 1 QUANTUM
STATISTICS: GRAND CANONICAL PARTITION FUNCTION 638
K LANDAU DIAMAGNETISM 641
K.I ANALYSIS 641
K. 1.1 MULTIPLICITY FACTOR 642
L SPECIFIC HEAT FOR THE BE GAS 647
L. 1 ANALYSIS 647
INDEX 649 |
| any_adam_object | 1 |
| author | Tahir-Kheli, Raza A. |
| author_GND | (DE-588)1017190615 |
| author_facet | Tahir-Kheli, Raza A. |
| author_role | aut |
| author_sort | Tahir-Kheli, Raza A. |
| author_variant | r a t k rat ratk |
| building | Verbundindex |
| bvnumber | BV039544006 |
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| ctrlnum | (OCoLC)725239219 (DE-599)DNB1011458160 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV039544006 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:07:46Z |
| institution | BVB |
| isbn | 9783642214806 3642214800 9783642214813 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024396031 |
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| owner_facet | DE-706 DE-83 DE-703 DE-634 DE-19 DE-BY-UBM DE-20 |
| physical | XXIX, 677 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series2 | Graduate texts in physics |
| spelling | Tahir-Kheli, Raza A. Verfasser (DE-588)1017190615 aut General and statistical thermodynamics Raza Tahir-Kheli Berlin [u.a.] Springer 2012 XXIX, 677 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3725893&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024396031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tahir-Kheli, Raza A. General and statistical thermodynamics Statistische Thermodynamik (DE-588)4126251-7 gnd |
| subject_GND | (DE-588)4126251-7 |
| title | General and statistical thermodynamics |
| title_auth | General and statistical thermodynamics |
| title_exact_search | General and statistical thermodynamics |
| title_full | General and statistical thermodynamics Raza Tahir-Kheli |
| title_fullStr | General and statistical thermodynamics Raza Tahir-Kheli |
| title_full_unstemmed | General and statistical thermodynamics Raza Tahir-Kheli |
| title_short | General and statistical thermodynamics |
| title_sort | general and statistical thermodynamics |
| topic | Statistische Thermodynamik (DE-588)4126251-7 gnd |
| topic_facet | Statistische Thermodynamik |
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