Preface ........................................................ xv
Reference tables ............................................. xvii
Table A Counting and combinatorics formulae .................. xvii
Table В Useful integrals, expansions, and approximations ..... xvii
Table С Extensive thermodynamic potentials .................. xviii
Table D Intensive per-particle thermodynamic potentials for
single-component systems ............................ xviii
Table E Thermodynamic calculus manipulations .................. xix
Table F Measurable quantities .................................. xx
Table G Common single-component statistical-mechanical
ensembles ............................................. xxi
Table H Fundamental physical constants ....................... xxii
1 Introduction and guide for this text ......................... 1
2 Equilibrium and entropy ...................................... 6
2.1 What is equilibrium? .................................... 6
2.2 Classical thermodynamics ................................ 7
2.3 Statistical mechanics .................................. 11
2.4 Comparison of classical thermodynamics and
statistical mechanics .................................. 14
2.5 Combinatorial approaches to counting ................... 15
Problems .................................................... 18
3 Energy and how the microscopic world works .................. 21
3.1 Quantum theory ......................................... 21
3.2 The classical picture .................................. 25
3.3 Classical microstates illustrated with the ideal gas ... 29
3.4 Ranges of microscopic interactions and scaling with
system size ............................................ 32
3.5 From microscopic to macroscopic ........................ 34
3.6 Simple and lattice molecular models .................... 37
3.7 A simple and widely relevant example: the two-state
system ................................................. 38
Problems .................................................... 41
4 Entropy and how the macroscopic world works ................. 50
4.1 Microstate probabilities ............................... 50
4.2 The principle of equal a priori probabilities .......... 51
4.3 Ensemble averages and time averages in isolated
systems ................................................ 54
4.4 Thermal equilibrium upon energy exchange ............... 58
4.5 General forms for equilibrium and the principle of
maximum entropy ........................................ 65
4.6 The second law and internal constraints ................ 69
4.7 Equivalence with the energy-minimum principle .......... 70
4.8 Ensemble averages and Liouville's theorem in
classical systems ...................................... 72
Problems .................................................... 75
5 The fundamental equation .................................... 82
5.1 Equilibrium and derivatives of the entropy ............. 82
5.2 Differential and integrated versions of the
fundamental equations .................................. 83
5.3 Intensive forms and state functions .................... 85
Problems .................................................... 91
6 The first law and reversibility ............................. 93
6.1 The first law for processes in closed systems .......... 93
6.2 The physical interpretation of work .................... 95
6.3 A classic example involving work and heat .............. 97
6.4 Special processes and relationships to the
fundamental equation ................................... 98
6.5 Baths as idealized environments ....................... 101
6.6 Types of processes and implications from the second
law ................................................... 101
6.7 Heat engines .......................................... 105
6.8 Thermodynamics of open, steady-flow systems ........... 107
Problems ................................................... 114
7 Legendre transforms and other potentials ................... 123
7.1 New thermodynamic potentials from baths ............... 123
7.2 Constant-temperature coupling to an energy bath ....... 123
7.3 Complete thermodynamic information and natural
variables ............................................. 126
7.4 Legendre transforms: mathematical convention .......... 128
7.5 Legendre transforms: thermodynamic convention ......... 130
7.6 The Gibbs free energy ................................. 132
7.7 Physical rationale for Legendre transforms ............ 133
7.8 Extremum principles with internal constraints ......... 134
7.9 The enthalpy and other potentials ..................... 136
7.10 Integrated and derivative relations ................... 137
7.11 Multicomponent and intensive versions ................. 141
7.12 Summary and look ahead ................................ 142
Problems ................................................... 143
8 Maxwell relations and measurable properties ................ 149
8.1 Maxwell relations ..................................... 149
8.2 Measurable quantities ................................. 151
8.3 General considerations for calculus manipulations ..... 154
Problems ................................................... 156
9 Gases ...................................................... 161
9.1 Microstates in monatomic ideal gases .................. 161
9.2 Thermodynamic properties of ideal gases ............... 165
9.3 Ideal gas mixtures .................................... 167
9.4 Nonideal or "imperfect" gases ......................... 170
9.5 Nonideal gas mixtures ................................. 171
Problems ................................................... 172
10 Phase equilibrium .......................................... 176
10.1 Conditions for phase equilibrium ...................... 176
10.2 Implications for phase diagrams ....................... 181
10.3 Other thermodynamic behaviors at a phase transition ... 184
10.4 Types of phase equilibrium ............................ 187
10.5 Microscopic view of phase equilibrium ................. 188
10.6 Order parameters and general features of phase
equilibrium ........................................... 194
Problems ................................................... 195
11 Stability .................................................. 201
11.1 Metastability ......................................... 201
11.2 Common tangent line perspective on phase equilibrium .. 202
11.3 Limits of metastability ............................... 205
11.4 Generalized stability criteria ........................ 209
Problems ................................................... 212
12 Solutions: fundamentals .................................... 217
12.1 Ideal solutions ....................................... 217
12.2 Ideal vapor-liquid equilibrium and Raoult's law ....... 220
12.3 Boiling-point elevation ............................... 221
12.4 Freezing-point depression ............................. 224
12.5 Osmotic pressure ...................................... 224
12.6 Binary mixing with interactions ....................... 227
12.7 Nonideal solutions in general ......................... 230
12.8 The Gibbs-Duhem relation .............................. 231
12.9 Partial molar quantities .............................. 233
Problems ................................................... 236
13 Solutions: advanced and special cases ...................... 246
13.1 Phenomenology of multicomponent vapor-liquid
equilibrium ........................................... 246
13.2 Models of multicomponent vapor-liquid equilibrium ..... 248
13.3 Bubble- and dew-point calculations at constant
pressure .............................................. 250
13.4 Flash calculations at constant pressure and
temperature ........................................... 252
13.5 Relative volatility formulation ....................... 254
13.6 Nonideal mixtures ..................................... 255
13.7 Constraints along mixture vapor-liquid phase
boundaries ............................................ 258
13.8 Phase equilibrium in polymer solutions ................ 260
13.9 Strong electrolyte solutions .......................... 266
Problems ................................................... 274
14 Solids ..................................................... 280
14.1 General properties of solids .......................... 280
14.2 Solid-liquid equilibrium in binary mixtures ........... 281
14.3 Solid-liquid equilibrium in multicomponent solutions .. 287
14.4 A microscopic view of perfect crystals ................ 290
14.5 The Einstein model of perfect crystals ................ 292
14.6 The Debye model of perfect crystals ................... 296
Problems ................................................... 300
15 The third law .............................................. 305
15.1 Absolute entropies and absolute zero .................. 305
15.2 Finite entropies and heat capacities at absolute
zero .................................................. 309
15.3 Entropy differences at absolute zero .................. 310
15.4 Attainability of absolute zero ........................ 312
Problems ................................................... 315
16 The canonical partition function ........................... 319
16.1 A review of basic statistical-mechanical concepts ..... 319
16.2 Microscopic equilibrium in isolated systems ........... 320
16.3 Microscopic equilibrium at constant temperature ....... 321
16.4 Microstates and degrees of freedom .................... 328
16.5 The canonical partition function for independent
molecules ............................................. 332
Problems ................................................... 335
17 Fluctuations ............................................... 343
17.1 Distributions in the canonical ensemble ............... 343
17.2 The canonical distribution of energies ................ 345
17.3 Magnitude of energy fluctuations ...................... 350
Problems ................................................... 353
18 Statistical mechanics of classical systems ................. 357
18.1 The classical canonical partition function ............ 357
18.2 Microstate probabilities for continuous degrees of
freedom ............................................... 361
18.3 The Maxwell-Boltzmann distribution .................... 368
18.4 The pressure in the canonical ensemble ................ 372
18.5 The classical microcanonical partition function ....... 375
Problems ................................................... 376
19 Other ensembles ............................................ 387
19.1 The isothermal-isobaric ensemble ...................... 387
19.2 The grand canonical ensemble .......................... 392
19.3 Generalities and the Gibbs entropy formula ............ 396
Problems ................................................... 397
20 Reaction equilibrium ....................................... 404
20.1 A review of basic reaction concepts ................... 404
20.2 Reaction equilibrium at the macroscopic level ......... 405
20.3 Reactions involving ideal gases ....................... 407
20.4 Reactions involving ideal solutions ................... 409
20.5 Temperature and pressure dependence of Keq ............ 410
20.6 Reaction equilibrium at the microscopic level ......... 412
20.7 Fluctuations .......................................... 414
Problems ................................................... 417
21 Reaction coordinates and rates ............................. 425
21.1 Kinetics from statistical thermodynamics .............. 425
21.2 Macroscopic considerations for reaction rates ......... 426
21.3 Microscopic origins of rate coefficients .............. 428
21.4 General considerations for rates of rare-event
molecular processes ................................... 438
Problems ................................................... 441
22 Molecular simulation methods ............................... 444
22.1 Basic elements of classical simulation models ......... 445
22.2 Molecular-dynamics simulation methods ................. 450
22.3 Computing properties .................................. 453
22.4 Simulations of bulk phases ............................ 457
22.5 Monte Carlo simulation methods ........................ 459
Problems ...................................................... 464
Index ......................................................... 470
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