Download Statistical Mechanics Thermodynamics and Kinetics

D
foknbdie Hodndmle Darmstadt
Lehrstuhl Mechanik HI
Statistical Mechanics
Thermodynamics
and Kinetics
Oscar Knefler Rice
The University of North Carolina
W. H. Freeman and Company
San Francisco and London
CONTENTS
Chapter One
Introduction
1-1.
1-2.
1-3.
174.
1-5.
1-6.
1-7.
1-8.
1-9.
1-10.
1-11.
Thermodynamics 1
Scope and Application of Statistical Mechanics
Phase Space 3
Quantization 5
Energy Levels of Molecules 7
Wave Functions 14
Spin, Exchange, and Symmetry 15
Transformations of the Phase Space 18
Hamilton's Equations 23
Canonical Transformations 26
Liouville's Theorem 33
Chapter. Two
The Thermodynamic Approach
to Statistical Mechanics. I
2-1. The Ideal Gas: Internal Distribution Law 37
2-2. Thermodynamic Functions of the Ideal Gas 40
2-3. Evaluation of the Internal Partition Function
for Diatomic Molecules 43
2-4. Or.tho- and Parahydrogen 51
2-5. Polyatomic Molecules 55
2-6. Appendix: Integrals 63
Chapter Three
The Thermodynamic Approach
to Statistical Mechanics. II
3-1. Translational Partition Functions 67
3-2. Evaluation of the Translational Functions
for an Ideal Gas 71
3-3. Application to Mixtures 73
3-4. Alternate Method for the Classical Molecule
75
3-5. Free Lengths and Free Volumes 78
3-6. The Probability of Translational States
and the Law of Equipartition of Energy 80
Chapter Four
The Third Law of Thermodynamics
and the Statistical Definition of Entropy
4-1.
4-2.
4-3.
4-4.
4-5.
The Third Law of Thermodynamics 84
Entropy and Probability: The Classical Case 87
Entropy and Probability: A Generalization 92
Mixtures and Polyphase Systems 93
An Alternative Expression for the Entropy 95
Chapter Five
The Statistical Basis
of Thermodynamics
5-1. Fundamental Assumptions 99
5-2. Pressure and Temperature:
The Thermodynamic Equations 101
5-3. Other Kinds of Forces 107
5-4. Fluctuations 110
5-5. Entropy of Fluctuation 112
5-6. Pressure in a Canonical Ensemble 113
5-7. An Assembly in Contact with a Reservoir 116
Chapter Six
Statistical Calculation of the
Thermodynamic Functions for an Ideal Gas
6-1.
6-2.
6-3.
6-4.
6-5.
Maximization of Probability 120
Interpretation of P 127
Interpretation of a: The Chemical Potential 128
Fluctuations 130
The Chemical Potential in Mixtures 131
Chapter Seven
Chemical Equilibrium
7-1. Use of the Canonical Partition Function 135
7-2. Maximization of Q, 139-
.7-3. Heuristic Discussion 141
7-4. Dissociation of a Diatomic Molecule 141
.7-5. Equilibrium Involving Two Like Molecules:
Effect of Symmetry 144
7-6. Combination of Complex Molecules 146
7-7. The Chemical Potential and the
General Chemical Equilibrium 152
7-8. Phase Equilibrium 154
7-9. Solid—Vapor Equilibrium 157
7-10. Some Relations Which Hold for a Change of Phase
7-11. Stability of'Phases 161
159
Chapter Eight
Imperfect Gases: Classical Case
8-1. The Second Virial Coefficient
as an Association Phenomenon 165
8-2. The Second Virial Coefficient
for a Pair of Atoms 170
8-3. The Lennard-Jones Potential:
Comparison with Experiment- 171
8-4. An Approximate Interpretation
of the Virial Coefficient 173
8-5. Mixtures of Imperfect Gases 177
8-6. Use of the Approximate Formula:
The Interaction of Iodine and Benzene
180
Chapter Nine
The Solid State
9-1. The Einstein Model 183
9-2. The Debye Model
185
9-3. Calculation of the Einstein Frequency
from the Intermolecular Forces 195
9-4. Effective Value of 6 at Low Temperatures 200
9-5. Estimate of 9 as a Function of Temperature 206
9-6. Effect of Thermal Expansion 209
9-7. The Thermodynamic Properties of Solid Argon 211
Chapter Ten
The Grand Partition Function
10-1. Grand Ensembles 220
10-2. Fluctuations 223
10-3.
10-4.
10-5.
10-6.
The Thermodynamic Functions Tib
Further Analysis of Density Fluctuations
The Perfect Gas 233
Many-Component Systems 234
231
Chapter Eleven
Cluster Expansions for Imperfect Gases
11-1. The Virial Expansion and the Irreducible Integrals 240
11-2. The Cluster Integrals 249
11-3. The Relation Between the Cluster Integrals
and the Irreducible Integrals 253
11-4. Some Properties of the Expansions: Condensation 256
Chapter Twelve
Mixtures: Order-Disorder Phenomena
12-1.
12-2.
12-3.
12-4.
12-5.
12-6.
12-7.
12-8.
Ideal Solutions 270
Regular Solutions 21A
The Quasi-chemical Approximation 281
Case with Ae Negative 290
The Grand Partition Function of Mixing
Series Expansions 300
The Lattice Gas 307
The Ising Lattice 309
298
Chapter Thirteen
The Liquid State
13-1.
13-2.
13-3.
13-4.
13-5.
13-6.
13-7.
13-8.
13-9,
Introduction 315
Cell Theories and Communal Entropy 316
Modified Lattice Theory of a Liquid 323
The Radial Distribution Function 329
The Virial Theorem of Clausius 331
Determination of the Radial Distribution Function
Effect of a Field of Force 342
Theory of Surface Tension 345
Fluctuations and the Distribution Function 349
335
Chapter Fourteen
Ideal Gases: Quantum Theory
14-1. Bose-Einstein and Fermi-Dirac Statistics 362
14-2. Partition Functions (p-f.)
and Thermodynamic Relations 367
14-3. The Bose-Einstein Condensation 369
14-4. Thermodynamic Functions of the Bose-Einstein Gas
14-5. The Fermi-Dirac Gas 380
374
Chapter Fifteen
Quantum Liquids
15-1.
15-2.
15-3.
15-4.
15-5.
15-6.
15-7.
15-8.
15-9.
15-10.
15-11.
Properties of Liquid Helium 391
Liquid AHe: The Phonon Spectrum 394
Liquid 4He: The Roton Excitations 396
Momentum and Energy Relations 399
Pressure in the Superfiuid 406
Fluctuations in Energy 408
The Nature of the Rotons 411
Thermodynamic Properties of Liquid zHe 419
Magnetic Properties of 3He 426
Solutions of sHe in *He 430
Some Observations on Effective Mass 434
Chapter Sixteen
Quantum Statistics
16-1.
16-2.
16-3.
16-4.
16-5.
16-6.
Imperfect Gases: The Quantum Case 439
The Slater Sum and the Ideal Quantum Gas 445
The General Imperfect Gas: The Quantum Case 455
The Density Matrix
463
Appendix: Evaluation of Gs 464
Appendix: Proof of Eq. (3.77) 466
Chapter Seventeen
Microscopic Reversibility, Approach
to Equilibrium, and Irreversible Thermodynamics
17-1. The Law of Microscopic Reversibility
17-2. The Approach to Equilibrium 473
470
17-3.
17-4.
17-5.
17-6.
The Steady State in Transfer Processes 481
Irreversible Thermodynamics 484
The Soret Effect 487
Appendix: Law of Microscopic Reversibility
in Quantum Mechanics 490
Chapter Eighteen
Equilibrium Theory of Chemical Reaction Rates
18-1. Rate of Association and Dissociation
of Atoms at Equilibrium 495
18-2. .Effect of Rotation on the Rate of Dissociation 499
18-3. The Rate of Association: The Collision Number 502
18-4. The Effect of Spin Multiplicity
503
18-5. Some Remarks on Reaction Mechanisms 505
18-6. Polyatomic Molecules:
Calculation of Rate Constants 507
18-7. The Temperature Coefficient 511
18-8. Experimental Results and Discussion 514
18-9. Appendix: Potential-energy Surfaces 519
Cliapter Nineteen
Recombination of Atoms and
Dissociation of Diatomic Molecules
19-1. General Considerations 525
19-2. Rate of Dissociation of Diatomic Molecules '
by Collision 529
19-3. The Complex Mechanism for Dissociation
of a Diatomic Molecule 535
19-4. Method of P/iase-space Trajectories 539
19-5. Some Experimental Material on Atom Recombination
546
Chapter Twenty
Unimolecular Reactions
20-1. Reactions at Low Pressures 555
20-2. Calculations on Intramolecular Energy Exchange
20-3. Applications of Unimolecular Rate Theory
to Experimental Results 564
20-4. Appendix: Evaluation of P( 570
Index
574
563