Thermodynamics and Statistical Mechanics : An Integrated Approach

[BOOK DESCRIPTION]

This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference.
The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the modern student's knowledge of the atomic nature of matter. Another unique aspect of the book is the treatment of the mathematics involved. The essential mathematical concepts are briefly reviewed before using them, and the similarity of the mathematics to that employed in other fields of physics is emphasized.
The text gives in depth treatments of low density gases, harmonic solids, magnetic and dielectric materials, phase transitions, and the concept of entropy.The microcanonical, canonical, and grand canonical ensembles of statistical mechanics are derived and used as the starting point for the analysis of fluctuations, blackbody radiation, the Maxwell distribution, Fermi-Dirac statistics, Bose-Einstein condensation, and the statistical basis of computer simulations.

[TABLE OF CONTENTS]

Preface                                            xiii
Part I Elements of Thermal Physics                 1   (88)
  1 Fundamentals                                   3   (16)
    1.1 PVT Systems                                3   (3)
    1.2 Equilibrium States                         6   (4)
    1.3 Processes and Heat                         10  (2)
    1.4 Temperature                                12  (1)
    1.5 Size Dependence                            13  (1)
    1.6 Heat Capacity and Specific Heat            14  (3)
    Problems                                       17  (2)
  2 First Law of Thermodynamics                    19  (8)
    2.1 Work                                       19  (2)
    2.2 Heat                                       21  (1)
    2.3 The First Law                              21  (1)
    2.4 Applications                               22  (4)
    Problems                                       26  (1)
  3 Properties and Partial Derivatives             27  (18)
    3.1 Conventions                                27  (1)
    3.2 Equilibrium Properties                     28  (6)
    3.3 Relationships between Properties           34  (6)
    3.4 Series Expansions                          40  (1)
    3.5 Summary                                    41  (1)
    Problems                                       42  (3)
  4 Processes in Gases                             45  (16)
    4.1 Ideal Gases                                45  (3)
    4.2 Temperature Change with Elevation          48  (2)
    4.3 Cyclic Processes                           50  (2)
    4.4 Heat Engines                               52  (6)
    Problems                                       58  (3)
  5 Phase Transitions                              61  (14)
    5.1 Solids, Liquids, and Gases                 61  (4)
    5.2 Latent Heats                               65  (2)
    5.3 Van der Waals Model                        67  (3)
    5.4 Classification of Phase Transitions        70  (2)
    Problems                                       72  (3)
  6 Reversible and Irreversible Processes          75  (14)
    6.1 Idealization and Reversibility             75  (1)
    6.2 Nonequilibrium Processes and               76  (3)
    Irreversibility
    6.3 Electrical Systems                         79  (3)
    6.4 Heat Conduction                            82  (4)
    Problems                                       86  (3)
Part II Foundations of Thermodynamics              89  (146)
  7 Second Law of Thermodynamics                   91  (18)
    7.1 Energy, Heat, and Reversibility            91  (2)
    7.2 Cyclic Processes                           93  (2)
    7.3 Second Law of Thermodynamics               95  (3)
    7.4 Carnot Cycles                              98  (2)
    7.5 Absolute Temperature                       100 (3)
    7.6 Applications                               103 (4)
    Problems                                       107 (2)
  8 Temperature Scales and Absolute Zero           109 (8)
    8.1 Temperature Scales                         109 (2)
    8.2 Uniform Scales and Absolute Zero           111 (3)
    8.3 Other Temperature Scales                   114 (1)
    Problems                                       115 (2)
  9 State Space and Differentials                  117 (22)
    9.1 Spaces                                     117 (4)
    9.2 Differentials                              121 (2)
    9.3 Exact Versus Inexact Differentials         123 (4)
    9.4 Integrating Differentials                  127 (2)
    9.5 Differentials in Thermodynamics            129 (5)
    9.6 Discussion and Summary                     134 (2)
    Problems                                       136 (3)
  10 Entropy                                       139 (26)
    10.1 Definition of Entropy                     139 (3)
    10.2 Clausius' Theorem                         142 (3)
    10.3 Entropy Principle                         145 (3)
    10.4 Entropy and Irreversibility               148 (3)
    10.5 Useful Energy                             151 (4)
    10.6 The Third Law                             155 (1)
    10.7 Unattainability of Absolute Zero          156 (2)
    Problems                                       158 (1)
    Appendix 10.A Entropy Statement of the         158 (7)
    Second Law
  11 Consequences of Existence of Entropy          165 (20)
    11.1 Differentials of Entropy and Energy       165 (2)
    11.2 Ideal Gases                               167 (3)
    11.3 Relationships Between Cv, Cp, BT, Bs,     170 (2)
    and αv
    11.4 Clapeyron's Equation                      172 (2)
    11.5 Maximum Entropy, Equilibrium, and         174 (4)
    Stability
    11.6 Mixing                                    178 (6)
    Problems                                       184 (1)
  12 Thermodynamic Potentials                      185 (16)
    12.1 Internal Energy                           185 (1)
    12.2 Free Energies                             186 (2)
    12.3 Properties From Potentials                188 (5)
    12.4 Systems in Contact with a Heat            193 (1)
    Reservoir
    12.5 Minimum Free Energy                       194 (3)
    Problems                                       197 (1)
    Appendix 12.A Derivatives of Potentials        197 (4)
  13 Phase Transitions and Open Systems            201 (18)
    13.1 Two-Phase Equilibrium                     201 (5)
    13.2 Chemical Potential                        206 (5)
    13.3 Multi-Component Systems                   211 (3)
    13.4 Gibbs Phase Rule                          214 (1)
    13.5 Chemical Reactions                        215 (2)
    Problems                                       217 (2)
  14 Dielectric and Magnetic Systems               219 (16)
    14.1 Dielectrics                               219 (5)
    14.2 Magnetic Materials                        224 (5)
    14.3 Critical Phenomena                        229 (4)
    Problems                                       233 (2)
Part III Statistical Thermodynamics                235 (54)
  15 Molecular Models                              237 (18)
    15.1 Microscopic Descriptions                  237 (1)
    15.2 Gas Pressure                              238 (5)
    15.3 Equipartition of Energy                   243 (3)
    15.4 Internal Energy of Solids                 246 (1)
    15.5 Inactive Degrees of Freedom               247 (1)
    15.6 Microscopic Significance of Heat          248 (5)
    Problems                                       253 (2)
  16 Kinetic Theory of Gases                       255 (18)
    16.1 Velocity Distribution                     255 (1)
    16.2 Combinatorics                             256 (2)
    16.3 Method of Undetermined Multipliers        258 (2)
    16.4 Maxwell Distribution                      260 (5)
    16.5 Mean-Free-Path                            265 (2)
    Problems                                       267 (1)
    Appendix 16.A Quantum Distributions            267 (6)
  17 Microscopic Significance of Entropy           273 (16)
    17.1 Boltzmann Entropy                         273 (1)
    17.2 Ideal Gas                                 274 (4)
    17.3 Statistical Interpretation                278 (1)
    17.4 Thermodynamic Properties                  279 (5)
    17.5 Boltzmann Factors                         284 (2)
    Problems                                       286 (1)
    Appendix 17.A Evaluation of I3N                286 (3)
Part IV Statistical Mechanics I                    289 (126)
  18 Ensembles                                     291 (20)
    18.1 Probabilities and Averages                291 (2)
    18.2 Two-Level Systems                         293 (2)
    18.3 Information Theory                        295 (3)
    18.4 Equilibrium Ensembles                     298 (4)
    18.5 Canonical Thermodynamics                  302 (3)
    18.6 Composite Systems                         305 (3)
    Problems                                       308 (1)
    Appendix 18.A Uniqueness Theorem               308 (3)
  19 Partition Function                            311 (20)
    19.1 Hamiltonians and Phase Space              311 (1)
    19.2 Model Hamiltonians                        312 (4)
    19.3 Classical Canonical Ensemble              316 (2)
    19.4 Thermodynamic Properties and Averages     318 (4)
    19.5 Ideal Gases                               322 (4)
    19.6 Harmonic Solids                           326 (2)
    Problems                                       328 (3)
  20 Quantum Systems                               331 (18)
    20.1 Energy Eigenstates                        331 (2)
    20.2 Quantum Canonical Ensemble                333 (1)
    20.3 Ideal Gases                               334 (3)
    20.4 Einstein Model                            337 (4)
    20.5 Classical Approximation                   341 (3)
    Problems                                       344 (1)
    Appendix 20.A Ideal Gas Eigenstates            344 (5)
  21 Independent Particles and Paramagnetism       349 (22)
    21.1 Averages                                  349 (2)
    21.2 Statistical Independence                  351 (2)
    21.3 Classical Systems                         353 (4)
    21.4 Paramagnetism                             357 (3)
    21.5 Spin Systems                              360 (5)
    21.6 Classical Dipoles                         365 (2)
    Problems                                       367 (1)
    Appendix 21.A Negative Temperature             367 (4)
  22 Fluctuations and Energy Distributions         371 (22)
    22.1 Standard Deviation                        371 (4)
    22.2 Energy Fluctuations                       375 (1)
    22.3 Gibbs Paradox                             376 (4)
    22.4 Microcanonical Ensemble                   380 (6)
    22.5 Comparison of Ensembles                   386 (5)
    Problems                                       391 (2)
  23 Generalizations and Diatomic Gases            393 (22)
    23.1 Generalized Coordinates                   393 (4)
    23.2 Diatomic Gases                            397 (5)
    23.3 Quantum Effects                           402 (3)
    23.4 Density Matrices                          405 (3)
    23.5 Canonical Ensemble                        408 (2)
    Problems                                       410 (1)
    Appendix 23.A Classical Approximation          410 (5)
Part V Statistical Mechanics II                    415 (86)
  24 Photons and Phonons                           417 (18)
    24.1 Plane Wave Eigenstates                    417 (4)
    24.2 Photons                                   421 (4)
    24.3 Harmonic Approximation                    425 (4)
    24.4 Phonons                                   429 (5)
    Problems                                       434 (1)
  25 Grand Canonical Ensemble                      435 (10)
    25.1 Thermodynamics of Open Systems            435 (2)
    25.2 Grand Canonical Ensemble                  437 (1)
    25.3 Properties and Fluctuations               438 (3)
    25.4 Ideal Gases                               441 (2)
    Problems                                       443 (2)
  26 Fermions and Bosons                           445 (16)
    26.1 Identical Particles                       445 (2)
    26.2 Exchange Symmetry                         447 (5)
    26.3 Fermi-Dirac and Bose-Einstein             452 (4)
    Statistics
    Problems                                       456 (1)
    Appendix 26.A Fermions in the Canonical        457 (4)
    Ensemble
  27 Fermi and Bose Gases                          461 (14)
    27.1 Ideal Gases                               461 (4)
    27.2 Fermi Gases                               465 (1)
    27.3 Low Temperature Heat Capacity             466 (3)
    27.4 Bose Gases                                469 (3)
    Problems                                       472 (3)
  28 Interacting Systems                           475 (14)
    28.1 Ising Model                               475 (6)
    28.2 Nonideal Gases                            481 (6)
    Problems                                       487 (2)
  29 Computer Simulations                          489 (12)
    29.1 Averages                                  489 (1)
    29.2 Virial Formula for Pressure               490 (6)
    29.3 Simulation Algorithms                     496 (5)
A Mathematical Relations, Constants, and           501 (4)
Properties
  A.1 Partial Derivatives                          501 (1)
  A.2 Integrals and Series                         501 (1)
  A.3 Taylor Series                                502 (1)
  A.4 Hyperbolic Functions                         502 (1)
  A.5 Fundamental Constants                        503 (1)
  A.6 Conversion Factors                           503 (1)
  A.7 Useful Formulas                              503 (1)
  A.8 Properties of Water                          504 (1)
  A.9 Properties of Materials                      504 (1)
Answers to Problems                                505 (4)
Index                                              509