Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics

An Integrated Approach

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.

Autorentext

ROBERT J. HARDY and CHRISTIAN BINEK
Department of Physics, University of Nebraska-Lincoln, USA

Klappentext
Thermodynamics and Statistical Mechanics An Integrated Approach 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.

Zusammenfassung
Thermodynamics and Statistical Mechanics Thermodynamics and Statistical MechanicsAn Integrated Approach 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.

Inhalt
Preface xiii

Part I Elements of Thermal Physics 1

1. Fundamentals 3

1.1 PVT Systems 3

1.2 Equilibrium States 6

1.3 Processes and Heat 10

1.4 Temperature 12

1.5 Size Dependence 13

1.6 Heat Capacity and Specific Heat 14

Problems 17

2. First Law of Thermodynamics 19

2.1 Work 19

2.2 Heat 21

2.3 The First Law 21

2.4 Applications 22

Problems 26

3. Properties and Partial Derivatives 27

3.1 Conventions 27

3.2 Equilibrium Properties 28

3.3 Relationships between Properties 34

3.4 Series Expansions 40

3.5 Summary 41

Problems 42

4. Processes in Gases 45

4.1 Ideal Gases 45

4.2 Temperature Change with Elevation 48

4.3 Cyclic Processes 50

4.4 Heat Engines 52

Problems 58

5. Phase Transitions 61

5.1 Solids, Liquids, and Gases 61

5.2 Latent Heats 65

5.3 Van der Waals Model 67

5.4 Classification of Phase Transitions 70

Problems 72

6. Reversible and Irreversible Processes 75

6.1 Idealization and Reversibility 75

6.2 Nonequilibrium Processes and Irreversibility 76

6.3 Electrical Systems 79

6.4 Heat Conduction 82

Problems 86

Part II Foundations of Thermodynamics 89

7. Second Law of Thermodynamics 91

7.1 Energy, Heat, and Reversibility 91

7.2 Cyclic Processes 93

7.3 Second Law of Thermodynamics 95

7.4 Carnot Cycles 98

7.5 Absolute Temperature 100

7.6 Applications 103

Problems 107

8. Temperature Scales and Absolute Zero 109

8.1 Temperature Scales 109

8.2 Uniform Scales and Absolute Zero 111

8.3 Other Temperature Scales 114

Problems 115

9. State Space and Differentials 117

9.1 Spaces 117

9.2 Differentials 121

9.3 Exact Versus Inexact Differentials 123

9.4 Integrating Differentials 127

9.5 Differentials in Thermodynamics 129

9.6 Discussion and Summary 134

Problems 136

10. Entropy 139

10.1 Definition of Entropy 139

10.2 Clausius' Theorem 142

10.3 Entropy Principle 145

10.4 Entropy and Irreversibility 148

10.5 Useful Energy 151

10.6 The Third Law 155

10.7 Unattainability of Absolute Zero 156

Problems 158

Appendix 10.A. Entropy Statement of the Second Law 158

11. Consequences of Existence of Entropy 165

11.1 Differentials of Entropy and Energy 165

11.2 Ideal Gases 167

11.3 Relationships Between CV, CP, BT , BS, and V 170

11.4 Clapeyron's Equation 172

11.5 Maximum Entropy, Equilibrium, and Stability 174

11.6 Mixing 178

Problems 184

12. Thermodynamic Potentials 185

12.1 Internal Energy 185

12.2 Free Energies 186

12.3 Properties From Potentials 188

12.4 Systems in Contact with a Heat Reservoir 193

12.5 Minimum Free Energy 194

Problems 197

Appendix 12.A. Derivatives of Potentials 197

13. Phase Transitions and Open Systems 201

13.1 Two-Phase Equilibrium 201

13.2 Chemical Potential 206

13.3 Multi-Component Systems 211

13.4 Gibbs Phase Rule 214

13.5 Chemical Reactions 215

Problems 217

14. Dielectric and Magnetic Systems 219

14.1 Dielectrics 219

14.2 Magnetic Materials 224 <p...