Statistical Thermodynamics - Aubin, Christopher

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Résumé :

Preface xiii

Acknowledgments xv

About the Companion Website xvii

1 Introduction 1

1.1 What is Thermodynamics? 2

1.2 What Is Statistical Mechanics? 5

1.3 Our Approach 6

2 Introduction to Probability Theory 9

2.1 Understanding Probability 9

2.2 Randomness, Fairness, and Probability 10

2.3 Mean Values 15

2.4 Continuous Probability Distributions 18

2.5 Common Probability Distributions 20

2.5.1 Binomial Distribution 20

2.5.2 Gaussian Distribution 21

2.6 Summary 22

Problems 23

References 28

3 Introduction to Information Theory 31

3.1 Missing Information 31

3.2 Missing Information for a General Probability Distribution 37

3.3 Summary 41

Problems 42

References 45

Further Reading 45

4 Statistical Systems and the Microcanonical Ensemble 47

4.1 From Probability and Information Theory to Physics 47

4.2 States in Statistical Systems 48

4.3 Ensembles in Statistical Systems 50

4.4 From States to Information 54

4.5 Microcanonical Ensemble: Counting States 59

4.5.1 Discrete Systems 59

4.5.2 Continuous Systems 62

4.5.3 From ? ? ? 64

4.5.4 Classical Ideal Gas 67

4.6 Interactions Between Systems 70

4.6.1 Thermal Interaction 70

4.6.2 Mechanical Interaction 71

4.7 Quasistatic Processes 73

4.7.1 Exact vs. Inexact Differentials 74

4.7.2 Physical Examples 77

4.8 Summary 79

Problems 79

References 85

5 Equilibrium and Temperature 87

5.1 Equilibrium and the Approach to it 87

5.1.1 Equilibrium 87

5.1.2 Irreversible and Reversible Processes 89

5.1.3 Two Systems in Equilibrium 90

5.1.4 Approaching Thermal Equilibrium 93

5.2 Temperature 95

5.3 Properties of Temperature 96

5.3.1 Negative Absolute Temperature 97

5.3.2 Temperature Scales 98

5.4 Summary 101

Problems 101

References 103

6 Thermodynamics: The Laws and the Mathematics 105

6.1 Interactions Between Systems 105

6.1.1 Quasistatic Thermal Interaction 105

6.1.2 The Heat Reservoir 106

6.1.3 General Interactions Between Systems 108

6.1.4 The Entropy in the Ground state 116

6.2 The First Derivatives 119

6.2.1 Heat Capacity 120

6.2.2 Coefficient of Thermal Expansion 125

6.2.3 Isothermal Compressibility 125

6.3 The Legendre Transform and Thermodynamic Potentials 125

6.3.1 Naturally Independent Variables 126

6.3.2 Legendre Transform 127

6.3.3 Thermodynamic Potentials 130

6.3.4 Fundamental Relations and the Equations of State 135

6.4 Derivative Crushing 136

6.5 More About the Classical Ideal Gas 142

6.6 First Derivatives Near Absolute Zero 145

6.7 Empirical Determination of the Entropy and Internal Energy 146

6.8 Summary 150

Problems 150

References 157

7 Applications of Thermodynamics 159

7.1 Adiabatic Expansion 159

7.2 Cooling Gases 162

7.2.1 Free Expansion 162

7.2.2 Throttling (Joule-Thomson) Process 165

7.3 Heat Engines 168

7.3.1 Carnot Cycle 171

7.4 Refrigerators 173

7.5 Summary 175

Problems 175

References 180

Further Reading 180

8 The Canonical Distribution 181

8.1 Restarting Our Study of Systems 181

8.1.1 A as an Isolated System 182

8.1.2 System in Contact with a Heat Reservoir 182

8.2 Connecting to the Microcanonical Ensemble 188

8.2.1 Mean Energy 189

8.2.2 Variance in ? 189

8.2...

Biographie:

Christopher Aubin, PhD, is Professor in the Department of Physics and Engineering Physics at Fordham University in the Bronx, New York, USA. He earned his doctorate in Physics at Washington University in 2004. His research is focused on the area of lattice QCD.