Thermal Physics: Entropy and Free Energies / Edition 2

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Overview

This book is an informal, readable introduction to the basic ideas of thermal physics. It is aimed at making the reader feel comfortable with the extremum principles of entropy and free energies. There is a repeating theme: Molecules (spins) do X to maximize their entropy, and molecules (spins) do XX to minimize their free energy. This finally leads to the idea of the Landau–Ginzburg free energy functional. The author illustrates how powerful the idea is by using two examples from phase transitions.
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Editorial Reviews

From The Critics
This informal, readable introduction to the basic ideas of thermal physics covers the extremum principles of entropy and free energies. Prerequisite material on mathematics and quantum mechanics is reviewed, then chapters cover isolated thermal systems, systems in contact with a thermal reservoir, phase and phase transitions, and the Landau-Ginzburg free energy functional, employing analogies between what goes on in the thermal world and what goes on in the human world. The book assumes familiarity with introductory physics and with basic ideas of modern physics. Lee teaches in the Department of Physics and Astronomy at the University of Southern Mississippi. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9789814340762
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 2/28/2011
  • Edition number: 2
  • Pages: 375
  • Product dimensions: 6.20 (w) x 9.10 (h) x 1.10 (d)

Table of Contents

Preface vii

1 Introduction to Thermal Physics 1

1.1 Bird's-Eye view of Thermal Physics 1

2 All you Need to Know to Read the Rest of the Book 5

2.1 Several Taylor Series Expansions (*) 5

2.2 The Dirac δ Function (**) 6

2.3 Gamma Function (***) 6

2.4 The Gaussian Integrals (***) 10

2.5 Hypersphere in d-Dimensional Space (***) 10

2.6 Fourier Transformations (**) 13

2.7 Functional Derivative (**) 14

2.8 The Method of Undetermined Lagrange Multiplier (*) 15

2.9 Permutations Combinatorial and Arrangements (*) 16

2.10 Distribution Function (***) 17

2.11 The Central Limit Theorem (***) 22

2.12 Quantum Mechanics (***) 26

2.13 Thermal Physics on Computer 30

3 Isolated Thermal Systems 33

3.1 Introduction 33

3.2 The Fundamental Postulate 34

3.3 The Microcanonical Ensemble 35

3.4 Entropy and the Second Law of Thermodynamics 37

3.5 Entropy of Ideal Gas Mobile Particles 40

3.5.1 With Position- and Momentum-Definite Microstates 41

3.5.2 With Energy-Definite Microstates 46

3.6 The Fundamental Thermodynamic Equations 49

3.7 Temperature, Pressure and Chemical Potential 49

3.8 The Approach to Equilibrium 53

3.8.1 Temperature 54

3.8.2 Pressure 55

3.8.3 Chemical Potential 56

3.8.4 Multiple Traffic Control Systems 58

3.8.5 Some Reflections 59

3.9 Macrostates 65

3.9.1 The Largest Macrostate 65

3.9.2 How Dominant? 66

3.10 First Law of Thermodynamics 68

3.11 Extensive and Intensive Variables 71

3.12 Entropy of Mixing 73

3.13 Entropy-Driven Forces 76

3.13.1 Rubber Bands 76

3.13.2 Colloidal suspensions 77

3.13.3 Osmosis 78

3.13.4 Ideal Gas 80

3.14 Non-Mobile Thermal Systems 81

3.14.1 Magnets 92

3.14.2 Negative Temperature 88

3.15 Rubger Bands 91

3.16 Schottky Defects 95

4 Systems in Contact with a Thermal Reservior 97

4.1 Introduction 97

4.2 Helmholtz Free Energy 98

4.3 The Minimum Free Energy Principle 99

4.4 The Modified Postulate and the Boltzmann Factor 102

4.5 Response Functions and Fluctuations 108

4.5.1 Energy 109

4.5.2 Magnetization 110

4.6 Canonical Ensemble 112

4.6.1 Ising Spins 113

4.6.2 Schottky Defects 115

4.6.3 Ideal Gas 116

4.6.4 Equipartition Theorem 121

4.7 Maxwell-Boltzmann Distribution 122

4.8 Maxwell Velocity Distribution 125

4.9 Specific Heat and Einstein's Solid 127

4.10 Specific Heat and Debye's Solid 130

4.11 Solids and Gas in Equilibrium 132

4.12 Black Body Radiation 134

5 Entropy as a Measure of Disorder 141

5.1 Introduction 141

5.2 Order and Disorder 141

5.2 Uncertainity and Missing Information: Shannon's Entropy and Information Theory 147

5.4 Disorder Verses Uncertainty 153

6 Open Systems Exposed to Heat and Particle Reservoir 155

6.1 Introduction 155

6.2 Open Systems 155

6.3 Grand Canonical Ensemble Formalism 157

6.4 Hemoglobin and Myoglobin 161

7 Flexible Systems: Systems in Contact with Heat and Volume Reservoir 163

7.1 Introduction 163

7.2 Gibbs Free Energy 163

7.3 Constant Pressure Ensemble Formalism 165

7.3.1 Constant Pressure Ensemble Formalism I 166

7.3.2 Constant Pressure Ensemble Formalism I 167

7.4 Weak Solutions and Osmosis 169

7.5 External Chemcial Potential 173

8 Two More Energy-Like Functions and Concluding Remarks 177

8.1 Introdution 177

8.2 Energy 177

8.3 Enthalpy 177

8.4 Extensivities of Free Energies 179

8.5 Do Free Energies Have a Physical Meaning on Their Own? Maximum (Minimum) Work Theorem and Thermodynamic Potential 180

9 Quantum Ideal Gas 185

9.1 Introdution 185

9.2 The Occupation Number Formalism and Slightly Degenerate Ideal Gas 186

9.3 Fermi-Dirac and Bose-Einstein Distribution Functions 194

9.4 Degenerate Electron Gas Near and At T = 0 195

9.5 Degenerate Ideal Boson Gas At and Near T=0 201

9.6 The Classical Regime Revisited 204

10 Thermodynamics 207

10.1 Introduction 207

10.2 Carnot Heat Enging I 208

10.3 Carnot Heat Engine II 210

10.4 Relationships Between Thermodynamic Derivatives 214

10.5 Important Thermodynamic Derivatives and Their Mutual Relationships 219

10.6 Thermodynamic Stability 220

11 Energy Versus Free Energy 227

11.1 Introduction 227

11.2 Boltzmann Factor for Macrostates and Macrostate Free Energy 228

11.3 Thermodynamic Work and Thermodynamic Potential 231

11.4 Is Some Energy Really Free? 234

12 Phases and Phase Transitions 237

12.1 Introduction 237

12.2 Liquid State and Solid State 238

12.3 Phase Diagrams 244

12.4 Phase Rule 246

12.5 Coexistence Curves 246

12.6 Interface 249

12.7 The Van der Waals Theory 251

12.8 Dynamics of First Order Phase Transitions 261

12.8.1 Unstable Region 263

12.8.2 Metastable Region 263

12.9 Binary Systems: Mixing and Demixing 265

12.9 More on Binary Mixtures: Their Phase Equilibria 270

13 Second-Order Phase Transitions 275

13.1 Introduction 275

13.2 Liquid-Gas Molecular Systems 279

13.3 Spin Systems 284

13.3.1 Broken Symmetry, Order Parameter 286

13.4 Universality 289

13.5 Susceptibility and Spatial Correlations 289

13.6 Interacting Ising Spins on a Chain 292

13.7 Mean-Field Theory: Magnetism 296

13.8 Mean Field Theory: Liquid-Gas Sytems 302

13.9 Landau Mean Field Theory 305

13.10 The Static Scaling Hyposthesis 310

14 Landau-Ginzburg Free Energy Functional and Applications 319

14.1 Introduction 319

14.2 Landau-Ginzburg Free Engergy 319

14.3 The Renormalization Group Theory 322

14.4 Phase Separation Dynamics 330

14.4.1 The Time Evolution of the Order Parameter Function 332

15 Quantum Fluid 341

15.1 Introduction 341

15.2 Superfluidity 342

15.3 Bose-Einstein Codensation 349

16 Computer Simulations 355

16.1 Introdution 355

16.2 Monte Carlo Method I 355

16.3 Monte Carlo Method II: The Master Equation 357

16.4 Finite Size Scaling 366

Bibliography 369

Index 373

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