Entropy: The Truth, The Whole Truth, And Nothing But The Truth

by Arieh Ben-naim

Overview

'Ben-Naim convincingly argues that SMI not only gives a simpler and more broadly applicable definition of entropy, but also clears up much of the historical and modern confusion surrounding the second law. This book will interest any individual who wants to understand how SMI gives a clear definition of entroy.'
CHOICE ConnectThis book discusses the proper definitions of entropy, the valid interpretation of entropy and some useful applications of the concept of entropy. Unlike many books which apply the concept of entropy to systems for which it is not even defined (such as living systems, black holes and the entire universe), these applications will help the reader to understand the meaning of entropy. It also emphasizes the limitations of the applicability of the concept of entropy and the Second Law of Thermodynamics. As with the previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in thermodynamics — the entropy.In this book, the concepts of entropy and the Second Law are presented in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.

Product Details

ISBN-13:	9789813147669
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	12/01/2016
Pages:	296
Sales rank:	707,017
Product dimensions:	6.20(w) x 9.10(h) x 0.70(d)

Table of Contents

Preface xiii

Acknowledgments xix

Test Yourself Before Reading This Book 1

Chapter 1 The Various Definitions of Entropy and the Second Law of Thermodynamics 5

1.1 Introduction 5

1.2 The Clausius Definition and Its Extensions 7

1.2.1 Heat Engines and Carnot's Efficiency 7

1.2.2 Clausius' Definition of Entropy 10

1.2.3 Entropy Change in an Expansion of an Ideal Gas 17

1.3 The Microscopic Definition of Entropy 22

1.3.1 Introduction 22

1.3.2 Boltzmann's Definition of Entropy 23

1.3.3 Objections to Boltzmann's Entropy 24

1.3.4 Absolute Values of Entropy and the Third Law 25

1.3.5 Extension of the Second Law to Non-Isolated Systems 26

1.4 The Definition of Entropy Based on the Shannon's Measure of Information 27

1.4.1 Introduction 27

1.4.2 What is the SMI? 29

1.4.3 Uniform and Non-Uniform Distribution 32

1.4.4 Interpretation of the SMI 41

1.4.5 Applying the SMI to Obtain the Entropy of an Ideal Gas 45

1.4.6 Extension to Systems with Interacting Particles 57

1.5 The Entropy Formulation of the Second Law of Thermodynamics 58

1.5.1 An Expansion of an Ideal Gas in an Isolated System 59

1.5.2 What Drives the System to an Equilibrium State? 61

1.5.3 The Evolution of the SMI in the Expansion Process 67

1.5.4 Summary of Facts 69

1.5.5 Examples of Processes Associated with the Second Law 74

1.6 The Different Formulations of the Second Law of Thermodynamics 77

1.6.1 A Brief Survey of the Various Ensembles 78

1.6.2 The Formulation of the Second Law for Isolated Systems 83

1.6.3 The (T, V, N) Formulation of the Second Law 93

1.6.4 The (T, P, N) Formulation of the Second Law 94

1.7 A Few Misdefinitions of Entropy and the Second Law 96

1.8 Conclusion 98

Chapter 2 Interpretation and Misinterpretations of Entropy 103

2.1 Introduction 103

2.2 What are the Sources of the Mystery? 105

2.2.1 The Very New Word "Entropy" 105

2.2.2 Entropy Always Increases 108

2.2.3 Saying that Entropy is a Mystery, Renders Entropy a Mystery 109

2.2.4 Entropy, as the Almighty "Driving Force" Underlying All Processes 109

2.2.5 The Multiple Interpretations of Entropy 111

2.2.6 The "Reversal Paradox" and the "Recurrence Paradox" 113

2.2.7 The Unwarranted Application of Entropy to Life and the Entire Universe 115

2.3 A Necessary Criterion a Descriptor of Entropy Must Satisfy 115

2.3.1 Volume Exchange Between Two Compartments 116

2.3.2 Energy Exchange Between Two Compartments 118

2.3.3 Material Exchange Between Two Compartments 119

2.4 The Association of Entropy with Disorder 120

2.5 The Association of Entropy with the Spreading/Dispersion/Sharing of Energy 128

2.6 The Association of Entropy with Information 135

2.7 Does Entropy Depend on Our Knowledge About the System? 140

2.7.1 Does Entropy Depend on the Precision We Choose to Describe the Configuration of the System? 141

2.7.2 Does Entropy Depend on Our Knowledge of the Intermolecular Interactions? 142

2.7.3 Does Entropy Depend on the Knowledge of the Composition of the System? 144

2.8 Entropy as a Measure of Freedom 148

2.9 Entropy as a Measure of Possibilities 149

2.10 Entropy as a Measure of Irreversibility 150

2.11 Entropy as "Heat Loss," "Thermal Energy Not Available To Work," "Unavailable Energy," Etc 152

2.12 A Challenging Problem 153

2.13 Caveat on the Interpretation of Entropy as Uncertainty 155

2.14 Conclusion 156

Chapter 3 Applications and Misapplications of Entropy 157

3.1 Introduction 157

3.2 Residual Entropy 160

3.2.1 Residual Entropy of Ice 165

3.3 Application of the Second Law for Processes in an Isolated System 173

3.4 Applications of Entropy and the Second Law for a Constant Temperature and Constant Pressure System 174

3.4.1 Formation of Hydrogen Molecules from Hydrogen Atoms 175

3.4.2 Protein-Protein Association 178

3.4.3 A Simple Chemical Equilibrium 181

3.4.4 Protein Folding 183

3.5 Entropy Change in Phase Transitions 187

3.5.1 Phase Diagram of Water 189

3.6 Trouton's Law 191

3.7 The Entropy of Solvation of Argon in Water 193

3.8 "Entropy of Mixing" 199

3.9 Racemization as a Pure Deassimilation Process 206

3.10 Misusing Entropy in Explaining the Low Solubility of Argon in Water 214

3.11 Application of Entropy and the Second Law to Living Systems 216

3.12 Application of Entropy and the Second Law to the Entire Universe 219

3.13 The Association of Entropy with the Arrow of Time 223

3.14 Conclusion 225

Test Yourself After Reading This Book 227

Notes 233

References and Suggested Reading 267

Index 273