Modern Thermodynamics

Dilip Kondepudi Wake Forest University, USA Ilya Prigogine Formerly Director, International Solvay Institutes, Belgium

• Preface to the Second Edition xiiiPreface to the First Edition: Why Thermodynamics? xvAcknowledgments xxiNotes for Instructors xxiiiList of Variables xxvI Historical Roots: From Heat Engines to Cosmology1 Basic Concepts and the Laws of Gases 3Introduction 31.1 Thermodynamic Systems 41.2 Equilibrium and Nonequilibrium Systems 61.3 Biological and Other Open Systems 81.4 Temperature, Heat and Quantitative Laws of Gases 91.5 States of Matter and the van der Waals Equation 171.6 An Introduction to the Kinetic Theory of Gases 24Appendix 1.1 Partial Derivatives 32Appendix 1.2 Elementary Concepts in Probability Theory 33Appendix 1.3 Mathematica Codes 34References 39Examples 39Exercises 412 The First Law of Thermodynamics 45The Idea of Energy Conservation Amidst New Discoveries 452.1 The Nature of Heat 462.2 The First Law of Thermodynamics: The Conservation of Energy 502.3 Elementary Applications of the First Law 572.4 Thermochemistry: Conservation of Energy in Chemical Reactions 612.5 Extent of Reaction: A State Variable for Chemical Systems 682.6 Conservation of Energy in Nuclear Reactions and Some General Remarks 692.7 Energy Flows and Organized States 71Appendix 2.1 Mathematica Codes 79Appendix 2.2 Energy Flow in the USA for the Year 2013 79References 82Examples 82Exercises 853 The Second Law of Thermodynamics and the Arrow of Time 893.1 The Birth of the Second Law 893.2 The Absolute Scale of Temperature 963.3 The Second Law and the Concept of Entropy 993.4 Modern Formulation of the Second Law 1043.5 Examples of Entropy Changes due to Irreversible Processes 1123.6 Entropy Changes Associated with Phase Transformations 1143.7 Entropy of an Ideal Gas 1153.8 Remarks about the Second Law and Irreversible Processes 116Appendix 3.1 The Hurricane as a Heat Engine 117Appendix 3.2 Entropy Production in Continuous Systems 120References 121Examples 122Exercises 1234 Entropy in the Realm of Chemical Reactions 1254.1 Chemical Potential and Affinity: The Thermodynamic Force for Chemical Reactions 1254.2 General Properties of Affinity 1324.3 Entropy Production Due to Diffusion 1354.4 General Properties of Entropy 136Appendix 4.1 Thermodynamics Description of Diffusion 138References 139Example 139Exercises 140II Equilibrium Thermodynamics5 Extremum Principles and General Thermodynamic Relations 145Extremum Principles in Nature 1455.1 Extremum Principles Associated with the Second Law 1455.2 General Thermodynamic Relations 1535.3 Gibbs Energy of Formation and Chemical Potential 1565.4 Maxwell Relations 1595.5 Extensivity with Respect to N and Partial Molar Quantities 1605.6 Surface Tension 162References 165Examples 165Exercises 1666 Basic Thermodynamics of Gases, Liquids and Solids 169Introduction 1696.1 Thermodynamics of Ideal Gases 1696.2 Thermodynamics of Real Gases 1726.3 Thermodynamics Quantities for Pure Liquids and Solids 180Reference 183Examples 183Exercises 1847 Thermodynamics of Phase Change 187Introduction 1877.1 Phase Equilibrium and Phase Diagrams 1877.2 The Gibbs Phase Rule and Duhem’s Theorem 1927.3 Binary and Ternary Systems 1947.4 Maxwell’s Construction and the Lever Rule 1987.5 Phase Transitions 201References 203Examples 203Exercises 2048 Thermodynamics of Solutions 2078.1 Ideal and Nonideal Solutions 2078.2 Colligative Properties 2118.3 Solubility Equilibrium 2178.4 Thermodynamic Mixing and Excess Functions 2228.5 Azeotropy 225References 225Examples 225Exercises 2279 Thermodynamics of Chemical Transformations 2319.1 Transformations of Matter 2319.2 Chemical Reaction Rates 2329.3 Chemical Equilibrium and the Law of Mass Action 2399.4 The Principle of Detailed Balance 2439.5 Entropy Production due to Chemical Reactions 2459.6 Elementary Theory of Chemical Reaction Rates 2489.7 Coupled Reactions and Flow Reactors 251Appendix 9.1 Mathematica Codes 256References 260Examples 260Exercises 26110 Fields and Internal Degrees of Freedom 265The Many Faces of Chemical Potential 26510.1 Chemical Potential in a Field 26510.2 Membranes and Electrochemical Cells 27010.3 Isothermal Diffusion 27710.4 Chemical Potential for an Internal Degree of Freedom 281References 284Examples 284Exercises 28511 Thermodynamics of Radiation 287Introduction 28711.1 Energy Density and Intensity of Thermal Radiation 28711.2 The Equation of State 29111.3 Entropy and Adiabatic Processes 29311.4 Wien’s Theorem 29511.5 Chemical Potential of Thermal Radiation 29611.6 Matter–Antimatter in Equilibrium with Thermal Radiation: The State of Zero Chemical Potential 29711.7 Chemical Potential of Radiation not in Thermal Equilibrium with Matter 29911.8 Entropy of Nonequilibrium Radiation 300References 302Example 302Exercises 302III Fluctuations and Stability12 The Gibbs Stability Theory 30712.1 Classical Stability Theory 30712.2 Thermal Stability 30812.3 Mechanical Stability 30912.4 Stability and Fluctuations in Nk 310References 313Exercises 31313 Critical Phenomena and Configurational Heat Capacity 315Introduction 31513.1 Stability and Critical Phenomena 31513.2 Stability and Critical Phenomena in Binary Solutions 31713.3 Configurational Heat Capacity 320Further Reading 321Exercises 32114 Entropy Production, Fluctuations and Small Systems 32314.1 Stability and Entropy Production 32314.2 Thermodynamic Theory of Fluctuations 32614.3 Small Systems 33114.4 Size-Dependent Properties 33314.5 Nucleation 336References 339Example 339Exercises 340IV Linear Nonequilibrium Thermodynamics15 Nonequilibrium Thermodynamics: The Foundations 34315.1 Local Equilibrium 34315.2 Local Entropy Production 34515.3 Balance Equation for Concentration 34615.4 Energy Conservation in Open Systems 34815.5 The Entropy Balance Equation 351Appendix 15.1 Entropy Production 354References 356Exercises 35616 Nonequilibrium Thermodynamics: The Linear Regime 35716.1 Linear Phenomenological Laws 35716.2 Onsager Reciprocal Relations and the Symmetry Principle 35916.3 Thermoelectric Phenomena 36316.4 Diffusion 36616.5 Chemical Reactions 37116.6 Heat Conduction in Anisotropic Solids 37516.7 Electrokinetic Phenomena and the Saxen Relations 37716.8 Thermal Diffusion 379References 382Further Reading 382Exercises 38317 Nonequilibrium Stationary States and Their Stability: Linear Regime 38517.1 Stationary States under Nonequilibrium Conditions 38517.2 The Theorem of Minimum Entropy Production 39117.3 Time Variation of Entropy Production and the Stability of Stationary States 398References 400Exercises 400V Order Through Fluctuations18 Nonlinear Thermodynamics 40518.1 Far-from-Equilibrium Systems 40518.2 General Properties of Entropy Production 40518.3 Stability of Nonequilibrium Stationary States 40718.4 Linear Stability Analysis 411Appendix 18.1 A General Property of dFP/dt 415Appendix 18.2 General Expression for the Time Derivative of 𝛿 2S 416References 418Exercises 41819 Dissipative Structures 42119.1 The Constructive Role of Irreversible Processes 42119.2 Loss of Stability, Bifurcation and Symmetry Breaking 42119.3 Chiral Symmetry Breaking and Life 42419.4 Chemical Oscillations 43119.5 Turing Structures and Propagating Waves 43619.6 Dissipative Structures and Machines 44019.7 Structural Instability and Biochemical Evolution 441Appendix 19.1 Mathematica Codes 442References 447Further Reading 448Exercises 44920 Elements of Statistical Thermodynamics 451Introduction 45120.1 Fundamentals and Overview 45220.2 Partition Function Factorization 45420.3 The Boltzmann Probability Distribution and Average Values 45620.4 Microstates, Entropy and the Canonical Ensemble 45720.5 Canonical Partition Function and Thermodynamic Quantities 46020.6 Calculating Partition Functions 46120.7 Equilibrium Constants 46720.8 Heat Capacities of Solids 46920.9 Planck’s Distribution Law for Thermal Radiation 472Appendix 20.1 Approximations and Integrals 474Reference 475Example 475Exercises 47521 Self-Organization and Dissipative Structures in Nature 47721.1 Dissipative Structures in Diverse Disciplines 47721.2 Towards a Thermodynamic Theory of Organisms 483References 485Epilogue 487Physical Constants and Data 489Standard Thermodynamic Properties 491Energy Units and Conversions 501Answers to Exercises 503Author Index 511Subject Index 513