MODERN THERMODYNAMICS From Heat Engines to Dissipative Structures Second Edition Modern Thermodynamics: From Heat Engines to Dissipative Structures, Second Edition presents a comprehensive introduction to 20th century thermodynamics that can be applied to both equilibrium and nonequilibrium systems, unifying what was traditionally divided into 'thermodynamics' and 'kinetics' into one theory of irreversible processes. This comprehensive text, suitable for introductory as well as advanced courses on thermodynamics, has been widely used by chemists, physicists, engineers and geologists. Fully revised and expanded, this new edition includes the following updates and features: - Includes a completely new chapter on Principles of Statistical Thermodynamics. - Presents new material on solar and wind energy flows and energy flows of interest to engineering. - Covers new material on self-organization in nonequilibrium systems and the thermodynamics of small systems. - Highlights a wide range of applications relevant to students across physical sciences and engineering courses. - Introduces students to computational methods using updated Mathematica codes. - Includes problem sets to help the reader understand and apply the principles introduced throughout the text. - Solutions to exercises and supplementary lecture material are provided online at http: //sites.google.com/site/modernthermodynamics/. Modern Thermodynamics: From Heat Engines to Dissipative Structures, Second Edition is an essential resource for undergraduate and graduate students taking a course in thermodynamics. Preface to the Second Edition xiii Preface to the First Edition: Why Thermodynamics? xv Acknowledgments xxi Notes for Instructors xxiii List of Variables xxv I HISTORICAL ROOTS: FROM HEAT ENGINES TO COSMOLOGY 1 Basic Concepts and the Laws of Gases 3 Introduction 3 1.1 Thermodynamic Systems 4 1.2 Equilibrium and Nonequilibrium Systems 6 1.3 Biological and Other Open Systems 8 1.4 Temperature, Heat and Quantitative Laws of Gases 9 1.5 States of Matter and the van der Waals Equation 17 1.6 An Introduction to the Kinetic Theory of Gases 24 Appendix 1.1 Partial Derivatives 32 Appendix 1.2 Elementary Concepts in Probability Theory 33 Appendix 1.3 Mathematica Codes 34 References 39 Examples 39 Exercises 41 2 The First Law of Thermodynamics 45 The Idea of Energy Conservation Amidst New Discoveries 45 2.1 The Nature of Heat 46 2.2 The First Law of Thermodynamics: The Conservation of Energy 50 2.3 Elementary Applications of the First Law 57 2.4 Thermochemistry: Conservation of Energy in Chemical Reactions 61 2.5 Extent of Reaction: A State Variable for Chemical Systems 68 2.6 Conservation of Energy in Nuclear Reactions and Some General Remarks 69 2.7 Energy Flows and Organized States 71 Appendix 2.1 Mathematica Codes 79 Appendix 2.2 Energy Flow in the USA for the Year 2013 79 References 82 Examples 82 Exercises 85 3 The Second Law of Thermodynamics and the Arrow of Time 89 3.1 The Birth of the Second Law 89 3.2 The Absolute Scale of Temperature 96 3.3 The Second Law and the Concept of Entropy 99 3.4 Modern Formulation of the Second Law 104 3.5 Examples of Entropy Changes due to Irreversible Processes 112 3.6 Entropy Changes Associated with Phase Transformations 114 3.7 Entropy of an Ideal Gas 115 3.8 Remarks about the Second Law and Irreversible Processes 116 Appendix 3.1 The Hurricane as a Heat Engine 117 Appendix 3.2 Entropy Production in Continuous Systems 120 References 121 Examples 122 Exercises 123 4 Entropy in the Realm of Chemical Reactions 125 4.1 Chemical Potential and Affinity: The Thermodynamic Force for Chemical Reactions 125 4.2 General Properties of Affinity 132 4.3 Entropy Production Due to Diffusion 135 4.4 General Properties of Entropy 136 Appendix 4.1 Thermodynamics Description of Diffusion 138 References 139 Example 139 Exercises 140 II EQUILIBRIUM THERMODYNAMICS 5 Extremum Principles and General Thermodynamic Relations 145 Extremum Principles in Nature 145 5.1 Extremum Principles Associated with the Second Law 145 5.2 General Thermodynamic Relations 153 5.3 Gibbs Energy of Formation and Chemical Potential 156 5.4 Maxwell Relations 159 5.5 Extensivity with Respect to N and Partial Molar Quantities 160 5.6 Surface Tension 162 References 165 Examples 165 Exercises 166 6 Basic Thermodynamics of Gases, Liquids and Solids 169 Introduction 169 6.1 Thermodynamics of Ideal Gases 169 6.2 Thermodynamics of Real Gases 172 6.3 Thermodynamics Quantities for Pure Liquids and Solids 180 Reference 183 Examples 183 Exercises 184 7 Thermodynamics of Phase Change 187 Introduction 187 7.1 Phase Equilibrium and Phase Diagrams 187 7.2 The Gibbs Phase Rule and Duhem’s Theorem 192 7.3 Binary and Ternary Systems 194 7.4 Maxwell’s Construction and the Lever Rule 198 7.5 Phase Transitions 201 References 203 Examples 203 Exercises 204 8 Thermodynamics of Solutions 207 8.1 Ideal and Nonideal Solutions 207 8.2 Colligative Properties 211 8.3 Solubility Equilibrium 217 8.4 Thermodynamic Mixing and Excess Functions 222 8.5 Azeotropy 225 References 225 Examples 225 Exercises 227 9 Thermodynamics of Chemical Transformations 231 9.1 Transformations of Matter 231 9.2 Chemical Reaction Rates 232 9.3 Chemical Equilibrium and the Law of Mass Action 239 9.4 The Principle of Detailed Balance 243 9.5 Entropy Production due to Chemical Reactions 245 9.6 Elementary Theory of Chemical Reaction Rates 248 9.7 Coupled Reactions and Flow Reactors 251 Appendix 9.1 Mathematica Codes 256 References 260 Examples 260 Exercises 261 10 Fields and Internal Degrees of Freedom 265 The Many Faces of Chemical Potential 265 10.1 Chemical Potential in a Field 265 10.2 Membranes and Electrochemical Cells 270 10.3 Isothermal Diffusion 277 10.4 Chemical Potential for an Internal Degree of Freedom 281 References 284 Examples 284 Exercises 285 11 Thermodynamics of Radiation 287 Introduction 287 11.1 Energy Density and Intensity of Thermal Radiation 287 11.2 The Equation of State 291 11.3 Entropy and Adiabatic Processes 293 11.4 Wien’s Theorem 295 11.5 Chemical Potential of Thermal Radiation 296 11.6 Matter–Antimatter in Equilibrium with Thermal Radiation: The State of Zero Chemical Potential 297 11.7 Chemical Potential of Radiation not in Thermal Equilibrium with Matter 299 11.8 Entropy of Nonequilibrium Radiation 300 References 302 Example 302 Exercises 302 III FLUCTUATIONS AND STABILITY 12 The Gibbs Stability Theory 307 12.1 Classical Stability Theory 307 12.2 Thermal Stability 308 12.3 Mechanical Stability 309 12.4 Stability and Fluctuations in Nk 310 References 313 Exercises 313 13 Critical Phenomena and Configurational Heat Capacity 315 Introduction 315 13.1 Stability and Critical Phenomena 315 13.2 Stability and Critical Phenomena in Binary Solutions 317 13.3 Configurational Heat Capacity 320 Further Reading 321 Exercises 321 14 Entropy Production, Fluctuations and Small Systems 323 14.1 Stability and Entropy Production 323 14.2 Thermodynamic Theory of Fluctuations 326 14.3 Small Systems 331 14.4 Size-Dependent Properties 333 14.5 Nucleation 336 References 339 Example 339 Exercises 340 IV LINEAR NONEQUILIBRIUM THERMODYNAMICS 15 Nonequilibrium Thermodynamics: The Foundations 343 15.1 Local Equilibrium 343 15.2 Local Entropy Production 345 15.3 Balance Equation for Concentration 346 15.4 Energy Conservation in Open Systems 348 15.5 The Entropy Balance Equation 351 Appendix 15.1 Entropy Production 354 References 356 Exercises 356 16 Nonequilibrium Thermodynamics: The Linear Regime 357 16.1 Linear Phenomenological Laws 357 16.2 Onsager Reciprocal Relations and the Symmetry Principle 359 16.3 Thermoelectric Phenomena 363 16.4 Diffusion 366 16.5 Chemical Reactions 371 16.6 Heat Conduction in Anisotropic Solids 375 16.7 Electrokinetic Phenomena and the Saxen Relations 377 16.8 Thermal Diffusion 379 References 382 Further Reading 382 Exercises 383 17 Nonequilibrium Stationary States and Their Stability: Linear Regime 385 17.1 Stationary States under Nonequilibrium Conditions 385 17.2 The Theorem of Minimum Entropy Production 391 17.3 Time Variation of Entropy Production and the Stability of Stationary States 398 References 400 Exercises 400 V ORDER THROUGH FLUCTUATIONS 18 Nonlinear Thermodynamics 405 18.1 Far-from-Equilibrium Systems 405 18.2 General Properties of Entropy Production 405 18.3 Stability of Nonequilibrium Stationary States 407 18.4 Linear Stability Analysis 411 Appendix 18.1 A General Property of dFP/dt 415 Appendix 18.2 General Expression for the Time Derivative of 2S 416 References 418 Exercises 418 19 Dissipative Structures 421 19.1 The Constructive Role of Irreversible Processes 421 19.2 Loss of Stability, Bifurcation and Symmetry Breaking 421 19.3 Chiral Symmetry Breaking and Life 424 19.4 Chemical Oscillations 431 19.5 Turing Structures and Propagating Waves 436 19.6 Dissipative Structures and Machines 440 19.7 Structural Instability and Biochemical Evolution 441 Appendix 19.1 Mathematica Codes 442 References 447 Further Reading 448 Exercises 449 20 Elements of Statistical Thermodynamics 451 Introduction 451 20.1 Fundamentals and Overview 452 20.2 Partition Function Factorization 454 20.3 The Boltzmann Probability Distribution and Average Values 456 20.4 Microstates, Entropy and the Canonical Ensemble 457 20.5 Canonical Partition Function and Thermodynamic Quantities 460 20.6 Calculating Partition Functions 461 20.7 Equilibrium Constants 467 20.8 Heat Capacities of Solids 469 20.9 Planck’s Distribution Law for Thermal Radiation 472 Appendix 20.1 Approximations and Integrals 474 Reference 475 Example 475 Exercises 475 21 Self-Organization and Dissipative Structures in Nature 477 21.1 Dissipative Structures in Diverse Disciplines 477 21.2 Towards a Thermodynamic Theory of Organisms 483 References 485 Epilogue 487 Physical Constants and Data 489 Standard Thermodynamic Properties 491 Energy Units and Conversions 501 Answers to Exercises 503 Author Index 511 Subject Index 513