# Modern Thermodynamics: From Heat Engines to Dissipative Structures, 2nd Edition

# Modern Thermodynamics: From Heat Engines to Dissipative Structures, 2nd Edition

ISBN: 978-1-118-69872-3

Nov 2014

552 pages

## Description

*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 non-equilibrium 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 non-equilibrium 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 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.

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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