Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, compensated and uncompensated heats, and dissipation, which make it possible to formulate the thermodynamic laws in more broadened forms than those in the conventional treatment of equilibrium thermodynamics. It thus strives to prepare students for more advanced subjects of irreversible processes, which are encountered in our everyday scientific activities. In addition, it also aims to provide them with functional and practical knowledge of equilibrium chemical thermodynamics of reversible processes in real fluids. It discusses temperature, work and heat, thermodynamic laws, equilibrium conditions and thermodynamic stability, thermodynamics of reversible processes in gases and liquids, in surfaces, chemical equilibria, reversible processes in electrolyte solutions and dielectrics in static electric and magnetic fields. A couple of examples for irreversible processes associated with fluid flows and chemical pattern formation and wave propagations are discussed as examples for applications of broader treatments of the thermodynamic laws in the realm of irreversible phenomena.


Contents:
Introduction
Temperature, Work, and Heat
The First Law of Thermodynamics
The Second Law of Thermodynamics
Equilibrium Conditions and Thermodynamic Stability
The Third Law of Thermodynamics
Thermodynamics of Mixtures and Open Systems
Heterogeneous Equilibria
Thermodynamics of Real Fluids
Canonical Equation of State
Thermodynamics of Real Gas Mixtures
Chemical Equilibria
Thermodynamics of Solutions
Thermodynamics of Surfaces
Electrolyte Solutions
Debye–Hückel Theory of Strong Electrolyte Solutions
Galvanic Cells and Electromotive Forces
Thermodynamics of Electric and Magnetic Fields
Thermodynamics of Nonequilibrium Processes
Appendices
Local Form of Energy Conservation Law
Various Coefficients Used in Chapter 10

Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, compensated and uncompensated heats, and dissipation, which make it possible to formulate the thermodynamic laws in more broadened forms than those in the conventional treatment of equilibrium thermodynamics. It thus strives to prepare students for more advanced subjects of irreversible processes, which are encountered in our everyday scientific activities. In addition, it also aims to provide them with functional and practical knowledge of equilibrium chemical thermodynamics of reversible processes in real fluids. It discusses temperature, work and heat, thermodynamic laws, equilibrium conditions and thermodynamic stability, thermodynamics of reversible processes in gases and liquids, in surfaces, chemical equilibria, reversible processes in electrolyte solutions and dielectrics in static electric and magnetic fields. A couple of examples for irreversible processes associated with fluid flows and chemical pattern formation and wave propagations are discussed as examples for applications of broader treatments of the thermodynamic laws in the realm of irreversible phenomena.


Contents:
Introduction
Temperature, Work, and Heat
The First Law of Thermodynamics
The Second Law of Thermodynamics
Equilibrium Conditions and Thermodynamic Stability
The Third Law of Thermodynamics
Thermodynamics of Mixtures and Open Systems
Heterogeneous Equilibria
Thermodynamics of Real Fluids
Canonical Equation of State
Thermodynamics of Real Gas Mixtures
Chemical Equilibria
Thermodynamics of Solutions
Thermodynamics of Surfaces
Electrolyte Solutions
Debye–Hückel Theory of Strong Electrolyte Solutions
Galvanic Cells and Electromotive Forces
Thermodynamics of Electric and Magnetic Fields
Thermodynamics of Nonequilibrium Processes
Appendices
Local Form of Energy Conservation Law
Various Coefficients Used in Chapter 10

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Contents
Preface vii
1. Introduction 1
2. Temperature, Work, and Heat 9
2.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Centigrade (Celsius) Scale . . . . . . . . . . . . . 12
2.1.2 Fahrenheit Scale . . . . . . . . . . . . . . . . . . 14
2.1.3 Absolute Temperature Scale and Ideal
Gas Thermometer . . . . . . . . . . . . . . . . . 14
2.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Reversible Processes and Reversible Work . . . . . . . . 28
3. The First Law of Thermodynamics 31
3.1 Equivalence of Heat and Energy . . . . . . . . . . . . . . 31
3.2 The First Law of Thermodynamics . . . . . . . . . . . . 33
3.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Differential Forms for Enthalpy . . . . . . . . . . 37
3.3.2 The Difference in Isobaric and Isochoric Heat
Capacities for Ideal Gases . . . . . . . . . . . . . 39
3.4 Work and Heat of Isothermal Reversible Expansion . . . 40
3.5 Work of Adiabatic Expansion . . . . . . . . . . . . . . . 40
3.6 Heat Capacity and Heat Change . . . . . . . . . . . . . 41
ix
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3.7 Thermochemistry . . . . . . . . . . . . . . . . . . . . . . 44
3.7.1 Heat of Reaction . . . . . . . . . . . . . . . . . . 44
3.7.2 Standard States and Heat of Formation . . . . . 45
3.7.3 Hess’s Law . . . . . . . . . . . . . . . . . . . . . 46
3.7.4 Kirchhoff’s Equation . . . . . . . . . . . . . . . . 49
3.8 Mathematical Notes . . . . . . . . . . . . . . . . . . . . . 50
3.8.1 Exact Differentials . . . . . . . . . . . . . . . . . 51
3.8.2 Chain Relations . . . . . . . . . . . . . . . . . . 52
3.8.3 Jacobians . . . . . . . . . . . . . . . . . . . . . . 54
4. The Second Law of Thermodynamics 57
4.1 Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2 Carnot’s Theorem . . . . . . . . . . . . . . . . . . . . . 65
4.3 Thermodynamic Temperature . . . . . . . . . . . . . . . 70
4.4 Entropy and Calortropy . . . . . . . . . . . . . . . . . . 72
4.4.1 Clausius Inequality . . . . . . . . . . . . . . . . . 72
4.4.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.3 Calortropy . . . . . . . . . . . . . . . . . . . . . 76
4.4.4 Inequalities of Entropy and Calortropy . . . . . . 79
4.5 Carnot’s Theorem and Real Gases . . . . . . . . . . . . 85
4.6 Examples of Other Cycles . . . . . . . . . . . . . . . . . 88
4.6.1 Rankine Cycle . . . . . . . . . . . . . . . . . . . 88
4.6.2 Otto Cycle . . . . . . . . . . . . . . . . . . . . . 88
4.6.3 Diesel Cycle . . . . . . . . . . . . . . . . . . . . . 89
4.7 Calculation of Entropy Change . . . . . . . . . . . . . . 90
4.7.1 Phase Transition and Entropy Change . . . . . . 90
4.7.2 Entropy Changes of an Ideal Gas . . . . . . . . . 91
4.8 Free Energies . . . . . . . . . . . . . . . . . . . . . . . . 93
4.8.1 Helmholtz Free Energy . . . . . . . . . . . . . . 93
4.8.2 Gibbs Free Energy . . . . . . . . . . . . . . . . . 93
4.9 Maxwell’s Relations . . . . . . . . . . . . . . . . . . . . 93
5. Equilibrium Conditions and Thermodynamic Stability 103
5.1 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . 106
5.3 Stability of Equilibrium . . . . . . . . . . . . . . . . . . . 112
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6. The Third Law of Thermodynamics 115
7. Thermodynamics of Mixtures and Open Systems 121
7.1 Chemical Potentials . . . . . . . . . . . . . . . . . . . . . 121
7.1.1 The Gibbs Theory . . . . . . . . . . . . . . . . . 121
7.1.2 Alternative Consideration . . . . . . . . . . . . . 123
7.1.3 Fundamental Relations for Open Systems . . . . 124
7.2 Partial Molar Properties . . . . . . . . . . . . . . . . . . 125
7.3 Measurement of Partial Molar Properties . . . . . . . . . 130
7.3.1 Method of Intercepts . . . . . . . . . . . . . . . . 131
7.3.2 Direct Method . . . . . . . . . . . . . . . . . . . 132
7.3.3 Method of Apparent Molar Property . . . . . . . 133
7.3.4 Density Dependence of Mi . . . . . . . . . . . . 133
8. Heterogeneous Equilibria 135
8.1 Equilibrium Conditions for a Multiphase System . . . . . 135
8.1.1 Mechanical Equilibrium . . . . . . . . . . . . . . 137
8.1.2 Thermal Equilibrium . . . . . . . . . . . . . . . . 139
8.1.3 Material Equilibrium . . . . . . . . . . . . . . . . 140
8.2 Gibbs Phase Rule . . . . . . . . . . . . . . . . . . . . . . 143
8.3 One-Component, Two-Phase Systems . . . . . . . . . . . 144
8.3.1 Vapor Pressure and Measurement of Äh . . . . . 147
8.3.2 Ramsay–Young Rule . . . . . . . . . . . . . . . . 148
8.4 Two-Component Systems . . . . . . . . . . . . . . . . . . 151
9. Thermodynamics of Real Fluids 159
9.1 Constitutive Equations . . . . . . . . . . . . . . . . . . . 159
9.1.1 Ideal Gas Equation of State . . . . . . . . . . . . 161
9.1.2 Caloric Equation of State . . . . . . . . . . . . . 161
9.1.3 Ratio of Specific Heats and Compressibility . . . 162
9.1.4 Sound Wave Velocity and Polytropic Ratio . . . 163
9.2 Virial Equation of State . . . . . . . . . . . . . . . . . . 166
9.3 van der Waals Equation of State . . . . . . . . . . . . . . 168
9.4 Law of Corresponding States . . . . . . . . . . . . . . . . 172
9.5 Thermodynamic Functions . . . . . . . . . . . . . . . . . 173
9.5.1 Reversible Work . . . . . . . . . . . . . . . . . . 174
9.5.2 Heat Change in Isothermal Expansion . . . . . . 175
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xii Chemical Thermodynamics
9.5.3 Standard States . . . . . . . . . . . . . . . . . . 176
9.5.4 Enthalpy . . . . . . . . . . . . . . . . . . . . . . 177
9.5.5 Internal Energy . . . . . . . . . . . . . . . . . . . 181
9.5.6 Entropy . . . . . . . . . . . . . . . . . . . . . . . 184
9.5.6.1 Real Gases . . . . . . . . . . . . . . . . 185
9.5.6.2 Substances in Condensed Phase . . . . 187
9.5.7 Gibbs Free Energy . . . . . . . . . . . . . . . . . 188
9.6 Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
9.7 Joule–Thomson Experiment . . . . . . . . . . . . . . . . 193
9.8 Liquefaction of Gases . . . . . . . . . . . . . . . . . . . . 198
9.9 Entropy Surface . . . . . . . . . . . . . . . . . . . . . . . 200
9.9.1 Ideal Gas . . . . . . . . . . . . . . . . . . . . . . 201
9.9.2 van der Waals Gas . . . . . . . . . . . . . . . . . 202
10. Canonical Equation of State 205
10.1 Canonical Equation of State . . . . . . . . . . . . . . . . 206
10.2 Reduced Variables . . . . . . . . . . . . . . . . . . . . . . 208
10.3 Reduced Canonical Equation of State . . . . . . . . . . . 210
10.4 Models for the GvdW Parameters . . . . . . . . . . . . . 211
10.4.1 Subcritical Regime . . . . . . . . . . . . . . . . . 211
10.4.2 Supercritical Regime . . . . . . . . . . . . . . . . 213
10.5 Reduced Chemical Potential . . . . . . . . . . . . . . . . 213
10.6 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . 215
10.7 Virial and Joule–Thomson Coefficients . . . . . . . . . . 216
10.7.1 Virial Coefficients . . . . . . . . . . . . . . . . . 217
10.7.2 Joule–Thomson Coefficient . . . . . . . . . . . . 218
10.7.3 Asymptotic Behavior of the Second
Virial Coefficient . . . . . . . . . . . . . . . . . . 219
10.8 Stability Conditions of Mechanical and
Material Equilibria . . . . . . . . . . . . . . . . . . . . . 219
10.8.1 Classical Definition of Critical Point . . . . . . . 219
10.8.2 Extended Definition . . . . . . . . . . . . . . . . 220
10.9 Critical Properties of Fluids . . . . . . . . . . . . . . . . 222
10.9.1 Critical Point . . . . . . . . . . . . . . . . . . . . 222
10.9.2 Critical Isotherm for Pressure . . . . . . . . . . . 223
10.9.3 Spinodal Curve . . . . . . . . . . . . . . . . . . . 225
10.9.4 Excess Chemical Potential . . . . . . . . . . . . . 227
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Contents xiii
10.9.5 Liquid–Vapor Coexistence Curve . . . . . . . . . 231
10.9.5.1 Equilibrium Conditions . . . . . . . . . 231
10.9.5.2 Coexistence Curve . . . . . . . . . . . . 232
10.9.6 Excess Heat Capacity . . . . . . . . . . . . . . . 235
10.9.7 Isothermal Compressibility . . . . . . . . . . . . 237
10.10 Quadratic Model . . . . . . . . . . . . . . . . . . . . . . 238
10.10.1 Subcritical Regime . . . . . . . . . . . . . . . . . 238
10.10.2 Supercritical Regime . . . . . . . . . . . . . . . . 240
10.10.3 Critical Point . . . . . . . . . . . . . . . . . . . . 241
10.10.4 Critical Isotherms . . . . . . . . . . . . . . . . . 242
10.10.5 Spinodal Curve . . . . . . . . . . . . . . . . . . . 242
10.11 Concluding Remarks . . . . . . . . . . . . . . . . . . . . 243
11. Thermodynamics of Real Gas Mixtures 247
11.1 Chemical Potentials for Mixtures . . . . . . . . . . . . . 247
11.2 Entropy of Mixing . . . . . . . . . . . . . . . . . . . . . . 253
11.3 Heat of Mixing . . . . . . . . . . . . . . . . . . . . . . . 256
11.4 Activity and Activity Coefficient . . . . . . . . . . . . . . 257
11.5 Canonical Equation of State for a Mixture . . . . . . . . 260
12. Chemical Equilibria 265
12.1 A Single Reaction . . . . . . . . . . . . . . . . . . . . . . 265
12.2 Coupled Chemical Reactions . . . . . . . . . . . . . . . 268
12.3 Chemical Reactions in a Multiphase System . . . . . . . 269
12.4 Equilibrium Constant . . . . . . . . . . . . . . . . . . . . 271
12.5 van’t Hoff Equation . . . . . . . . . . . . . . . . . . . . . 273
12.6 Equilibrium Constant for Real Gases . . . . . . . . . . . 276
13. Thermodynamics of Solutions 279
13.1 Chemical Potentials of Solutions . . . . . . . . . . . . . . 279
13.2 Ideal Solutions . . . . . . . . . . . . . . . . . . . . . . . . 283
13.3 Raoult’s Law . . . . . . . . . . . . . . . . . . . . . . . . . 286
13.4 Two-Component, Two-Phase Equilibrium
Reconsidered . . . . . . . . . . . . . . . . . . . . . . . . . 289
13.5 Margules Expansions . . . . . . . . . . . . . . . . . . . . 293
13.6 Regular Solutions . . . . . . . . . . . . . . . . . . . . . . 295
13.7 Real Solutions . . . . . . . . . . . . . . . . . . . . . . . . 298
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xiv Chemical Thermodynamics
13.8 Osmotic Coefficient of Bjerrum . . . . . . . . . . . . . . 303
13.9 Determination of Activity Coefficients . . . . . . . . . . 307
13.9.1 Vapor Fugacity . . . . . . . . . . . . . . . . . . . 308
13.9.2 Freezing Point Depression . . . . . . . . . . . . . 308
13.9.3 Boiling Point Elevation . . . . . . . . . . . . . . 313
13.9.4 Osmotic Pressure . . . . . . . . . . . . . . . . . . 317
13.9.5 Solubility . . . . . . . . . . . . . . . . . . . . . . 319
14. Thermodynamics of Surfaces 323
14.1 Dividing Surface . . . . . . . . . . . . . . . . . . . . . . . 324
14.2 Gibbs Relation for Interface . . . . . . . . . . . . . . . . 325
14.3 Nearly Planar Surface and Surface Tension . . . . . . . . 331
14.4 Gibbs–Duhem Relation for Interface . . . . . . . . . . . . 334
14.5 Location of the Dividing Surface and
Surface Tension . . . . . . . . . . . . . . . . . . . . . . . 335
14.6 Gibbs Phase Rule Including Interface . . . . . . . . . . . 336
14.7 Thermodynamics of Interface . . . . . . . . . . . . . . . 337
14.7.1 Invariance of Derivatives to the Position
of the Dividing Surface . . . . . . . . . . . . . . 337
14.7.2 Various Thermodynamic Relations
for Interface . . . . . . . . . . . . . . . . . . . . . 339
14.7.3 Liquid–Vapor Equilibrium . . . . . . . . . . . . . 340
14.7.3.1 Density Dependence of ã . . . . . . . . 340
14.7.3.2 Temperature Dependence of ã . . . . . 342
15. Electrolyte Solutions 345
15.1 Mean Activity and Mean Activity Coefficient . . . . . . 346
15.2 Isopiestic Method . . . . . . . . . . . . . . . . . . . . . . 348
15.3 Activity Coefficient from Freezing Point
Measurement . . . . . . . . . . . . . . . . . . . . . . . . 351
15.4 Activity Coefficient from Osmotic Pressure
Measurement . . . . . . . . . . . . . . . . . . . . . . . . 352
16. Debye–H¨uckel Theory of Strong Electrolyte Solutions 355
16.1 Ionic Atmosphere . . . . . . . . . . . . . . . . . . . . . . 356
16.2 Mean Potential and the Excess Free Energy . . . . . . . 357
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Contents xv
17. Galvanic Cells and Electromotive Forces 363
17.1 Reversible Galvanic Cells and Reversible Electrodes . . . 363
17.2 Electrochemical Potentials . . . . . . . . . . . . . . . . . 364
17.3 Galvanic Cells Without Liquid Junction . . . . . . . . . 366
17.3.1 Cell Diagrams and the Sign Convention . . . . . 367
17.4 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 371
17.5 Donnan Membrane Equilibrium . . . . . . . . . . . . . . 376
18. Thermodynamics of Electric and Magnetic Fields 379
18.1 Dielectrics in Electrostatic Field . . . . . . . . . . . . . . 379
18.2 Field Dependence of Thermodynamic Quantities . . . . . 384
18.2.1 Electrostriction . . . . . . . . . . . . . . . . . . . 384
18.2.2 Electrocaloric Effects . . . . . . . . . . . . . . . . 385
18.3 Static Magnetic Fields . . . . . . . . . . . . . . . . . . . 387
18.3.1 Magnetostriction . . . . . . . . . . . . . . . . . . 389
18.3.2 Magnetocaloric Effects . . . . . . . . . . . . . . . 389
19. Thermodynamics of Nonequilibrium Processes 393
19.1 Extended Gibbs Relation for Calortropy . . . . . . . . . 393
19.1.1 Differential Form for Calortropy . . . . . . . . . 395
19.1.2 Variables in the Tangent Manifold . . . . . . . . 398
19.1.2.1 Nonequilibrium Effect
on Temperature . . . . . . . . . . . . . 399
19.1.2.2 Nonequilibrium Effect on
Pressure . . . . . . . . . . . . . . . . . 400
19.1.2.3 Nonequilibrium Effect on
Chemical Potentials . . . . . . . . . . . 400
19.1.2.4 Nonequilibrium Effect on
Equilibrium Constants . . . . . . . . . 402
19.2 Flow of a Non-Newtonian Liquid . . . . . . . . . . . . . 403
19.2.1 Velocity Profile of Flow in a
Rectangular Channel . . . . . . . . . . . . . . . . 404
19.2.1.1 The Case of px =0 . . . . . . . . . . . 406
19.2.1.2 The Case of px =0 . . . . . . . . . . . 407
19.2.2 Non-Newtonian Viscosity . . . . . . . . . . . . . 409
19.3 Chemical Oscillations and Pattern Formation . . . . . . 412
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xvi Chemical Thermodynamics
Appendix A Local Form of Energy Conservation Law 425
Appendix B Various Coefficients Used in Chapter 10 431
B.1 Coefficients of Ð(i)(xsk, t) . . . . . . . . . . . . . . . . . . 431
B.2 Coefficients Pij . . . . . . . . . . . . . . . . . . . . . . . 432
B.3 Coefficients Ð(i)
j (t) . . . . . . . . . . . . . . . . . . . . . 433
B.4 Coefficients of the Spinodal Equations . . . . . . . . . . 436
Index 441