Table of Contents
Dedication v
Preface of the Second Edition vii
Preface of the First Edition ix
About the Authors xi
1 Scope 1
2 Why non-equilibrium thermodynamics? 7
2.1 Simple flux equations 8
2.2 Flux equations in non-equilibrium thermodynamics 10
2.3 The lost work of an industrial plant 13
2.4 The second law efficiency. The energy destruction footprint 18
2.5 Consistent thermodynamic modeling 21
3 The entropy production of one-dimensional transport processes 23
3.1 Balance equations 25
3.2 Entropy production 27
3.3 Examples 31
3.4 The frame of reference for fluxes 38
4 Flux equations and transport coefficients 41
4.1 Linear flux-force relations 42
4.2 Transport of heat and mass 45
4.3 Transport of heat and charge 52
4.4 Transport of mass and charge 58
4.4.1 The mobility model 62
4.5 Concluding remarks 63
5 Non-isothermal multi-component diffusion 65
5.1 Isothermal diffusion 66
5.1.1 Prigogine's theorem applied 67
5.1.2 Diffusion in the solvent frame of reference 68
5.1.3 Maxwell-Stefan equations 70
5.1.4 Changing a frame of reference 73
5.2 Non-isothermal diffusion 77
5.3 Concluding remarks 80
6 Systems with shear flow 81
6.1 Balance equations 82
6.1.1 Component balances 82
6.1.2 Momentum balance 82
6.1.3 Internal energy balance 83
6.2 Entropy production 83
6.3 Stationary pipe flow 91
6.4 The plug flow reactor 93
6.5 Transport coefficients: viscosity and thermal conductivity 94
6.6 Concluding remarks 97
7 Chemical reactions 99
7.1 The Gibbs energy change of a chemical reaction 101
7.2 The reaction path 105
7.2.1 The chemical potential 106
7.2.2 The entropy production 108
7.3 A rate equation with a thermodynamic basis 108
7.4 The law of mass action 110
7.5 The entropy production on the mesoscopic scale 112
7.6 Concluding remarks 114
8 The lost work in the aluminum electrolysis 115
8.1 The aluminum electrolysis cell 116
8.2 The thermodynamic efficiency 118
8.3 A simplified cell model 120
8.4 Lost work due to charge transfer 122
8.4.1 The bulk electrolyte 122
8.4.2 The diffusion layer at the cathode 122
8.4.3 The electrode surfaces 123
8.4.4 The bulk part of the anode and cathode 123
8.5 Lost work by excess carbon consumption 124
8.6 Lost work due to heat transport through the walls 125
8.6.1 Conduction across the walls 125
8.6.2 Surface radiation and convection 127
8.7 The energy destruction footprint 127
8.8 Concluding remarks 129
9 Coupled transport through surfaces 131
9.1 The Gibbs surface in local equilibrium 132
9.2 Balance equations 134
9.3 The excess entropy production 138
9.4 Stationary state evaporation and condensation 144
9.5 Equilibrium at the electrode surface. Nernst equation 147
9.6 Stationary states at electrode surfaces. The overpotential 149
9.7 Concluding remarks 151
10 Transport through membranes 153
10.1 Introduction 153
10.2 Osmosis 154
10.3 Thermal osmosis 156
10.3.1 Water and power production 157
10.4 Electro-osmosis at constant temperature 158
10.4.1 Contributions from the electrodes 159
10.4.2 Contributions from the membrane 159
10.5 Transport of ions and water across ion-exchange membranes 161
10.5.1 The isothermal, isobaric system 162
10.5.2 The isothermal, non-isobaric system 164
10.5.3 The non-isothermal, isobaric system 165
10.6 The salt power plant 168
10.7 Concluding remarks 170
11 The state of minimum entropy production 171
11.1 Isothermal expansion of an ideal gas 173
11.1.1 Expansion work 174
11.1.2 The entropy production 176
11.1.3 The optimization idea 177
11.2 Optimal control theory 179
11.3 Heat exchange 183
11.3.1 The entropy production 185
11.3.2 Optimal control theory and heat exchange 187
11.4 The plug now reactor 191
11.4.1 The entropy production 192
11.4.2 Optimal control theory and plug flow reactors 196
11.4.3 A highway in state space 197
11.4.4 Reactor design 201
11.5 Distillation columns 203
11.5.1 The entropy production 205
11.5.2 The state of minimum entropy production 207
11.5.3 Column design 212
11.6 Concluding remarks 214
Appendix A 217
A.1 Balance equations for mass, charge, momentum and energy 217
A.1.1 Mass balance 218
A.1.2 Momentum balance 220
A.1.3 Total energy balance 222
A.1.4 Kinetic energy balance 223
A.1.5 Potential energy balance 223
A.1.6 Balance of the electric field energy 224
A.1.7 Internal energy balance 224
A.1.8 Entropy balance 225
A.2 Partial molar thermodynamic properties 228
A.3 The chemical potential and its reference states 230
A.3.1 The equation of state as a basis 231
A.3.2 The excess Gibbs energy as a basis 232
A.3.3 Henry's law as a basis 233
A.4 Chemical driving forces and equilibrium constants 234
A.4.1 The ideal gas reference state 235
A.4.2 The pure liquid reference state 236
A.5 Minimizing the total entropy production of a K-step expansion process 237
A.6 The work production by a heat exchanger 239
A.7 Equipartition theorems 241
Bibliography 249
List of Symbols 267
Index 273
