Table of Contents
Preface vii
1 Scope 1
2 Why non-equilibrium thermodynamics? 7
2.1 Simple flux equations 8
2.2 Flux equations in non-equilibrium thermodynamics 11
2.3 The lost work of an industrial plant 13
2.4 The second law efficiency 19
2.5 Consistent thermodynamic models 21
3 The entropy production of one-dimensional transport processes 23
3.1 Balance equations 25
3.2 Entropy production 27
3.3 Examples 33
3.4 The frame of reference for fluxes 41
4 Flux equations and transport coefficients 45
4.1 Linear flux-force relations 46
4.2 Transport of heat and mass 49
4.3 Transport of heat and charge 58
4.4 Transport of mass and charge 63
4.4.1 The mobility model 69
4.5 Transport of volume and charge 70
4.6 Concluding remarks 73
5 Non-isothermal multi-component diffusion 75
5.1 Isothermal diffusion 76
5.1.1 Prigogine's theorem applied 77
5.1.2 Diffusion in the solvent frame of reference 78
5.1.3 Maxwell-Stefan equations 81
5.1.4 Changing a frame of reference 84
5.2 Maxwell-Stefan equations generalized 87
5.3 Concluding remarks 91
6 Systems with shear flow 93
6.1 Balance equations 94
6.1.1 Component balances 95
6.1.2 Momentum balance 95
6.1.3 Internal energy balance 96
6.2 Entropy production 98
6.3 Stationary pipe flow 104
6.3.1 The measurable heat flux 106
6.4 The plug flow reactor 107
6.5 Concluding remarks 108
7 Chemical reactions 109
7.1 The Gibbs energy change of a chemical reaction 112
7.2 The reaction path 116
7.2.1 The chemical potential 117
7.2.2 The entropy production 119
7.3 A rate equation with a thermodynamic basis 119
7.4 The law of mass action 122
7.5 The entropy production on the mesoscopic scale 124
7.6 Concluding remarks 126
8 The lost work in the aluminum electrolysis 129
8.1 The aluminum electrolysis cell 130
8.2 The thermodynamic efficiency 132
8.3 A simplified cell model 135
8.4 Lost work due to charge transfer 137
8.4.1 The bulk electrolyte 137
8.4.2 The diffusion layer at the cathode 137
8.4.3 The electrode surfaces 138
8.4.4 The bulk anode and cathode 139
8.5 Lost work by excess carbon consumption 139
8.6 Lost work due to heat transport through the walls 140
8.6.1 Conduction across the walls 141
8.6.2 Surface radiation and convection 142
8.7 A map of the lost work 143
8.8 Concluding remarks 145
9 The state of minimum entropy production and optimal control theory 147
9.1 Isothermal expansion of an ideal gas 148
9.1.1 Expansion work 150
9.1.2 The entropy production 151
9.1.3 The optimization idea 153
9.2 Optimal control theory 158
9.3 Heat exchange 163
9.3.1 The entropy production 165
9.3.2 The work production by a heat exchanger 168
9.3.3 Optimal control theory and heat exchange 171
9.4 Concluding remarks 176
10 The state of minimum entropy production in selected process units 177
10.1 The plug flow reactor 178
10.1.1 The entropy production 179
10.1.2 Optimal control theory and plug flow reactors 184
10.1.3 A highway in state space 185
10.1.4 Reactor design 191
10.2 Distillation columns 192
10.2.1 The entropy production 195
10.2.2 Column design 203
10.3 Concluding remarks 204
Appendix A 207
A.1 Balance equations for mass, charge, momentum and energy 207
A.1.1 Mass balance 208
A.1.2 Momentum balance 210
A.1.3 Total energy balance 213
A.1.4 Kinetic energy balance 214
A.1.5 Potential energy balance 215
A.1.6 Balance of the electric field energy 215
A.1.7 Internal energy balance 215
A.1.8 Entropy balance 217
A.2 Partial molar thermodynamic properties 219
A.3 The chemical potential and its reference states 222
A.3.1 The equation of state as a basis 223
A.3.2 The excess Gibbs energy as a basis 224
A.3.3 Henry's law as a basis 226
A.4 Driving forces and equilibrium constants 227
A.4.1 The ideal gas reference state 228
A.4.2 The pure liquid reference state 229
Bibliography 231
List of Symbols 245
Index 251
About the authors 259
