Non-equilibrium thermodynamics of heterogeneous systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hackensack, NJ [u.a.]
World Scientific
2008
|
| Series: | Series on advances in statistical mechanics
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 393 - 413 |
| Physical Description: | XV, 434 S. Ill., graph. Darst. |
| ISBN: | 9789812779137 9812779132 |
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MARC
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| 100 | 1 | |a Kjelstrup, Signe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Non-equilibrium thermodynamics of heterogeneous systems |c Signe Kjelstrup ; Dick Bedeaux |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XV, 434 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in statistical mechanics |v 16 | |
| 500 | |a Literaturverz. S. 393 - 413 | ||
| 650 | 4 | |a Termodinámica de no equilibrio | |
| 650 | 4 | |a Nonequilibrium thermodynamics | |
| 650 | 0 | 7 | |a Nichtgleichgewichtsthermodynamik |0 (DE-588)4130850-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transportprozess |0 (DE-588)4185932-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Heterogenes System |0 (DE-588)4159737-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Heterogenes System |0 (DE-588)4159737-0 |D s |
| 689 | 0 | 1 | |a Transportprozess |0 (DE-588)4185932-7 |D s |
| 689 | 0 | 2 | |a Nichtgleichgewichtsthermodynamik |0 (DE-588)4130850-5 |D s |
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| 700 | 1 | |a Bedeaux, Dick |d 1941- |e Verfasser |0 (DE-588)1011535602 |4 aut | |
| 830 | 0 | |a Series on advances in statistical mechanics |v 16 |w (DE-604)BV000019119 |9 16 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016992226 | ||
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| _version_ | 1804138360927682560 |
|---|---|
| adam_text | Contents
Preface
vu
1
Scope
1
1.1
What is non-equilibrium thermodynamics?
......... 1
1.2
Non-equilibrium thermodynamics in the context of
other theories
......................... 4
1.3
The purpose of this book
................... 4
2
Why Non-Equilibrium Thermodynamics?
7
2.1
Simple flux equations
..................... 8
2.2
Flux equations with coupling terms
............. 9
2.3
Experimental designs and controls
.............. 11
2.4
Entropy production, work and lost work
.......... 12
2.5
Consistent thermodynamic models
.............. 14
3
Thermodynamic Relations for Heterogeneous Systems
17
3.1
Two homogeneous phases separated by a surface in global
equilibrium
........................... 18
3.2
The contact line in global equilibrium
............ 22
3.3
Defining thermodynamic variables for the surface
..... 23
3.4
Local thermodynamic identities
............... 29
3.5
Defining local equilibrium
.................. 32
3.A Appendix: Partial molar properties
............. 35
3.A.1 Homogeneous phases
................. 36
3.A.2 The surface
...................... 38
3.A.3 The standard state
.................. 40
Part A: General Theory
45
4
The Entropy Production for a Homogeneous Phase
47
4.1
Balance equations
....................... 49
4.2
The entropy production
.................... 51
χ
Contents
4.2.1
Why one should not use the dissipation function
. 56
4.2.2
States with minimum entropy production
..... 57
4.3
Examples
............................ 58
4.4
Frames of reference for fluxes in homogeneous systems
. . 64
4.4.1
Definitions of frames of reference
.......... 64
4.4.2
Transformations between the frames of reference
. 66
4.A Appendix: The first law and the heat flux
......... 67
5
The Excess Entropy Production for the Surface
73
5.1
The discrete nature of the surface
.............. 74
5.2
The behavior of the electric fields and potential through the
surface
............................. 75
5.3
Balance equations
....................... 77
5.4
The excess entropy production
................ 79
5.4.1
Reversible processes at the interface and the Nernst
equation
....................... 84
5.4.2
The surface potential jump at the hydrogen
electrode
....................... 86
5.5
Examples
............................ 87
6
The Excess Entropy Production for a Three Phase
Contact Line
91
6.1
The discrete nature of the contact line
........... 92
6.2
Balance equations
....................... 94
6.3
The excess entropy production
................ 95
6.4
Stationary states
....................... 96
6.5
Concluding comment
..................... 97
7
Flux Equations and Onsager Relations
99
7.1
Flux-force relations
...................... 99
7.2
Onsager s reciprocal relations
................ 100
7.3
Relaxation to equilibrium. Consequences of violating
Onsager relations
....................... 104
7.4
Force-flux relations
...................... 105
7.5
Coefficient bounds
...................... 106
7.6
The Curie principle applied to surfaces and contact lines
. 108
8
Transport of Heat and Mass 111
8.1
The homogeneous phases
................... 112
8.2
Coefficient values for homogeneous phases
......... 114
8.3
The surface
.......................... 117
8.3.1
Heats of transfer for the surface
.......... 119
Contents xj
8.4
Solution
for the heterogeneous system
............ 122
8.5
Scaling relations between surface and bulk resistivities
. . 125
9
Transport of Heat and Charge
127
9.1
The homogeneous phases
................... 128
9.2
The surface
.......................... 130
9.3
Thermoelectric coolers
.................... 132
9.4
Thermoelectric generators
.................. 133
9.5
Solution for the heterogeneous system
............ 135
10
Transport of Mass and Charge
139
10.1
The electrolyte
......................... 140
10.2
The electrode surfaces
.................... 143
10.3
Solution for the heterogeneous system
............ 146
10.4
A salt power plant
...................... 147
10.5
Electric power from volume flow
............... 148
10.6
Ionic mobility model for the electrolyte
........... 150
10.7
Ionic and electronic model for the surface
.......... 154
Part B: Applications
155
11
Evaporation and Condensation
157
11.1
Evaporation and condensation in a pure fluid
....... 158
11.1.1
The entropy production and the flux equations
. . 158
11.1.2
Interface resistivities from kinetic theory
..... 165
11.2
The sign of the heats of transfer of the surface
....... 167
11.3
Coefficients from molecular dynamics simulations
..... 169
11.4
Evaporation and condensation in a two-component fluid
. 176
11.4.1
The entropy production and the flux equations
. . 176
11.4.2
Interface resistivities from kinetic theory
..... 179
12
Multi-Component Heat and Mass Diffusion
183
12.1
The homogeneous phases
................... 184
12.2
The Maxwell-Stefan equations for multi-component
diffusion
............................ 186
12.3
The Maxwell-Stefan equations for the surface
....... 188
12.4
Multi-component diffusion
.................. 192
12.4.1
Prigogine s theorem
................. 192
12.4.2
Diffusion in the solvent frame of reference
..... 193
12.4.3
Other frames of reference
.............. 195
12.4.4
An example: Kinetic demixing of oxides
...... 200
xii Contents
12.5
A relation between the heats of transfer and
the enthalpy
.......................... 202
13
A Nonisothermal Concentration Cell
205
13.1
The homogeneous phases
................... 207
13.1.1
Entropy production and flux equations for
the anode
....................... 207
13.1.2
Position dependent transport coefficients
..... 210
13.1.3
The profiles of the homogeneous anode
...... 211
13.1.4
Contributions from the cathode
.......... 212
13.1.5
The electrolyte contribution
............ 213
13.2
Surface contributions
..................... 214
13.2.1
The anode surface
.................. 214
13.2.2
The cathode surface
................ 217
13.3
The thermoelectric potential
................ 218
14
The Transported Entropy
221
14.1
The Seebeck coefficient of cell a
............... 222
14.2
The transported entropy of Pb2+ in cell a
......... 226
14.3
The transported entropy of the cation in cell
b
....... 227
14.4
The transported entropy of the ions cell
с
......... 228
14.5
Transformation properties
.................. 230
14.6
Concluding comments
..................... 232
15
Adiabatic Electrode Reactions
235
15.1
The homogeneous phases
................... 236
15.1.1
The silver phases
................... 236
15.1.2
The silver chloride phases
.............. 236
15.1.3
The electrolyte
.................... 237
15.2
The interfaces
......................... 237
15.2.1
The silver-silver chloride interfaces
......... 237
15.2.2
The silver chloride-electrolyte interfaces
...... 239
15.3
Temperature and electric potential profiles
......... 240
16
The Liquid Junction Potential
249
16.1
The flux equations for the electrolyte
............ 250
16.2
The liquid junction potential
................. 253
16.3
Liquid junction potential calculations compared
...... 255
16.4
Concluding comments
..................... 258
Contents xjjj
17 The Formation
Cell
261
17.1
The isothermal cell......................
263
17.1.1
The electromotive force
............... 263
17.1.2
The transference coefficient of the salt in
the electrolyte
.................... 263
17.1.3
An electrolyte with a salt concentration gradient
. 265
17.1.4
The Planck potential derived from ionic fluxes
and forces
....................... 267
17.2
A non-isothermal cell with a non-uniform electrolyte
. . . 268
17.2.1
The homogeneous anode phase
........... 269
17.2.2
The electrolyte
.................... 270
17.2.3
The surface of the anode
.............. 272
17.2.4
The homogeneous phases and the surface of
the cathode
...................... 273
17.2.5
The cell potential
.................. 275
17.3
Concluding comments
..................... 275
18
Power from Regular and Thermal Osmosis
277
18.1
The potential work of a salt power plant
.......... 277
18.2
The membrane as a barrier to transport of heat
and mass
............................ 279
18.3
Membrane transport of heat and mass
........... 281
18.4
Osmosis
............................ 283
18.5
Thermal osmosis
........................ 285
19
Modeling the Polymer Electrolyte Fuel Cell
289
19.1
The potential work of a fuel cell
............... 290
19.2
The cell and its five subsystems
............... 291
19.3
The electrode backing and the membrane
.......... 293
19.3.1
The entropy production in the homogeneous
phases
......................... 293
19.3.2
The anode backing
.................. 295
19.3.3
The membrane
.................... 298
19.3.4
The cathode backing
................ 300
19.4
The electrode surfaces
.................... 301
19.4.1
The anode catalyst surface
............. 304
19.4.2
The cathode catalyst surface
............ 306
19.5
A model in agreement with the second law
......... 307
19.6
Concluding comments
..................... 310
xiv Contents
20
Measuring
Membrane Transport
Properties
311
20.1
The membrane in equilibrium with electrolyte solutions
. . 312
20.2
The membrane resistivity
................... 312
20.3
Ionic transport numbers
................... 316
20.4
The transference number of water and the
water permeability
...................... 319
20.5
The Seebeck coefficient
.................... 322
20.6
Interdiffusion
coefficients
................... 323
21
The Impedance of an Electrode Surface
327
21.1
The hydrogen electrode. Mass balances
........... 328
21.2
The oscillating field
...................... 331
21.3
Reaction Gibbs energies
................... 332
21.4
The electrode surlace impedance
............... 332
21.4.1
The adsorption-diffusion layer in front of
the catalyst
...................... 332
21.4.2
The charge transfer reaction
............ 336
21.4.3
The impedance spectrum
.............. 337
21.5
A test of the model
...................... 338
21.6
The reaction overpotential
.................. 339
22
Non-Equilibrium Molecular Dynamics Simulations
341
22.1
The system
.......................... 344
22.1.1
The interaction potential
.............. 346
22.2
Calculation techniques
.................... 347
22.3
Verifying the assumption of local equilibrium
........ 351
22.3.1
Local equilibrium in a homogeneous binary
mixture
........................ 351
22.3.2
Local equilibrium in a gas-liquid interface
..... 353
22.4
Verifications of the Onsager relations
............ 356
22.4.1
A homogeneous binary mixture
........... 356
22.4.2
A gas-liquid interface
................ 358
22.5
Linearity of the flux-force relations
............. 359
22.6
Molecular mechanisms
.................... 359
23
The Non-Equilibrium Two-Phase van
der Waals
Model
361
23.1
Van
der Waals
equation of states
.............. 363
23.2
Van
der Waals
square gradient model for the
interfacial
region
.............................. 366
23.3
Balance equations
....................... 369
23.4
The entropy production
.................... 371
23.5
Flux equations
......................... 372
Contents xv
23.6
A numerical solution method
................. 373
23.7
Procedure for extrapolation of bulk densities and fluxes
. . 376
23.8
Defining excess densities
................... 378
23.9
Thermodynamic properties of Gibbs surface
........ 379
23.10
An autonomous surface
.................... 380
23.11
Excess densities depend on the choice of dividing surface
. 384
23.11.1
Properties of dividing surfaces
........... 384
23.11.2
Surface excess densities for two dividing
surfaces
........................ 385
23.11.3
The surface temperature from excess
density differences
.................. 386
23.12
The entropy balance and the excess entropy production
. . 388
23.13
Resistivities to heat and mass transfer
........... 390
23.14
Concluding comments
. .................... 392
References
393
Symbol Lists
415
Index
423
About the Authors
433
|
| adam_txt |
Contents
Preface
vu
1
Scope
1
1.1
What is non-equilibrium thermodynamics?
. 1
1.2
Non-equilibrium thermodynamics in the context of
other theories
. 4
1.3
The purpose of this book
. 4
2
Why Non-Equilibrium Thermodynamics?
7
2.1
Simple flux equations
. 8
2.2
Flux equations with coupling terms
. 9
2.3
Experimental designs and controls
. 11
2.4
Entropy production, work and lost work
. 12
2.5
Consistent thermodynamic models
. 14
3
Thermodynamic Relations for Heterogeneous Systems
17
3.1
Two homogeneous phases separated by a surface in global
equilibrium
. 18
3.2
The contact line in global equilibrium
. 22
3.3
Defining thermodynamic variables for the surface
. 23
3.4
Local thermodynamic identities
. 29
3.5
Defining local equilibrium
. 32
3.A Appendix: Partial molar properties
. 35
3.A.1 Homogeneous phases
. 36
3.A.2 The surface
. 38
3.A.3 The standard state
. 40
Part A: General Theory
45
4
The Entropy Production for a Homogeneous Phase
47
4.1
Balance equations
. 49
4.2
The entropy production
. 51
χ
Contents
4.2.1
Why one should not use the dissipation function
. 56
4.2.2
States with minimum entropy production
. 57
4.3
Examples
. 58
4.4
Frames of reference for fluxes in homogeneous systems
. . 64
4.4.1
Definitions of frames of reference
. 64
4.4.2
Transformations between the frames of reference
. 66
4.A Appendix: The first law and the heat flux
. 67
5
The Excess Entropy Production for the Surface
73
5.1
The discrete nature of the surface
. 74
5.2
The behavior of the electric fields and potential through the
surface
. 75
5.3
Balance equations
. 77
5.4
The excess entropy production
. 79
5.4.1
Reversible processes at the interface and the Nernst
equation
. 84
5.4.2
The surface potential jump at the hydrogen
electrode
. 86
5.5
Examples
. 87
6
The Excess Entropy Production for a Three Phase
Contact Line
91
6.1
The discrete nature of the contact line
. 92
6.2
Balance equations
. 94
6.3
The excess entropy production
. 95
6.4
Stationary states
. 96
6.5
Concluding comment
. 97
7
Flux Equations and Onsager Relations
99
7.1
Flux-force relations
. 99
7.2
Onsager's reciprocal relations
. 100
7.3
Relaxation to equilibrium. Consequences of violating
Onsager relations
. 104
7.4
Force-flux relations
. 105
7.5
Coefficient bounds
. 106
7.6
The Curie principle applied to surfaces and contact lines
. 108
8
Transport of Heat and Mass 111
8.1
The homogeneous phases
. 112
8.2
Coefficient values for homogeneous phases
. 114
8.3
The surface
. 117
8.3.1
Heats of transfer for the surface
. 119
Contents xj
8.4
Solution
for the heterogeneous system
. 122
8.5
Scaling relations between surface and bulk resistivities
. . 125
9
Transport of Heat and Charge
127
9.1
The homogeneous phases
. 128
9.2
The surface
. 130
9.3
Thermoelectric coolers
. 132
9.4
Thermoelectric generators
. 133
9.5
Solution for the heterogeneous system
. 135
10
Transport of Mass and Charge
139
10.1
The electrolyte
. 140
10.2
The electrode surfaces
. 143
10.3
Solution for the heterogeneous system
. 146
10.4
A salt power plant
. 147
10.5
Electric power from volume flow
. 148
10.6
Ionic mobility model for the electrolyte
. 150
10.7
Ionic and electronic model for the surface
. 154
Part B: Applications
155
11
Evaporation and Condensation
157
11.1
Evaporation and condensation in a pure fluid
. 158
11.1.1
The entropy production and the flux equations
. . 158
11.1.2
Interface resistivities from kinetic theory
. 165
11.2
The sign of the heats of transfer of the surface
. 167
11.3
Coefficients from molecular dynamics simulations
. 169
11.4
Evaporation and condensation in a two-component fluid
. 176
11.4.1
The entropy production and the flux equations
. . 176
11.4.2
Interface resistivities from kinetic theory
. 179
12
Multi-Component Heat and Mass Diffusion
183
12.1
The homogeneous phases
. 184
12.2
The Maxwell-Stefan equations for multi-component
diffusion
. 186
12.3
The Maxwell-Stefan equations for the surface
. 188
12.4
Multi-component diffusion
. 192
12.4.1
Prigogine's theorem
. 192
12.4.2
Diffusion in the solvent frame of reference
. 193
12.4.3
Other frames of reference
. 195
12.4.4
An example: Kinetic demixing of oxides
. 200
xii Contents
12.5
A relation between the heats of transfer and
the enthalpy
. 202
13
A Nonisothermal Concentration Cell
205
13.1
The homogeneous phases
. 207
13.1.1
Entropy production and flux equations for
the anode
. 207
13.1.2
Position dependent transport coefficients
. 210
13.1.3
The profiles of the homogeneous anode
. 211
13.1.4
Contributions from the cathode
. 212
13.1.5
The electrolyte contribution
. 213
13.2
Surface contributions
. 214
13.2.1
The anode surface
. 214
13.2.2
The cathode surface
. 217
13.3
The thermoelectric potential
. 218
14
The Transported Entropy
221
14.1
The Seebeck coefficient of cell a
. 222
14.2
The transported entropy of Pb2+ in cell a
. 226
14.3
The transported entropy of the cation in cell
b
. 227
14.4
The transported entropy of the ions cell
с
. 228
14.5
Transformation properties
. 230
14.6
Concluding comments
. 232
15
Adiabatic Electrode Reactions
235
15.1
The homogeneous phases
. 236
15.1.1
The silver phases
. 236
15.1.2
The silver chloride phases
. 236
15.1.3
The electrolyte
. 237
15.2
The interfaces
. 237
15.2.1
The silver-silver chloride interfaces
. 237
15.2.2
The silver chloride-electrolyte interfaces
. 239
15.3
Temperature and electric potential profiles
. 240
16
The Liquid Junction Potential
249
16.1
The flux equations for the electrolyte
. 250
16.2
The liquid junction potential
. 253
16.3
Liquid junction potential calculations compared
. 255
16.4
Concluding comments
. 258
Contents xjjj
17 The Formation
Cell
261
17.1
The isothermal cell.
263
17.1.1
The electromotive force
. 263
17.1.2
The transference coefficient of the salt in
the electrolyte
. 263
17.1.3
An electrolyte with a salt concentration gradient
. 265
17.1.4
The Planck potential derived from ionic fluxes
and forces
. 267
17.2
A non-isothermal cell with a non-uniform electrolyte
. . . 268
17.2.1
The homogeneous anode phase
. 269
17.2.2
The electrolyte
. 270
17.2.3
The surface of the anode
. 272
17.2.4
The homogeneous phases and the surface of
the cathode
. 273
17.2.5
The cell potential
. 275
17.3
Concluding comments
. 275
18
Power from Regular and Thermal Osmosis
277
18.1
The potential work of a salt power plant
. 277
18.2
The membrane as a barrier to transport of heat
and mass
. 279
18.3
Membrane transport of heat and mass
. 281
18.4
Osmosis
. 283
18.5
Thermal osmosis
. 285
19
Modeling the Polymer Electrolyte Fuel Cell
289
19.1
The potential work of a fuel cell
. 290
19.2
The cell and its five subsystems
. 291
19.3
The electrode backing and the membrane
. 293
19.3.1
The entropy production in the homogeneous
phases
. 293
19.3.2
The anode backing
. 295
19.3.3
The membrane
. 298
19.3.4
The cathode backing
. 300
19.4
The electrode surfaces
. 301
19.4.1
The anode catalyst surface
. 304
19.4.2
The cathode catalyst surface
. 306
19.5
A model in agreement with the second law
. 307
19.6
Concluding comments
. 310
xiv Contents
20
Measuring
Membrane Transport
Properties
311
20.1
The membrane in equilibrium with electrolyte solutions
. . 312
20.2
The membrane resistivity
. 312
20.3
Ionic transport numbers
. 316
20.4
The transference number of water and the
water permeability
. 319
20.5
The Seebeck coefficient
. 322
20.6
Interdiffusion
coefficients
. 323
21
The Impedance of an Electrode Surface
327
21.1
The hydrogen electrode. Mass balances
. 328
21.2
The oscillating field
. 331
21.3
Reaction Gibbs energies
. 332
21.4
The electrode surlace impedance
. 332
21.4.1
The adsorption-diffusion layer in front of
the catalyst
. 332
21.4.2
The charge transfer reaction
. 336
21.4.3
The impedance spectrum
. 337
21.5
A test of the model
. 338
21.6
The reaction overpotential
. 339
22
Non-Equilibrium Molecular Dynamics Simulations
341
22.1
The system
. 344
22.1.1
The interaction potential
. 346
22.2
Calculation techniques
. 347
22.3
Verifying the assumption of local equilibrium
. 351
22.3.1
Local equilibrium in a homogeneous binary
mixture
. 351
22.3.2
Local equilibrium in a gas-liquid interface
. 353
22.4
Verifications of the Onsager relations
. 356
22.4.1
A homogeneous binary mixture
. 356
22.4.2
A gas-liquid interface
. 358
22.5
Linearity of the flux-force relations
. 359
22.6
Molecular mechanisms
. 359
23
The Non-Equilibrium Two-Phase van
der Waals
Model
361
23.1
Van
der Waals
equation of states
. 363
23.2
Van
der Waals
square gradient model for the
interfacial
region
. 366
23.3
Balance equations
. 369
23.4
The entropy production
. 371
23.5
Flux equations
. 372
Contents xv
23.6
A numerical solution method
. 373
23.7
Procedure for extrapolation of bulk densities and fluxes
. . 376
23.8
Defining excess densities
. 378
23.9
Thermodynamic properties of Gibbs' surface
. 379
23.10
An autonomous surface
. 380
23.11
Excess densities depend on the choice of dividing surface
. 384
23.11.1
Properties of dividing surfaces
. 384
23.11.2
Surface excess densities for two dividing
surfaces
. 385
23.11.3
The surface temperature from excess
density differences
. 386
23.12
The entropy balance and the excess entropy production
. . 388
23.13
Resistivities to heat and mass transfer
. 390
23.14
Concluding comments
. . 392
References
393
Symbol Lists
415
Index
423
About the Authors
433 |
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| id | DE-604.BV035185531 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:59:30Z |
| indexdate | 2024-07-09T21:26:58Z |
| institution | BVB |
| isbn | 9789812779137 9812779132 |
| language | English |
| lccn | 2008299321 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016992226 |
| oclc_num | 427535308 |
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| physical | XV, 434 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on advances in statistical mechanics |
| series2 | Series on advances in statistical mechanics |
| spelling | Kjelstrup, Signe Verfasser aut Non-equilibrium thermodynamics of heterogeneous systems Signe Kjelstrup ; Dick Bedeaux Hackensack, NJ [u.a.] World Scientific 2008 XV, 434 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in statistical mechanics 16 Literaturverz. S. 393 - 413 Termodinámica de no equilibrio Nonequilibrium thermodynamics Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd rswk-swf Transportprozess (DE-588)4185932-7 gnd rswk-swf Heterogenes System (DE-588)4159737-0 gnd rswk-swf Heterogenes System (DE-588)4159737-0 s Transportprozess (DE-588)4185932-7 s Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 s DE-604 Bedeaux, Dick 1941- Verfasser (DE-588)1011535602 aut Series on advances in statistical mechanics 16 (DE-604)BV000019119 16 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016992226&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kjelstrup, Signe Bedeaux, Dick 1941- Non-equilibrium thermodynamics of heterogeneous systems Series on advances in statistical mechanics Termodinámica de no equilibrio Nonequilibrium thermodynamics Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd Transportprozess (DE-588)4185932-7 gnd Heterogenes System (DE-588)4159737-0 gnd |
| subject_GND | (DE-588)4130850-5 (DE-588)4185932-7 (DE-588)4159737-0 |
| title | Non-equilibrium thermodynamics of heterogeneous systems |
| title_auth | Non-equilibrium thermodynamics of heterogeneous systems |
| title_exact_search | Non-equilibrium thermodynamics of heterogeneous systems |
| title_exact_search_txtP | Non-equilibrium thermodynamics of heterogeneous systems |
| title_full | Non-equilibrium thermodynamics of heterogeneous systems Signe Kjelstrup ; Dick Bedeaux |
| title_fullStr | Non-equilibrium thermodynamics of heterogeneous systems Signe Kjelstrup ; Dick Bedeaux |
| title_full_unstemmed | Non-equilibrium thermodynamics of heterogeneous systems Signe Kjelstrup ; Dick Bedeaux |
| title_short | Non-equilibrium thermodynamics of heterogeneous systems |
| title_sort | non equilibrium thermodynamics of heterogeneous systems |
| topic | Termodinámica de no equilibrio Nonequilibrium thermodynamics Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd Transportprozess (DE-588)4185932-7 gnd Heterogenes System (DE-588)4159737-0 gnd |
| topic_facet | Termodinámica de no equilibrio Nonequilibrium thermodynamics Nichtgleichgewichtsthermodynamik Transportprozess Heterogenes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016992226&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000019119 |
| work_keys_str_mv | AT kjelstrupsigne nonequilibriumthermodynamicsofheterogeneoussystems AT bedeauxdick nonequilibriumthermodynamicsofheterogeneoussystems |