NON-EQUILIBRIUM THERMODYNAMICS

Transcription

1 NON-EQUILIBRIUM THERMODYNAMICS S. R. DE GROOT Professor of Theoretical Physics University of Amsterdam, The Netherlands E MAZUR Professor of Theoretical Physics University of Leiden, The Netherlands DOVER PUBLICATIONS, INC., NEW YORK

2 TABLE OF CONTENTS PREFACE TABLE OF CONTENTS V VII I INTRODUCTION 1. Historical background of non-equilibrium thermodynamics Systematic development of the theory 3 PART A. GENERAL THEORY II CONSERVATION LAWS 1. Introduction Conservation of mass The equation of motion Conservation of energy 17 III ENTROPY LAW AND ENTROPY BALANCE 1. The second law of thermodynamics The entropy balance equation Alternative expressions for the entropy production; on different definitions of the heat flow Kinetic energy of diffusion 28 IV THE PHENOMENOLOGICAL EQUATIONS 1. The linear laws Influence of symmetry properties of matter on the linear laws; Curie principle The Onsager reciprocal relations The differential equations 41 vn

3 VIII CONTENTS V THE STATIONARY STATES 1. Introduction Mechanical equilibrium Stationary states with minimum entropy production Stationary states without minimum entropy production.. 53 PROPERTIES OF THE PHENOMENOLOGICAL EQUATIONS AND THE ONSAGER RELATIONS 1. Introduction The Curie principle Dependent fluxes and thermodynamic forces Onsager relations for vectorial (and tensorial) phenomena Transformation properties of the Onsager relations DISCUSSION OF THE STATISTICAL FOUNDATIONS 1. Introduction State variables and fluctuations Microscopic reversibility Derivation of the Onsager reciprocal relations Further properties of the matrix of phenomenological coefficients Gaussian Markoff processes Ill 7. Gaussian Markoff processes: Langevin equations Entropy and random fluctuations VI VII VIII THE FLUCTUATION DISSIPATION THEOREM 1. Introduction The correlation function of stationary processes; the Wiener- Khinchin theorem The principle of causality; the Kramers-Kronig relations Derivation of the fluctuation dissipation theorem The entropy production in a system subjected to external driving forces 156 DISCUSSION OF FOUNDATIONS BY MEANS OF KINETIC THEORY 1. Introduction The Boltzmann equation The hydrodynamic equations The entropy balance equation; Boltzmann's H-theorem The Enskog method of solution of the Boltzmann equation The entropy balance equation in the rirst approximation of Enskog The Onsager relations Brownian motion 187 IX

4 CONTENTS DC PARTB. APPLICATIONS X CHEMICAL REACTIONS AND RELAXATION PHENOMENA 1. Introduction Chemical reactions Coupled chemical reactions Unimolecular reactions; the principle of detailed balance Relaxation phenomena Internal degrees of freedom 226 HEAT CONDUCTION, DIFFUSION AND CROSS-EFFECTS 1. Heat conduction Diffusion. General remarks Thermodynamic symmetry relations for chemical potentials Diffusion in binary systems Diffusion in multi-component systems Diffusion in rotating systems Thermal diffusion (Soret effect) and Dufour effect Heat conduction and thermal diffusion in reacting systems XI VISCOUS FLOW AND RELAXATION PHENOMENA 1. Viscous flow in an isotropic fluid Viscous flow in a magnetic field Propagation of sound Acoustical relaxation The influence of viscosity and heat conduction on the propagation of sound Elastic relaxation 333 XII XIII ELECTRICAL CONDUCTION 1. Introduction The Maxwell equations Conservation laws and entropy balance in systems without polarization Entropy balance (continued) Electric resistance Thermo-electric potential and Peltier effect Galvanomagnetic and thermomagnetic effects Sedimentation potential and electrophoresis Diffusion and thermal diffusion potentials; thermopotential of a thermocell 367

5 X CONTENTS XIV IRREVERSIBLE PROCESSES IN POLARIZED SYSTEMS 1. Conservation laws in polarized systems The entropy balance equation in polarized systems Pressure and ponderomotive force The chemical potential in a polarized medium Dielectric and magnetic relaxation XV DISCONTINUOUS SYSTEMS 1. Introduction Conservation laws Entropy law and entropy balance Phenomenological equations and Onsager reciprocal relations Thermomolecular pressure effect, thermal effusion and mechanocaloric effect Osmotic pressure and permeability of membranes Electrokinetic effects Thermomolecular pressure effect, thermal effusion and mechanocaloric effect in reacting mixtures Electrochemistry APPENDIX I. On matrix and tensor notation 453 APPENDIX II. On thermodynamic relations 457 APPENDIX III. The Gaussian distribution for macroscopic variables 462 PROBLEMS 470 NAME INDEX 502 SUBJECT INDEX 505