On Thermodynamic Stability Theory

On Thermodynamic Stability Theory Abstract The necessary and sufficient conditions for stability of non-equilibrium systems are derived using a novel and simple approach. The resulting inequalities, based on the postulate of local equilibrium, include the equilibrium stability criteria proposed previously by Gibbs, and Landau and Lifshitz as special cases as well as the Glansdorff-Prigogine stability criterion for non-equilibrium systems. Difficulties associated with the introduction of mathematical definitions for stability of motion in the context of thermodynamics are exemplified and a kinetic potential is proposed. Introduction The original stability criterion for equilibrium states proposed by Gibbs [1] states that a homogeneous system is stable if for arbitrary perturbations AE + PAV-TAS£ ,/,), (1) where , , 5, and mi denote, respectively, total energy, volume, entropy, and mass of component i; T, P, and are temperature, pressure and chemical potential of component L Landau and Lifshitz [2] employed the Maxwell and Gouy Theorem [3] A(E+P0V-T0S)>0 (2) to derive stability conditions for systems with identical particles. They also showed that a stable binary mixture with a fixed number of moles of solvent satisfies the inequality (3) where 0, and P0 are temperature, and pressure of an external medium and is the chemical potential of the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Non-Equilibrium Thermodynamics de Gruyter

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0340-0204
eISSN
1437-4358
DOI
10.1515/jnet.1993.18.3.271
Publisher site
See Article on Publisher Site

Abstract

Abstract The necessary and sufficient conditions for stability of non-equilibrium systems are derived using a novel and simple approach. The resulting inequalities, based on the postulate of local equilibrium, include the equilibrium stability criteria proposed previously by Gibbs, and Landau and Lifshitz as special cases as well as the Glansdorff-Prigogine stability criterion for non-equilibrium systems. Difficulties associated with the introduction of mathematical definitions for stability of motion in the context of thermodynamics are exemplified and a kinetic potential is proposed. Introduction The original stability criterion for equilibrium states proposed by Gibbs [1] states that a homogeneous system is stable if for arbitrary perturbations AE + PAV-TAS£ ,/,), (1) where , , 5, and mi denote, respectively, total energy, volume, entropy, and mass of component i; T, P, and are temperature, pressure and chemical potential of component L Landau and Lifshitz [2] employed the Maxwell and Gouy Theorem [3] A(E+P0V-T0S)>0 (2) to derive stability conditions for systems with identical particles. They also showed that a stable binary mixture with a fixed number of moles of solvent satisfies the inequality (3) where 0, and P0 are temperature, and pressure of an external medium and is the chemical potential of the

Journal

Journal of Non-Equilibrium Thermodynamicsde Gruyter

Published: Jan 1, 1993

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