Variational-lagrangian Thermodynamics of Evolution of Collective Chemical Systems
نویسنده
چکیده
New concepts in thermodynamics are further extended and combined with a principle of virtual dissipation to provide general equations of evolution of collective open chemical systems. A new definition of the chemical potential is introduced, and some new expressions for the affinity are discussed. Application of the principle of virtual dissipation leads very simply to quite general continuum field equations for thermomolecular diffusion coupled to chemical reactions in a body force field. An energy flux theorem is established. Complementary scalar field equations and corresponding variational principles are derived along with a general mathematical formulation of chemical waves. The power of the variational laprangian formulation of thermodynamics is well illustrated by a simple and very general treatment of active transport in biological membranes. It is indicated how this lagrangian approach originated by the author in 1954 constitutes the fundamental conceptual and analytical tool unifying nonequilibrium thermodynamics and classical mechanics.
منابع مشابه
Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia.
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a v...
متن کاملVariational-lagrangian Irreversible Thermodynamics of Initially-stressed Solids with Thermomolecular Diffusion and Chemical Reactions
A GENERAL principle of virtual dissipation in irreversible thermodynamics is applied to a solid under initial stress with small non-isothermal incremental deformations and coupled thermomolecular diffusion and chemical reactions. Dynamical field and Lagrangian equations are obtained directly by variational procedures. In addition, the treatment embodies new fundamental concepts and methods in t...
متن کاملNew Stability Criteria for Reaction-diffusion
A new variational approach to irreversible thermodynamics has been developed leading to lagrangian equations of evolution. The essential results have been presented recently in the form of a short monograph [l]. Its foundation rests on a fundamental principle of virtual dissipation. Our purpose here is to derive new stability criteria for a steady state evolution based on lagrangian equations i...
متن کاملGeneralized Lagrangian Equations of Nonlinear Reaction-diffusion
The principle of virtual dissipation for irreversible processes in open systems is given a new formulation where variations are unconstrained everywhere including the boundary. As a complementary development a new chemical thermodynamics of open systems initiated earlier is given a simplified derivation and new results are presented. A new evaluation of entropy production for fully nonlinear re...
متن کاملA Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constrai...
متن کامل