GEOMETRIC PROGRAMMING, CHEMICAL EQUILIBRIUM, AND THE ANTI-ENTROPY FUNCTION*

AUTOR(ES)

Duffin, R. J.

RESUMO

The culmination of this paper is the following duality principle of thermodynamics: maximum S = minimum S*. (1) The left side of relation (1) is the classical characterization of equilibrium. It says to maximize the entropy function S with respect to extensive variables which are subject to certain constraints. The right side of (1) is a new characterization of equilibrium and concerns minimization of an anti-entropy function S* with respect to intensive variables. Relation (1) is applied to the chemical equilibrium of a mixture of gases at constant temperature and volume. Then (1) specializes to minimum F = maximum F*, (2) where F is the Helmholtz function for free energy and F* is an anti-Helmholtz function. The right-side of (2) is an unconstrained maximization problem and gives a simplified practical procedure for calculating equilibrium concentrations. We also give a direct proof of (2) by the duality theorem of geometric programming. The duality theorem of geometric programming states that minimum cost = maximum anti-cost. (30)

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