On the Gibbsian thermostatics of mixtures
type: Item
instance of: scholarly article
title: On the Gibbsian thermostatics of mixtures
zbMATH Open document ID: 0594.49030
DOI: 10.1007/BF00281498
author: Jorge G. S. Patiño
author: Roger Fosdick
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The work considers the problem of maximizing \(\int_{\Omega}f(y(x)) dx\), \(\Omega \subset {\mathbb{R}}^ 3\), \(y: \Omega\) \(\to {\mathbb{R}}^ m\) integrable, \(\int_{\Omega}y dx=c\), f real, continuous, in the context of thermostatics of mixtures. Necessary and sufficient conditions for the existence of maximizers are derived. The dependence of maximizers on the vector c and conditions for uniqueness are shown; these results are interpreted in the context of thermostatics and compared with such classical relations as e.g. the Clausius-Clapeyron relation.
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 49J10
zbMATH DE Number: 3955845
zbMATH Keywords: thermostatics of mixtures
zbMATH Keywords: existence of maximizers
MaRDI profile type: Publication
cites work: On certain convex sets of measures and on phases of reacting mixtures
cites work: The morphology and stability of material phases
cites work: Convex Analysis
cites work: Material stability, the Gibbs conjecture and the first phase rule for substances
description: scientific article; zbMATH DE number 3955845