Showing papers on "Gibbs–Duhem equation published in 1979"
TL;DR: In this paper, several methods are reviewed for determining compositions in multiphase, reacting mixtures at equilibrium. Wolfe's quadratic programming algorithm is applied and results compared with the Rand method (Dluzniewski and Adler 1972), NASA method (Gordon and McBride 1971) and the George et al. (1976) implementation of Powell's method.
Abstract: Several methods are reviewed for determining compositions in multiphase, reacting mixtures at equilibrium. Wolfe's quadratic programming algorithm is applied and results compared with the Rand method (Dluzniewski and Adler 1972), NASA method (Gordon and McBride 1971) and the George et al. (1976) implementation of Powell's method. For poor guesses in compositions, local and constrained minima in Gibbs free energy may arise, giving incorrect phase distributions.
137 citations
TL;DR: In this paper, it was shown that the surface tension of symmetric two component lattice systems obtained at large (equal) values of the fugacity is given by an integral over the density variation in the Gibbs' formula.
Abstract: We prove cluster properties of the spatially inhomogeneous Gibbs states in symmetric two component lattice systems obtained at large (equal) values of the fugacity. We also prove that the surface tension of these systems is given by an integral over the density variation in this state Gibbs' formula. An alternative formula for the surface tension is also derived.
28 citations
TL;DR: In this paper, the authors obtained the correlation function of heat fluctuations from a generalized Gibbs equation and from the Einstein formula for the probability of fluctuations, and used it to obtain the temperature correlation function.
16 citations
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15 citations
TL;DR: In this article, the solution of groups concept is extended to cover the total Gibbs energy of any system, pure or mixed, relative to a well-defined standard state, which is a correlation which is capable of predicting simultaneously pure component vapor pressures and standard Gibbs energies of formation and mixture vapor-liquid equilibrium compositions.
Abstract: The UNIFAC group contribution method has already proved highly valuable for predicting excess Gibbs energies of liquid mixtures and hence vapor-liquid equilibria. The solution of groups concept is extended to cover the total Gibbs energy of any system, pure or mixed, relative to a well-defined standard state. The result is a correlation which is capable of predicting simultaneously pure component vapor pressures and standard Gibbs energies of formation and mixture vapor-liquid equilibrium compositions. The results presented strongly support the approach and indicate that the method should be further developed.
14 citations
2 citations
TL;DR: In this article, the GD equation is described as a differential equation in the contact space in which all the densities and fields are regarded as independent variables and the Gibbs phase rule is found to be valid for these solutions, although they can be regarded as resulting from the intersection of single-phase solutions.
Abstract: It is shown that a new, fully consistent thermodynamic description is possible. This approach is characterised by a local study of the solutions of the GD equation, regarded as a differential equation in the contact space in which all the densities and fields are regarded as independent variables. An m-phase solution is described as one in which (m-1) densities may be fixed arbitrarily and the others are linear functions of these. The Gibbs phase rule is found to be valid for these solutions, although in no way can they be regarded as resulting from the intersection of single-phase solutions. Changes of variables in thermodynamics are identified with contact transformations leaving the fundamental equation invariant.
2 citations
01 Nov 1979
TL;DR: In this paper, two approximate representations of a one-particle Gibbs state, both of which become asymptotically exact in trace norm as m → ∞, were obtained.
Abstract: We obtain two approximate representations of a one-particle Gibbs state, both of which become asymptotically exact in trace norm as m → ∞. The second representation is an integral of pure coherent states over phase space, and can therefore be regarded as a classical approximation to the Gibbs state. We also obtain a version of the second representation applicable to the microcanonical ensemble.
1 citations