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Gibbs–Duhem equation
About: Gibbs–Duhem equation is a research topic. Over the lifetime, 393 publications have been published within this topic receiving 6248 citations. The topic is also known as: Gibbs-Duhem equation.
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TL;DR: In this paper, the authors define a hierarchical model in d>2 dimensions with a phi 4 interaction which is a true model of statistical mechanics in that it can be described by a set of potentials admitting Gibbs states.
Abstract: The author defines a hierarchical model in d>2 dimensions with a phi 4 interaction which is a true model of statistical mechanics in that it can be described by a set of potentials admitting Gibbs states. The author shows that the renormalisation of this model leads to a transformation of local potentials which corresponds to a transformation of Gibbs measures in the thermodynamic limit. Finally the author shows how this transformation can be used to obtain a continuum limit in the three-dimensional case, using analyticity techniques developed by Gawedzki and Kupiainen (1983).
TL;DR: In this article, a simple model of an amphiphilic monolayer at an air-water interface is used to demonstrate that the Gibbs formalism for surface excess parameters correctly takes into account the volume work performed by the interface during the course of a thermodynamic process.
01 Jan 1992
TL;DR: In this paper, the authors proposed to add an elastic energy term to the classical Gibbs' equation to take into account the deformability of the solid. But their derivation led them to the conclusion that the Gibbs' equations had to be modified to account for the deformation of the sample and the exchange of work with the environment.
Abstract: The chemical potential of a component of the solid in solution is given by the equilibrium condition between the stressed solid and its solution. This condition was first established by Gibbs (1877) for a plane interface and then generalized to any curved interface. It was rederived later by Lehner & Bataille (1985) and Mullins & Sekerka (1985). Gibbs (1877) chose to have the solid and the fluid phases enclosed within rigid walls, thus preventing any exchange of mechanical work between the system (solid + fluid) and the environment. However, in the experience described in our reference paper, samples are subjected to constant stress conditions, which induce a deformation of the samples and thus an exchange of work with the environment. One may wonder if Gibbs’ classical equation is still valid under these conditions which are the usual conditions for creep of rocks by pressure solution. We tried to give an answer to this question by using an approach similar to the Griffith’s crack approach. Our derivation led us to the conclusion that Gibbs’ equation had to be modified to take into account the deformability of the solid. We thus proposed to add an elastic energy term to the classical Gibbs’ equation. The question arose as to whether or not Gibbs’ and Griffith’s approaches are compatible. In this corrigendum we want to correct our previous derivation by showing that it contained some omissions leading to an incorrect conclusion. In the reference paper, we proposed to write the variation AU of the internal energy of the system (solid+fluid) as follows (equation 9 of the reference paper): AU = AQ + AW = AU, + AU, + (uf - us) 6n (9)
TL;DR: In this paper, it was shown that an equilibrium state of a spatially confined quantum system is described by the Gibbs canonical ensemble, under a stability assumption which amounts essentially to the zeroth law of thermodynamics.
Abstract: We show, without the use of ad hoc hypotheses and employing only elementary mathematical techniques, that an equilibrium state of a spatially confined quantum system is described by the Gibbs canonical ensemble, under a stability assumption which amounts essentially to the zeroth law of thermodynamics.
TL;DR: In this paper, the Gibbs free energy changes and temperatures of the FAC/AZ91D Mg alloy-Cenosphere composites were calculated and the analysis result provided the theoretical basis for the reaction temperature and the solution treatment temperature.
Abstract: The thermodynamic calculation is valuable for judging the feasibility of a reaction. In the present paper, the enthalpy change (∆HR), entropy change (∆SR) and Gibbs free energy change (∆GR) among various components in AZ91D Mg alloy-Cenosphere composites (FAC/AZ91D) were calculated. Through the calculation, we obtained the relationships between the Gibbs free energy changes and temperatures. The difficulty degree of every potential reaction could be directly reflected by the correlation curve between the temperature and the Gibbs free energy change. The analysis result provided the theoretical basis for the reaction temperature and the solution treatment temperature of the FAC/AZ91D system. At the same time, the analysis based on the minimum principle of the reaction free energy revealed the final components (MgO, Mg2Si and MgAl2O4), which was partially similar to the result of XRD analysis (MgO, Mg2Si and Mg17Al12).