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Showing papers on "Gibbs–Duhem equation published in 1985"


Journal ArticleDOI
TL;DR: In this paper, a set of parameters describing the Gibbs energy of the various phases as a function of temperature and pressure is presented, and the agreement between experimental data and calculated values is satisfactory.
Abstract: The thermodynamic properties and the pressure-temperature phase diagram of pure Mo have been evaluated from experimental information using thermodynamic models for the Gibbs energy of the individual phases. A set of parameters describing the Gibbs energy of the various phases as a function of temperature and pressure is presented. The agreement between experimental data and calculated values is satisfactory.

50 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that Ialenti and Caramazza have incorrectly equated the terms on the two sides of the Gibbs-Duhem cross-differential equation and hence have arrived at a false conclusion.
Abstract: It is shown that Ialenti and Caramazza have incorrectly equated the terms on the two sides of the Gibbs–Duhem cross-differential equation and hence have arrived at a false conclusion. In this paper the Harned equations are developed by a correct application of the cross-differentiation condition required by the Gibbs–Duhem equation so as to obtain inter-relations among the Harned coefficients, including one general relation which is required. A necessary condition for the general Gibbs–Duhem equation to hold is also derived and the methods of Scatchard, Pitzer and the higher-order limiting law are all shown to satisfy this condition. For a special case in which a further inter-relation also applies, it is shown that Ak and Bk must be constants for k 2. Relations between the Harned coefficients and the mixing coefficients in ΔmGex and their derivatives are also obtained.

6 citations


Journal ArticleDOI
TL;DR: In this paper, the existence of phase transitions in the sense of uniqueness of the tempered Gibbs state is proved for potentials without hard core by first proving uniqueness of Gibbs measures for related hard-core potentials and then taking an appropriate limit of those Gibbs measures.
Abstract: We investigate one-dimensional continuum grandcanonical Gibbs states corresponding to finite range superstable many-body potentials. Absence of phase transitions in the sense of uniqueness of the tempered Gibbs state is proved for potentials without hard-core by first proving uniqueness of the Gibbs measures for related hard-core potentials and then taking an appropriate limit of those Gibbs measures.

6 citations


Journal ArticleDOI
TL;DR: In this article, a multiple linear regression technique to represent partial excess property data for one component (A) in a ternary A-B-C system is presented, following the methodology of Pelton and Flengas, recognizing the need to satisfy Henry's law for components B and C in solutions rich in component A as well as independent experimental knowledge which may be available for the B-C binary.
Abstract: A multiple linear regression technique to represent partial excess property data for one component (A) in a ternary A–B–C system is presented. The procedure, following the methodology of Pelton and Flengas, recognizes the need to satisfy Henry's law for components B and C in solutions rich in component A as well as independent experimental knowledge which may be available for the B–C binary.

2 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that a microcanonical Gibbs measure on a classical discrete lattice system is a mixture of canonical Gibbs measures, provided the potential is approximately periodic, has finite range and possesses a commensurability property.
Abstract: It is proven that a microcanonical Gibbs measure on a classical discrete lattice system is a mixture of canonical Gibbs measures, provided the potential is “approximately periodic,” has finite range and possesses a commensurability property. No periodicity is imposed on the measure. When the potential is not approximately periodic or does not have the commensurability property, the inclusion does not hold.

1 citations


Book ChapterDOI
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.

Journal ArticleDOI
TL;DR: In this article, the Gibbs distributions characterising the states of lattice systems are determined by generating functionals that satisfy Bogolyubov's equation, and it is shown that to different regularity conditions of the Gibbs distribution there correspond different natures of the continuous dependence of the solutions of the Bogoyubov equation on the external field.
Abstract: This paper considers lattice systems with binary interaction. The Gibbs distributions characterising the states of the systems are determined by generating functionals that satisfy Bogolyubov's equation. It is shown that to different regularity conditions of the Gibbs distributions there correspond different natures of the continuous dependence of the solutions of the Bogoyubov equation on the external field. This makes it possible to regard the regularity conditions as conditions of stability of the Gibbs distributions with respect to weak perturbations of them by external fields.