Showing papers on "Gibbs–Duhem equation published in 1976"
TL;DR: In this paper, it was shown that for a large class of interactions, any canonical Gibbs state satisfying a natural temperedness condition is a mixture of Gibbs states with appropriate activities, and vice versa.
Abstract: It is shown that for a large class of interactions any canonical Gibbs state satisfying a natural temperedness condition is a mixture of Gibbs states with appropriate activities, and vice versa. Some general results on Gibbs states and canonical Gibbs states are established. In particular, a differential characterization of Gibbs states is given.
122 citations
65 citations
TL;DR: In this article, an equilibrium model for the calculation of the excess Gibbs free energy of binary liquid mixtures is developed, where the component A of which undergoes chain-forming self-association whilst the component B acts as an 'inert' solvent.
Abstract: Abstract In this paper equilibrium models for the calculation of the excess Gibbs free energy of binary liquid mixtures are developed, the component A of which undergoes chain-forming self-association whilst the component B acts as an 'inert' solvent. It is shown that the extension of the well-known chain-association model of Mecke and Kempter, in which the probability of chain prolongation is assumed to be independent of chain length, is unable to establish satisfactory results because it does not exhibit sufficient unsymmetry. Reduction of the probability of chain growth with in-creasing chain length leads to an improved model with the geometric series replaced by the exponential series. This model, in which only two parameters are used, i. e. the equilibrium constants K for mutual solvation of A and B, and ρ for self-association of A, allows fitting of isothermal experimental GE /R T literature data on cycloalkanol-cycloalkane, alkanol-alkane, and NMF -CCl4 systems within the limits of experimental error. Compared with the two-parameter Wilson equation which gives equally small standard deviations, our equilibrium model has the advantage of allowing passage from GE to HE data and of being applicable to liquid-liquid equilibria.
5 citations
01 Sep 1976-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, the Gibbs-Duhem equation was applied to calculate the quotient of a mattes containing oxygen from quotients in mattes free of oxygen, and it was shown how one may apply this equation to Cu-Fe-S-O mattes in particular.
Abstract: It is shown how one may apply the Gibbs-Duhem equation to Cu-Fe-S-O mattes in particular in order to calculate the quotient\(aFeS/a^2 CuS_{0.5} \) in mattes containing oxygen from quotients in mattes free of oxygen.
2 citations