Application of the gibbs-duhem equation to Cu-Fe-S-O mattes

1976 ◽  
Vol 7 (3) ◽  
pp. 339-342 ◽  
Author(s):  
Carl Wagner
Keyword(s):  
Duhem Equation

An analytical solution of the Gibbs–Dehem equation in multicomponent systems

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Multicomponent Systems ◽  
Duhem Equation ◽  
Number Of Components ◽  
Analytical Power

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.

LIQUID–VAPOUR EQUILIBRIUM FOR THE SYSTEM ETHANOL–ACETONE

1946 ◽  
Vol 24b (5) ◽  
pp. 254-262 ◽  
Author(s):  
A. R. Gordon ◽  
W. G. Hines
Keyword(s):  
Solvent System ◽  
Corresponding States ◽  
Heat Of Mixing ◽  
Duhem Equation ◽  
Moderate Agreement

Vapour pressures and equilibrium liquid–vapour mole fractions have been determined for the solvent system ethanol–acetone at 32°, 40°, and 48 °C. in a modified form of the apparatus developed by Ferguson and Funnell. It is shown that the data are consistent with the Gibbs Duhem equation if it be assumed that deviations from ideality in the vapours may be computed from the principle of Corresponding States. It is also shown that the variation of the activities of the components in the liquid with temperature is in moderate agreement with the heat of mixing data for the system.

TWO-MODE GAUSSIAN DENSITY MATRICES AND SQUEEZING OF PHOTONS

1992 ◽  
Vol 06 (10) ◽  
pp. 1657-1709 ◽  
Author(s):  
ROBERT R. TUCCI
Keyword(s):  
Fundamental Equation ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Second Law ◽  
Gaussian State ◽  
Density Matrices ◽  
Duhem Equation ◽  
Gaussian Density ◽  
Pure States ◽  
Necessary And Sufficient

In this paper, we generalize to 2-mode states the 1-mode state results obtained in a previous paper. We study 2-mode Gaussian density matrices (i.e., density matrices of the form: exponential of a quadratic polynomial in the creation and annihilation operators for the two modes). We find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows us to express the density matrix as a product of two 1mode density matrices. We find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. We discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered. We study the change in entropy that is produced when a 2-mode Gaussian state is subjected to a measurement of the complex amplitude of one of its two modes. We derive upper and lower bounds for the final (i.e., after the measurement) entropy of the unmeasured mode, and we give necessary and sufficient conditions for the achievement of these bounds. The existence of the bounds is shown to be a consequence of the concavity property of the entropy function.

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