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Trends in Physical Chemistry   Volumes    Volume 15 
An analysis of the properties of thermodynamic systems using projective differential geometry
L. Z. Pevzner
Pages: 65 - 74
Number of pages: 10
Trends in Physical Chemistry
Volume 15 

Copyright © 2014 Research Trends. All rights reserved

The fundamental relationships of equilibrium thermodynamics are shown to be invariant with respect to the projective transformations of the specific parameters. Expressions for the thermodynamic properties which are unaffected by these transformations are obtained. We discuss a positive definite quadratic differential form composed of the second differentials of the thermodynamic potential multiplied by some function. The form has been used as a metric, and its Gaussian curvature has been calculated for an arbitrary thermodynamic system, for an ideal gas and for ideal two- and three-component solutions. We show that ideal solutions and ideal one-component gases have very different curvatures. The conditions of projective applicability are formulated and their physical meaning is discussed for the surface described by the fundamental equation of а thermodynamic system. Invariants of the projective transformations are calculated for the virial expansion of the properties of two-component gas solutions at а constant temperature; it is shown that if the second and third virial coefficients are taken into account, the conditions of projective applicability are satisfied.
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