Geometry of the Vapor Liquid Coexistence in the Gibbs Space

TL;DR

This paper explores the geometric structure of vapor-liquid coexistence in Gibbs space, providing insights into phase equilibrium and critical phenomena through geometric analysis of thermodynamic variables.

Contribution

It introduces a geometric framework for understanding phase coexistence and estimates critical exponents using geometric properties of the coexistence curve.

Findings

Identification of the edge of regression with tangent lines connecting coexistence points

Geometric approach to estimate critical exponents

Insights into the shape and angles of the coexistence curve near the critical point

Abstract

The phase coexistence is illuminated with geometric views of the thermodynamic variables, according to Gibbs' choices. Quantities and relations between them are obtained. The existence of the edge of regression with tangents coincident with the straight lines connecting the coexistence points of phase equilibrium is stressed. A geometric approach to the critical point leads to estimation of the values of the critical exponents for the angles formed by the coexistence curve and the straight lines with the principal direction along the minimal curvature.