Stability Conditions

Abstract

Stability exists when a thermodynamic phase remains homogenous instead of separating into phases of high and low density (clumping). Certain conditions on the second partial derivatives of extensive variables are necessary for stability, even when the first derivatives do not vanish. These conditions can be expressed in terms of the compressibility and specific heat. Inequalities involving second partial derivatives with respect to intensive variables are derived. We have been assuming that the density of a gas will remain uniform, rather than having most of the particles clump together in one part of the container, leaving the rest of the volume nearly empty.