Thermodynamic stability criterion for pure substances and mixtures

Criteria are derived to specify the limit of stability for pure material and multicomponent thermodynamic systems. Through the use of Legendre transforms, the criteria may be expressed in a very simple form that only involves the determination of positiveness of a single second‐order partial derivative of a potential function. Alternate and equivalent criteria are shown to result from a simple reordering of the independent variables in the Fundamental Equation of Gibbs. Certain criteria that are often stated as necessary conditions of stability (for example, C v > 0 ) are shown to be insufficient for specifying the limit of stability; that is, a system will always become unstable for other reasons before C b can attain a negative value.