Thermodynamic equations for tri- or third order critical points

Abstract

Thermodynamic equations which state the criteria which certain thermodynamic derivatives must satisfy at tricritical, or third order critical, points in fluid mixtures are derived. The method used is an extension of Gibbs' original derivation of ordinary critical point equations and, in particular, analyticity about the tricritical point is assumed. In the molar Gibbs free energy representation, the tricritical equations are ∂ μ̃1/∂ x1 = ∂2μ̃1/ ∂ x12=∂3μ̃1/∂ x13=∂4 μ̃1/∂ x14=0, where μ̃1 is related to the chemical potential of component ``1'', x1 is the mole fraction of that component, and the temperature, pressure and chemical potentials relevant to the remaining independent components are held constant during the partial differentiations. General thermodynamic representations are considered, and the results are generalizable to critical points of arbitrary order.