Thermodynamics of the Critical Point: Liquid—Vapor Systems

Two separate Taylor series in pressure are necessary to describe behavior in the G and L single-phase regions of a one-component fluid. It is shown that (∂3P/∂ρ3)c is zero or very nearly so, (∂4P/∂ρ4)c,G=−(∂4P/∂ρ4)c,L and (∂2P/∂ρ∂T)c,G=(∂2P/∂ρ∂T)c,L. Derivations are given for a cubic coexistence curve and the gas branch of the critical isotherm. Higher-order critical coefficients are evaluated and discussed. The theory is consistent with a line of singularities or discontinuities along the critical isochore.