This is the equation-of-state function derived from G(T,P,N1,N) by differentiation with respect to N1. Temperature is again fixed to give the equimolar critical-point composition. As expected, the surface forms a cusp catastrophe and covers the pressure range 1.1 > Pr > 0.8. The red-yellow-boundaries give states at the limit of stability as defined by the first diffusional stability criterion:

Note that when the data set is specified as N1, N2, …, Nn-1, N rather than N1, N2, …, Nn, the correct chemical-potential variable is

Scaling is then carried out using the total mole number N so as to give molar energies, molar entropies, etc., and compositions in mole fractions.

This surface is repeated in the next two images, but the pressure range is extended to successively lower values where the red (unstable) region begins to fold back on itself — a mathematical artifact only.

Iowa State University