Modified Helmholtz energy density A´/V plotted against the molar density of normal butane in the mixture N2/V and ethylene chemical potential µ1. As with the previous plot of Gibbs-energy, this function is a second Legendre transform for the binary and therefore shows phase equilibrium through common tangent lines. The constant-chemical-potential tangent line here marks a liquid (red cross) with about 3.5 times the molar density of nC4H10 as in the equilibrium vapor (green cross). The function is obtained as follows
Scaling is with the volume; differencing, as before, magnifies the dependent variable.