Josiah Willard Gibbs, Gibbs Models: computer-visualized thermodynamic surfaces

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.



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		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.