Actually, the figure was not produced by solving the cubic and integrating, rather g ( v , T ) was obtained from its definition by first obtaining u ( v , T ) and s ( v , T ) , which is easily done analytically for the van der Waals equation, and plotting it parametrically with p ( v , T ) , using v as the parameter. Considering only its stable states g ( p , T ) is continuous with discontinuous partial derivatives, ∂ ∂ p g | T = v and ∂ ∂ T g | p = − − s , at the phase transition point. In the Ehrenfest classification, a first order phase transition refers to the discontinuity of the first partial derivatives of g while a second order phase transition would involve discontinuities of the second partial derivatives.