A plot of this function for the same subcritical isotherm of the vdW equation as Figs. 1 and 2 is shown in Fig. 3. Included in this figure is the (dashed/solid) straight line that has a double (common) tangent with the curve of the function f at B and F. This straight line is, f = f 0 + ∂ ∂ v f T v = f 0 − − p v , with p constant, which can be written as f 0 = f + p v = g . The last equality follows from the relation f = u − − T s , together with g = u − − T s + p v . All this means that every point on the line has the same values of g , p , T , in particular the points B and F, which produces the Gibbs condition for material equilibrium g f = g g as well as eqality of temperature and pressure. Therefore this construction is equivalent to both the Gibbs conditions and the Maxwell construction.