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Another view of the differenced HSP surface (the N-subscripts have been omitted and the entropy direction reversed). The transparent structure is the locus of all isobaric tangent lines for 1.0 > P_r > 0.7. The light-blue curves are isotherms.

On the undifferenced enthalpy surface (not shown in this collection), each tangent line has a slope

and intersects the plane S = 0 at a vertical coordinate equal to H-TS = G = µ for each state touched by the line. Since the tangent shown here at touches the surface at two points, the common tangencies have the same P, T, and µ and thus satisfy the criteria for states in phase equilibrium. The locus of all such states in this drawing is highlighted in black.