As depicted in Fig. 8, the region on the green curve f ( T R , v ) for v ≤ ≤ v f ( v f is designated by the left green circle) is the liquid. As v increases past v f the curvature of f (proportional to ∂ ∂ v 2 2 f = − − ∂ ∂ v p ) continually decreases. The point characterized by ∂ ∂ v 2 2 f = − − ∂ ∂ v p = 0 , is a spinodal point, and between these two points is the metastable superheated liquid. For further increases in v the curvature decreases to a minimum then increases to another spinodal point; between these two spinodal points is the unstable region in which the fluid cannot exist in a homogeneous equilibrium state. With a further increase in v the curvature increases to a maximum at v g , where the slope is p s ; the region between this point and the second spinodal point is the metastable subcooled vapor. Finally, the region v ≥ ≥ v g is the vapor. In this region the curvature continually decreases until it is zero at infinitely large v . The double tangent line is rendered solid between its saturated liquid and vapor values to indicate that states on it are stable, as opposed to the metastable and unstable states, above it (with larger Helmholtz free energy), but black, not green, to indicate that these states are heterogeneous, not homogeneous solutions of the vdW equation.