van der Waals equation of state with Maxwell equal-area construction. Below T_c, the isotherm becomes unphysical (spinodal). Maxwell's rule replaces it with the physical liquid-gas coexistence plateau.
van der Waals (1873): (P + a/V²)(V − b) = RT. Critical point: T_c = 8a/27Rb, V_c = 3b, P_c = a/27b². Maxwell construction (equal areas above and below P_sat) gives the physical coexistence pressure. The unstable region (∂P/∂V > 0) is the spinodal; between spinodal and binodal lies the metastable region (nucleation).