Critical temperature T_c = 8a/(27Rb): above T_c, gas cannot be liquefied by pressure alone. Critical pressure P_c = a/(27b^2): minimum pressure to liquefy at T_c. Critical volume V_c = 3b: volume at critical point. Z_c = P_cV_c/(RT_c) = 3/8 = 0.375 (van der Waals prediction; actual ~0.27). Relationships: T_c/P_c = 8b/R (eliminates a). Andrews' experiments on CO2: isotherms below T_c show liquid-gas coexistence; above T_c, smooth curves (no phase transition). Supercritical fluids (above T_c and P_c) have properties intermediate between liquid and gas.