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Critical constants from van der Waals: T_c = 8a/(27Rb), P_c = a/(27b^2), V_c = 3b. Z_c = P_cV_c/(RT_c) = 3/8. Above T_c: gas cannot be liquefied regardless of pressure (supercritical fluid). Below T_c: isotherms show liquid-gas phase transition (flat region where P is constant during phase change). Boyle temperature: T_B = a/(Rb) = 27T_c/8. Inversion temperature: T_i = 2a/(Rb) = 2T_B. Joule-Thomson effect: expansion below T_i causes cooling. Above T_i: expansion causes heating. Liquefaction methods: Linde (Joule-Thomson cooling with countercurrent heat exchange) and Claude (adiabatic expansion against piston). For H2 (T_i = 202 K) and He (T_i = 40 K): must pre-cool below inversion temperature first. From critical constants, a and b can be calculated: a = 27R^2T_c^2/(64P_c), b = RT_c/(8P_c).