Critical temperature $T_c$ = 8$\frac{a}{27Rb}$: above $T_c$, gas cannot be liquefied by pressure alone. Critical pressure $P_c$ = $\frac{a}{27b^2}$: minimum pressure to liquefy at $T_c$. Critical volume $V_c$ = 3b: volume at critical point. $Z_c$ = $\frac{P_cV_c}{RT_c}$ = 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.