Critical Point on Van der Waals Isotherms
The critical point is the unique point on the original van der Waals isotherms (before the Maxwell construction) where both the first and second derivatives of P with respect to V (at fixed T) are zero. Use this fact to show that: V_c = 3Nb, P_c = (1/27) (a/b2), kT_c = (8/27) (a/b).