Physical Chemistry Real gases Critical data and equations of state At the critical point aP a-P 0 (8.12) rt a Differentiating the van der Waals equation(8.2)P=v-6 aP rT 2a 02P 2RT 6a (V-b)2 3 and am(m-b)V Application of the conditions(812)gives RT RT 3a (mc-b) v and m c mc . b) (813) m, cCritical data and equations of state Differentiating the van der Waals equation (8.2) 2 3 2 ( ) m T m Vm a V b RT V P + − = −           and = 0           m T V P 0 2 2 =           m T V P At the critical point: (8.12) 2 m Vm a V b RT P − − = 2 3 4 2 6 ( ) 2 m T m Vm a V b RT V P − − =           Application of the conditions (8.12) gives 3 , 2 , 2 ( ) m c m c c V a V b RT = − and 4 , 3 , 3 ( ) m c m c c V a V b RT = − (8.13) Physical Chemistry Real Gases