( 148 ) 



r 



= O and 



— ) = still inter- 

 dvj x 



remarkable point for which plaïtpoint 



and critical point of the mixture 

 taken as homogeneous coincide. So 

 at this temperature the two curves 

 dp s 



dx y 



sect in two points. The other point 



of intersection lies, of course, at 



greater volume. With further rise of 



temperature the two curves contract 



fdp\ 

 further. The line — = moves to 

 \dxj v 



Fig. 31. 



the right and the line 



to 



the left. At a certain temperature these two curves touch, and at 

 still higher temperature they have got quite detached. This point of 

 contact of the two curves lies, of course, on the vapour branch of 



( — 1 = 0, and so has a greater volume than the critical volume. 

 \dvj x 



dv t 

 We can calculate the volume in case of contact. The condition of 



' d A = and f 



dvJx \dxji 



contact of 



- ] = is given by equal value of 



dv 

 dx 



in the two following equations 



and 



or from: 



d*p dv d*p 

 dv 9 dx dxdv 



d l p dv d*p 



-J- (__£- — 



dxdv dx dx* 



d*p d*p 

 oVoV 



d'p 

 dxdv 



(see p. 691). 



This latter equation and the two equations / — j= andf — j= 



form a set of three which is sufficient for the determination of the 

 three quantities x, v and T of the point of contact. If we assume 

 b to be constant in the equation of state these equations have the 

 following form: 



rf^Y *± r MBT d ± * , 



\dx) 1 dx*~\ r dx dxl 



~Y~v T ]~[_(v-b) i ~V] 



T MRT 3a 

 |_( v _6/ " V* 



MRT 



(v-b)* 



(1) 



