X, xp, r, ^ND THE CRITERIA OF EQUILIBRIUM 221 



the original value of the entropy is restored. The energy can 

 only decrease in the process. Hence we arrive at a new state of 

 uniform pressure for which 



(Ae),.„ < 0. 

 Now 



and hence in general 



Ax = Ae + pAv + vAp + ApAv. 



But in our case Av = 0. Hence here 



Ax = Ae + vAp. 

 Consequently 



Ax — vAp = Ae < 0. 



Now expand or compress adiahatically . For any such process, 

 the infinitesimal change of energy d'e is given by 



d't = —p d'v 

 and hence for this process 



d'x = d'{(: -]r pv) = V d'Pf 



whence for the finite change A' 



rpo + A'p 

 A'x = I V d'p. 



J PO 



Hence 



/*P0 



Ax + A'x < vAp — j V d'p. 



J pa + A'p 



