X, ^, r, AND THE CRITERIA OF EQUILIBRIUM 219 



If this state is not one of uniform pressure, let the pressure 

 equahze itself at constant temperature and constant volume. 

 Then by general theory, since this is an irreversible process, the 

 function \p must decrease in the process. (For if A" denotes the 

 change in question, and A"Q is the heat absorbed 



A"r, ^ A"Q/t = A"e/t, 



or 



A"€ - t A"rt ^ 0, or A' V < 0.) 



Hence we have constructed a new state of uniform pressure for 

 which 



(A.^),. „ < 0. 

 Now 



Ar = A{^P + vv) 

 and here Av = 0. Hence 



Ar = Avi' + vAj), 

 or 



Af < vAj). 



Now change the pressure and volume reversibly at constant 

 temperature. For this change, infinitesimal increments are 

 given by 



d'e = t d'-r] — p d'v, 



d'f = d'{e - 7)t + vv) 



= V d'p, 



since d't = 0. Hence the new finite increment A'f is given by 



rpo + A'p 

 A'^ = V d'p, 



J Pa 



