THERMODYNAMIC AL SYSTEM OF GIBBS 83 



Now, if the system is brought from the first to the second state 

 by a reversible process in which work W is done by the system 

 and heat Q absorbed, we have as before 



^' - ," = W - Q, 



Q = t(v"-v'), 



so that 



^' - ^" = W + p(v' - y") = W - p(v" - v'). (27) 



Now p(v" — v') is the work done by the system in increasing its 

 vokime from v' to v" at the constant pressure p, and the quantity 



w - vW - v') = w, 



i.e., the maximum work of the change at constant temperature 

 and pressure less the work done on account of the change of 

 volume, is often known as the "net work" of the change. Just 

 as the decrease in ^i' in a change at constant temperature is 

 equal to the maximum work obtainable, the decrease in f in a 

 change at constant temperature and pressure is equal to the 

 "net work" obtainable. Thus f is the "net work function" of 

 the system. From considerations similar to those cited in 

 discussing \p, it can be seen that — f is the force function of the 

 system for constant temperature and pressure. 

 Equation (27) may be written in the form 



-Ar = W, (28) 



so that, for an infinitesimal reversible change of state, we may 

 write 



-(80t,p = dW. (29) 



Now, a system is in equilibrium at constant temperature and 

 pressure if there is no possible change of state for which the net 

 work is positive. We may therefore write as a criterion of 

 equilibrium ; 



mt,P^O, (30) [117] 



that is, a system is in equilibrium when the variation of f for 

 every possible change of state, which does not affect the tem- 



