THERMODYNAMIC AL SYSTEM OF GIBBS 81 



have then definite numerical values in any state of the homo- 

 geneous body. 

 The definition 



xf^ = e - tr] (17) [105] 



may evidently be extended to any material system whatever 

 which has a uniform temperature throughout. Consider two 

 states of the system at the same temperature, in which ^ has 

 the values \f/' and \p". The decrease in i/' in the change from 

 the first to the second state is 



^' - ^" = e' - t" - tW - ri"). (18) [106] 



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

 by a reversible process in which a quantity of work W is done 

 by the system and a quantity of heat Q absorbed, the decrease 

 of energy is: 



e' - e" = IF - Q, (19) [107] 



and since the process is reversible ; 



Q = tw - V), (20) [108] 



so that; 



^> - ^" = W; (21) [109] 



i.e. the decrease in i/', in a change of state at constant tem- 

 perature, is equal to the work done by the system when the 

 change of state is carried out by a reversible process. Thus i^ 

 can be regarded as the maximum work function of the system for 

 changes at constant temperature. Equation (21) can be written 

 as: 



- (A^), = W, (22) 



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

 write : 



-(5^)t = dW, (23) [llD] 



In mechanics the potential of a particle in a field of force is a 

 quantity such that the work obtained in a small displacement 

 of the particle is 



dW = -d4>. 



