AND OF THE SECOND LAW 97 



or, what amounts to the same thing, by 



dU+pdV 

 dS= j; , (42) 



which reduced to the unit of mass becomes 



(43) 



j. 



" This is evidently identical with the value found for an ideal 

 gas. But it is equally applicable to every body when its energy 

 U = Mu and volume V=Mv are known as functions, say, of p 

 and T, for the expression for entropy can then be directly deter- 

 mined by integration. But since these functions are not com- 

 pletely known for any other substance we must in general rest 

 content with the differential equation. For the present proof, 

 however, and for many applications of the Second Law it suffices 

 to know that this differential equation really contains a unique 

 definition of entropy." 



As with an ideal gas, we can now always speak of the entropy 

 of any substance as a certain finite magnitude determined by 

 the values of the temperature and volume at the instant, and 

 can so speak even when the substance experiences any reversible 

 or irreversible change. Moreover, the differential equation (43) 

 is applicable to any change of state, even an irreversible one. 



In thus applying the idea of entropy there is no conflict with 

 its derivation. The entropy of a state is measured by a reversible 

 process which conducts the body from its present state to the 

 zero state, but this ideal process has nothing to do with the changes 

 of state that the body has experienced or is going to experience." 



" On the other hand, we must emphasize that differential 

 equation (43) for ds is valid only for changes of temperature and 

 volume and is not so for changes of mass or of chemical composi- 



