* 



AND OF THE SECOND LAW 95 



and then we know that there must be satisfied the condition 



-y-=o or S-^r = o, .... (36) 



which is the form in which CLAUSIUS first enunciated the Second 

 Law. 



(12) Another condition for the process considered is furnished 

 by the First Law. For each element of time d'Q+A =dU, where 

 U is the inner energy of the body and A the work expended upon 

 it in an element of time by external means. 



Now let us consider a more special case in which the external 

 pressure at each instant is equal to the pressure p of the suppos- 

 edly stationary body. Then the external work will be represented 

 by 



A--pdV, (37) 



and then it follows that 



d'Q=dU + pdV (38) 



(13) Furthermore let the temperature of each heat reservoir, 

 at the instant when it comes into use, be equal to the simultaneous 

 temperature of the body; then the cycle process becomes a revers- 

 ible one and the inequality of the second law becomes an equality, 



( 39 ) 



and substitution of above value for d'Q gives 



dU + pdV 

 -- = ....... (40) 



In this equation there occur only quantities referring to the 

 state of the body itself and therefore it can be interpreted without 



