186 



R. Clausius on the Application of the 



its increase, this expression represents the uncompensated trans- 

 formation occasioned bj the given change of condition. 



If in this manner we have investigated all the parts of the 

 whole circular process which are not invertable, and thereby de- 

 termined the values iVi, Nz\ &c, which must all singly be posi- 

 tive, their sum gives the magnitude N with reference to the 

 whole circular process, without its being necessary to bring into 

 the investigation those parts of which we know that they are in- 

 vertable. 



9. If we now apply equations (i) and (n) to the circular pro- 

 cess which takes place in the thermo-dynamic machine during a 

 period, we see in the first place that if the whole quantity of 

 heat which the mediating substance has taken up during this 

 time is given, then the work is also determined immediately by 

 the first equation, without its being necessary to know the nature 

 of the processes themselves of which the circular process con- 

 sists. In similar generality we may, by the combination of the 

 two equations, determine the work from other data also. 



We will assume that the quantities of heat which the variable 

 body receives one after the other, as well as the temperatures 

 which it has at the reception of each, are given, and that there is 

 only one temperature over and above, whose magnitude is not 

 known & priori, at which a quantity of heat is still communica- 

 ted to, or, if it be negative, taken from, the body. Let the sum 

 of all the known quantities of heat be Q J} and the unknown 

 quantity of heat Q 0 . 



Then resolve the integral in equation (n) into two parts, of 

 which one extends only over the known quantity of heat Q X1 and 

 the other over the unknown quantity Q 0 . In the last part the 

 integration may be directly executed, since T has in it a constant 

 value T Q , and gives the expression 



The equation (n) becomes hereby 



o 



whence follows 



o 



Further we have according to equation (i), as, for our case, 



If we substitute in this equation for Q 0 the value just found, we 

 have 



