Mechanical Theory of Heat to the Steam Engine. 185 



8. If the process have taken place in such a manner that it 

 may be executed inversely in the same way, N—0. If however 

 there occur in the circular process one or more changes of condi- 

 tion which have taken place in a manner which cannot be in- 

 verted, then uncompensated transformations have come into 

 play, and the magnitude N has an assignable value, which how- 

 ever can only be positive. 



Among the processes to which this last finds an application, 

 one in particular will in future be frequently discussed. When 

 a quantity of gas or vapor expands, and in so doing overcomes 

 a pressure corresponding to its whole expansive force, it may be 

 again compressed by an application of the same force, in which 

 case all the phenomena with which the expansion was accompa- 

 nied occur in an inverse manner. This is however no longer 

 the case when the gas (or vapor) does not meet in expanding the 

 full resistance which it could overcome, when, for instance, it 

 streams from one vessel, in which it was under a greater pres- 

 sure, into another in which a less pressure is exerted. In this 

 case a compression is not possible under the same circumstances 

 under which the expansion took place. 



The equation (n) gives us a means of determining the sum of 

 all the uncompensated transformations in a circular process. As 

 however a circular process may consist of many single changes 

 of condition of a given mass, of which some have taken place 

 in an invertable, and others in an uninvertable manner, it is in 

 many cases of interest to know how much each single one of 

 , the last has contributed to the production of the whole sum of 

 uncompensated transformations. For this purpose imagine that 

 the mass, after the change in condition which we wish in this 

 way to investigate, is brought back by an}^ invertable process to 

 its original condition. In this way we obtain a small circular 

 process to which equation (n) is as applicable as to the whole. 

 If we know also the quantities of heat which the mass has taken 

 up during the same, and the temperatures belonging to it, the 



negative integral — / —^f gives the uncompensated change which 



has occurred in it. Now as the restoration which has taken 

 place in an invertable manner can have contributed nothing to 



must be made on the minus sign before N, which does not occur in my previous me- 

 moir in the same equation. This difference depends only on the fact that there the 

 positive and negative sense of the quantities of heat is chosen otherwise than 

 here. There a quantity of heat taken up by the variable body w is calculated aa 

 negative because it is lost for the source of heat, here on the other hand it is consid- 

 ered as positive. All the elements of heat contained in the integral hereby change 

 their sign, and with them at the same time the whole integral, consequently in order 

 that the equation should remain correct notwithstanding the change, it was neces- 

 sary to change the sign on the other side also. 



SECOND SERIES, VOL. XXII, NO. 65. — SEPT., 1856. 



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