Fundamental Theorem in the Mechanical Theory of Heat, 89 



neous transformations above described, we shall first assume that 

 the temperatures of the three reservoirs of heat remain the same, 

 but that the circular processes through which the transform- 

 ations are effected are different. This will be the case when, 

 instead of a gas, some other body is submitted to similar trans- 

 formations, or when the circular processes are of any other kind, 

 subject only to the conditions that the three bodies K, Kj and 

 Kg are the only ones which receive or impart heat, and of the 

 two latter the one receives as much as the other loses. These 

 several processes can be either reversible, as in the foregoing 

 case, or not, and the law which governs the transformations will 

 vary accordingly. Nevertheless, the modification which the law 

 for non-reversible processes suffers may be easily applied after- 

 wards, so that at present we will confine ourselves to the con- 

 sideration of 7'eversible circular processes. 



With respect to all these it may be proved from the foregoing 

 principle, that the quantity of heat Qi, transferred from Kj to 

 Kg, has always the same relation to Q, the quantity of heat 

 transformed into work. For if there were two such processes 

 wherein, Q being the same, Qj was different, then the two pro- 

 cesses could be executed successively, the one in which Q^ was 

 smaller in a direct, the other in an opposite manner. Then the 

 quantity of heat Q, which by the first process was converted into 

 work, would be again transformed into heat by the second pro- 

 cess and restored to the body K, and in other respects every- 

 thing would ultimately return to its original condition ; with this 

 sole exception, however, that more heat would have passed from 

 Kg to Kj than in the opposite direction. On the whole, there- 

 fore, a transmission of heat from a colder body Kg to a warmer 

 Kj has occurred, which, in contradiction to the principle before 

 mentioned, has not been compensated in any manner. 



Of the two transformations in such a reversible process either 

 can replace the other, if the latter is taken in an opposite direc- 

 tion ; so that if a transformation of the one kind has occurred, 

 this can be again reversed, and a transformation of the other 

 kind may be substituted without any other permanent change 

 being requisite thereto. For example, let the quantity of heat 

 Q, produced in any manner whatever from work, be received by 

 the body K ; then by the foregoing circular process it can be 

 again withdrawn from K and transformed back into work, but 

 at the same time the quantity of heat Q^ will pass from Kj to 

 Kg; or if. the quantity of heat Qj had previously been trans- 

 ferred from Kj to Kg, this can be again restored to Kj by the 

 transformation of work into the quantity of heat Q of the tem- 

 perature of the body K. 



We see, therefore, that these two transformations may be 



