Fundamental Theorem in the Mechanical Theory of Heat. 91 



temperature t, was converted into work; this gives — Q , f{t) 

 as its equivalence-value, and that of the quantity of heat Q^ 

 transferred from the temperature t^ to t^, will be QiF(ti, t^), so 

 that we have the equation 



-Q./(i!)+Qi-F('..y=o (5) 



Let us now conceive a similar process executed in an opposite 

 manner, so that the bodies Kj and K^, and the quantity of heat 

 Qi, passing between them, remain the same as before ; but that 

 instead of the body K of the temperature /, another body K' of 

 the temperature / be employed ; and let us call the quantity of 

 heat produced by work in this case Q', — then, analogous to the 

 last, we shall have the equation 



Q!f{t') + <ii^{t^,ti)=0 (6) 



Adding these two equations, and applying (4), we have 



-Q/(0+Q'yi^')=o (7) 



If now we regard these two circular processes together as one 

 circular process, which is of course allowable, then in the latter 

 the transmissions of heat between Kj and Kg will no longer 

 enter into consideration, for they precisely cancel one another, 

 and there remain only the quantity of heat Q taken from K and 

 transformed into work, and the quantity Q' generated by work 

 and given to K'. These two transformations of the same kind, 

 however, may be so divided and combined as again to appear as 

 transformations of different kinds. If we hold simply to the 

 fact that a body K has lost the quantity of heat Q, and another 

 body K' has received the quantity Q', we may without hesitation 

 consider the part common to both as transferred from K to K', 

 and regard only the other part, the excess of one quantity over 

 the other, as a transformation from work into heat, or vice versd. 

 For example, let the temperature t' be greater than t, so that 

 the above, being a transmission from the colder to the warmer 

 body, will be negative. Then the other transformation must be 

 positive, that is, a transformation from work into heat, whence 

 it follows that the quantity of heat Q' imparted to K' must be 

 greater than the quantity Q lost by K, If >ye fcid^ ,Q'. into 

 the two parts ^,;.j,jj owi ^*rit (r'+iiw 



QandQ'-Q, 



the first will be the quantity of heat transferred from K to K|, 

 and the second the quantity generated from work. 



According to this view the double process appears as a 

 process of the same kind as the two simple ones of which 

 it consists, for the circumstance that the generated heat is 

 not imparted to a third body, but to one of the two between 

 which the transmission of heat takes place, makes no essential 



