Theorem of the Mechanical Theory of Heat, 411 



To get the equivalence-value of a transformation of heat into 

 ergon, or vice versa, prefix to the quantity of heat a positive or 

 negative sign according as it is generated by ergon or is trans- 

 formed into ergon, and divide by the corresponding absolute tem- 

 perature. 



It is not needful to consider in detail in this place the way in 

 which the equivalence-value of a change of disgregation can be 

 completely determined ; it is sufficient in relation to this point 

 to state a general theorem which contains what is really essential 

 to this determination, as well as the principal result of the inves- 

 gations, so far as they relate to the question hitherto considered 

 by us. This theorem, in which, in relation to the equivalence- 

 value of the transformation of heat into work, or vice versa, the 

 above rule has been taken as the standard, is as follows : — 



The disgregation of every body can be determined in such a man- 

 ner that it is a magnitude depending solely upon the condition of 

 the body at any moment, and not upon the way by which it came 

 into this condition, and so as further to fulfil the condition that, for 

 every reversible alteration of a body, the alteration of disgregation 

 thereby occasioned and the simultaneous transformation of heat into 

 ergon, or vice versa, have equal and opposite equivalence-values, so 

 that their algebraic sum is zero. 



Two simultaneously occurring transformations, however, which 

 have opposite signs and equal absolute values, so that their alge- 

 braic sum is nothing, may be said to compensate each other ; and 

 consequently the above statement may be more shortly expressed 

 thus : — The two transformations ivhich accompany any reversible 

 alteration of a body are mutually compensating. 



Hitherto we have directed our attention to two kinds of trans- 

 formations exclusively; we have still, however, to consider trans- 

 formations of a third kind. 



Let us again suppose the given body, whose condition is 

 changed, to be any body whatever ; but let it now be assumed 

 .that not merely a single alteration of condition occurs, but a 

 series of alterations which are so arranged that the body finally 

 returns to its original condition, and thus passes through a cy- 

 clical process. 



If the final condition of the body is the same as at the begin- 

 ning of the cycle, its final disgregation is the same as its original 

 disgregation, and hence, considering the cyclical process as a 

 whole, we may say that no alteration of disgregation is caused by 

 it. But, notwithstanding this, heat may be transformed by it 

 into ergon, or ergon into heat. 



Let us suppose that the alterations in the condition of the 

 body which constitute the cyclical process involve changes of vo- 

 lume, in such sort that the body expands at one temperature and 



