410 Prof. It. Clausius on the Second Fundamental 



simultaneously occurring positive and negative transformations 

 shall have the same absolute values. 



In order that the fulfilment of this condition may be possible, 

 regard must be had, in determining the equivalence-value of a 

 transformation of heat into ergon, or vice versa, to an element of 

 which no mention has hitherto been made. This will be most clearly 

 seen if we take, as an example, a perfect gas as the body through 

 whose changes the transformation in question is brought about. 



Let there be given a quantity of a perfect gas occupying some 

 definite volume. If this gas expands to some other volume (say 

 to twice its original volume), an increase of disgregation occurs 

 which is completely determined by the original and final vo- 

 lumes. Moreover the expansion is accompanied by the trans- 

 formation of heat into ergon. And since no internal ergon is 

 performed in a perfect gas, its molecules being already so far 

 apart that their mutual action may be disregarded, we have to 

 take account only of the external ergon which is exerted in over- 

 coming the external pressure — that is, of ergon which can be easily 

 defined as to magnitude. The heat expended in the production of 

 this quantity of ergon must be imparted to the gas from without, 

 if its temperature is to remain constant. 



Let us now assume that the same process, the expansion of 

 the gas from its originally given volume to twice this volume, 

 takes place again at a higher temperature. The pressure of the 

 gas is greater in this case than in the former one, just in the 

 same proportion as its absolute temperature is now higher than 

 it was before. Consequently the amount of ergon that is done, 

 and the quantity of heat expended in producing it, is also greater 

 in the same proportion. Hence in this case, although the in- 

 crease of disgregation remains the same as before, more heat is 

 transformed into ergon. 



The equivalence-values of the transformations of heat into 

 ergon which take place in the two cases must, however, be equal 

 to each other, since the absolute magnitude of each is to be the 

 same as that of the equivalence-value of one and the same change 

 of disgregation. Hence it follows that the equivalence-value of a 

 transformation of heat into ergon depends, not alone on the 

 quantity of heat that is transformed, but also on its temperature ; 

 so that in the two cases above supposed, in order to obtain equal 

 equivalence-values for the transformations, the quantities of heat 

 must be divided by the corresponding absolute temperatures. 



The way in which the equivalence-values of transformations of 

 heat into ergon, or, conversely, of ergon into beat, are to be de- 

 termined is thus completely denned. Condensing what has 

 been said as to the sign and absolute magnitude into one short 

 statement, we obtain the following rule : — 



