18 M. R. Clauaiua on the Moving Force of Heat, 



for, SB already mentioned, R dv represents the quantity yf 



exterior work produced by the expansion dv. According to this, 

 the function U, which appears in equation (Ha.), cannot contain 

 V, and hence the equation changes to 



rfQ=crf/ + AR^rft;, .... (lib.) 



wherein e can only be a function of / ; and it is even probable 

 that the quantity c, which denotes the specific heat of the gas at 

 a constant volume, is itself a constant. 



To apply this equation to particular cases, the peculiar con- 

 ditions of each case must be brought into connexion therewith, 

 80 as to render it integrable. We shall here introduce only a 

 few simple examples, which possess either an intrinsic interest, 

 or obtain an interest by comparison with other results connected 

 with this subject. 



In the first place, if we set in equation (11^.) v= const, and 

 /)s=: const., we obtain the specific heat of the gas at a constant 

 volume, and its specific heat under a constant pressure. In the 

 former case dv=iO, and (116.) becomes 



f =^ ao-) 



In the latter case, from the condition p = const., we obtain with 

 help of equation (I.), 



, ndt 



av= , 



P 

 or 



. :■< , dv dt 



V a-ht' 



which placed in (lib.), the specific heat under a constant pressure 

 being denoted by c/, gives us 



^=c'=c + AR (10a.) 



From this it may be inferred that the difference of both specific 

 heats for every gas is a constant quantity AR. But this quantity 

 expresses a simple relation for different gases also. The com- 

 plete expression for R is ^^ ^ , where Pq, Vq,] and /q denote the 



contemporaneous values of ^, v, and t for a unit of weight of the 

 gas in question ; and from this follows, as already mentioned in 

 expressing equation (I.), that R is inversely proportional to the 

 specific heat of the gas ; the same must be tme of the difference 

 cr-ocs AR, as A i» for all gases the same. 



