8 



M. R. Clausius on the Moving Force of Heat, 



of 100°, and the increase of expansive force observed. If, how- 

 ever, the pressure be allowed to remain constant, and the increase 

 of volume observed, we obtain the somewhat higher value 

 0*003670. Further, the values increase when the experiments 

 are made under a pressure exceeding that of the atmosphere, and 

 decrease when the pressure is less. It is clear from this, that 

 the exact value for the ideal condition, where the differences 

 pointed out would of course disappear, cannot be ascertained. 

 It is certain, however, that the number 0*003665 is not far from 

 the truth, especially as it very nearly agrees with the value found 

 for hydrogen, which, perhaps of all gases, approaches nearest the 



ideal condition. Retaining, therefore, the above value for -, we 



have 



«=273. 



One of the quantities in equation (I.), for instance p, may be 

 regai-ded as a function of the two others ; the latter will then be 

 the independent variables which determine the condition of the 

 gas. We will now endeavour to ascertain in what manner the 

 quantities which relate to the amount of heat depend upon v 

 and t. 



When any body whatever changes its volume, the change is 

 always accompanied by a mechanical work produced or expended. 

 In most cases, however, it is impossible to determine this with 

 accuracy, because an unknown interior work usually goes on at 

 the same time with the exterior. To avoid this difficulty, Carnot 

 adopted the ingenious contrivance before alluded to : he allowed 

 the body to undergo various changes, and finally brought it into 

 its primitive state ; hence if by any of the changes interior work 

 was produced, this was sure to be exactly nullified by some other 

 change ; and it was certain that the quantity of exterior work 

 which remained over and above was the total quantity produced. 

 Clapeyron has made this very evident by means of a diagram : 

 we propose following his method with permanent gases in the 

 first instance, introducing, however, some slight modifications 

 rendered necessai-y by our maxim. 



In the annexed figure let oe 

 represent the volume, and ea the 

 pressure of the unit weight of 

 gas when its temperature is t ; 

 let us suppose the gas to be 

 contained in an expansible bag, 

 with which, however, no ex- 

 change of heat is possible. If 

 the gas be permitted to expand, 

 no new heat being added, the 

 temperature will fall . To avoid 



