96 MOTIVE POWER OF HEAT. 



Let a and 1} be the quantities of heat employed 

 successively in the first of the two operations, and 

 let V and a' be the quantities of heat employed 

 successively in the second. As the final result of 

 these two operations is the same, the quantities of 

 heat employed in both should be equal. We have 



then 



a + b = a' + V, 



whence 



a' - a = b -b'. 



a' is the quantity of heat required to cause the 

 gas to rise from 1 to 100 when it occupies the 

 space abef. 



a is the quantity of heat required to cause the 

 gas to rise from 1 to 100 when it occupies the 

 space abed. 



The density of the air is less in the first than in 

 the second case, and according to the experiments 

 of MM. Delaroche and Berard, already cited on 

 page 87, its capacity for heat should be a little 

 greater. 



The quantity a' being found to be greater than 

 the quantity a, b should be greater than b'. Con- 

 sequently, generalizing the proposition, we should 

 say: 



The quantity of heat due to the change of volume 

 of a gas is greater as the temperature is higher. 



