MOTIVE POWER OF HEAT. 187 



48. In some very remarkable researches made 

 by Mr. Joule upon the heat developed by the 

 compression of air, the quantity of heat produced 

 in different experiments has been ascertained with 

 reference to the amount of work spent in the 

 operation. To compare the results which he has 

 obtained with the indications of theory, let us de- 

 termine the amount of work necessary actually to 

 produce the compression considered above. 



49. In the first place, to compress the gas from 

 the volume v + dv to v, the work required is pdv, 

 or, since 



PV =JV>.(1 + Et), 



Hence, if we denote by W the total amount of 

 work necessary to produce the compression from 

 Fto V 9 we obtain, by integration, 



W = p Q V Q (I + fit) log y,. 



Comparing this with the expression above, we find 

 W_(1+M) . . 



-Q = JE~ 

 50. Hence we infer that 

 (1) The amount of work necessary to produce 

 a unit of heat by the compression of a gas is the 

 same for all gases at the same temperature; 



