190 ' THOMSON ON CARNOT'S 



III. On the Specific Heats of Gases. 



52. The following proposition is proved by 

 Carnot as a deduction from his general theorem 

 regarding the specific heats of gases. 



The excess of specific heat* under a constant 

 pressure above the specific heat at a constant volume, 

 is the same for all gases at the same temperature 

 and pressure. 



53. To prove this proposition, and to determine 

 an expression for the "excess" mentioned in its 

 enunciation, let us suppose a unit of volume of a 

 gas to be elevated in temperature by a small 

 amount, T. The quantity of heat required to do 

 this will be AT, if A denote the specific heat at a 

 constant volume. Let us next allow the gas to 



O 



expand without going down in temperature, until 

 its pressure becomes reduced to its primitive value. 



ET 



The expansion which will take place will be -- , 



1 -j- Et 



if the temperature be denoted by t ; and hence, 

 by (8), the quantity of heat that must be supplied, 

 to prevent any lowering of temperature, will be 



Et 



* Or the capacity of a unit of volume for heat. 



