MOTIVE POWER OF HEAT. 87 



invariable volume, but, ; s we shall see, they would 

 follow the same law if they were taken under con- 

 stant pressure. 



To what cause is the difference between specific 

 heats at constant volume and at constant pressure 

 really due ? To the caloric required to produce in 

 the second case increase of volume. Now, accord- 

 ing to the law of Mariotte, increase of volume of a 

 gas should be, for a given change of temperature, 

 a determined fraction of the original volume, a . 

 fraction independent of pressure. According to 

 the theorem expressed on page 76, if the ratio be- 

 tween the primitive volume and the altered volume 

 is given, that determines the heat necessary to pro- 

 duce increase of volume. It depends solely on this 

 ratio and on the weight of the gas. We must then 

 conclude that : 



The difference between specific heat at constant 

 pressure and specific heat at constant volume is 

 alivays the same, whatever may be the density of the 

 gas, provided the weight remains the same. 



These specific heats both increase accordingly as 

 the density of the gas diminishes, but their differ- 

 ence does not vary.* 



*MM. Gay-Lussac and Welter have found by direct 

 experiments, cited in the Mecanique Celeste and in the 

 Annales de Chimie et de Physique, July, 1822, p. 267, that 



