288 HEAT. 



by Joule for water. He showed that on compression there was a very 

 slight cooling at 12 C., which changed to a very slight warming at 

 5 C., and the higher the temperature above 4 C. the greater was the 

 warming. 



The Specific Heats at Constant Pressure and at Constant 



Volume. The specific heat of a substance at a given temperature is not 

 an invariable quantity but depends to some extent on the conditions 

 under which the heat is communicated, this dependence being most marked 

 in the case of a gas. It is usual to consider especially two kinds of specific 

 heat, that when the pressure is maintained constant, and that when the 

 volume is maintained constant. For gases (as we have already seen in 

 chap, vi.) these two specific heats differ very nearly by the heat equivalent 

 of the external work done in the expansion, and the difference is a large 

 fraction of either. For solids and liquids the difference, though appreci- 

 able, is not nearly so important. We shall denote the specific heats at 

 constant pressure and constant volume, respectively, by C p and C u when 

 in heat units, and by K p and K,, when in work units. The elasticity of a 

 substance, i.e. the ratio of a small change of pressure to the consequent 

 change of volume per unit volume, is also a variable quantity depending 

 on the circumstances of the change. There are two especially important 

 cases, the elasticity when the change is adiabatic a condition \vhich 

 holds if the change is very sudden ; and the elasticity when the change 

 is isothermal a condition which holds if the change is suificiently slow. 

 The two are denoted respectively by e$ and e g . We shall now prove a 

 very important relation connecting the specific heats and the elasticities. 

 The ratio of the two specific heats y is equal to the ratio of the two 

 elasticities, 



K e* 



or ^r = - 



K,, et 



In Fig. 165 let BA and BC represent adiabatic and isothermal 

 elements through B, cutting a line of equal pressure in AC, and let BH 

 be perpendicular to AC 



change of pressure along BA 

 change of volume along BA 



BH 

 X HA 



Similarly 



BH 



Then 



Now HO _ heat received along HC (since both are at constant 

 HA " heat received along HA pressure) 



heat along HC 



, (since AB is an adiabatic) 



heat along HB 



