116 SPECIFIC HEAT AT CONSTANT PRESSURE. 



68. Comparison of Specific Heat at a Constant 

 Pressure with that at a Constant Volume. In the 



specific heat of gases there are two cases to be considered : 

 (1) when the pressure remains constant, the gas being 

 allowed to expand ; (2) when the volume is constant. 



Let the pressure p remain constant while the application 

 of a small quantity of heat H increases the temperature T 

 by T, and changes the density from p to p'. From (2) of 

 Art. 55, by putting lea = JT, we have 



p = KpT=Kp'(T+r). (1) 



Now if the air be rapidly compressed into its original 

 volume, its temperature will be increased (Art. 65), and we 

 shall have 



the increase of temperature _ p p' 

 ~~ ~~ 



where ^ is a constant. 



.'. the increase of temperature = JUT, (2) 



and hence the whole change of temperature produced by 

 the heat H, when the volume is constant, 



= T '+ /iT = AT. (3) 



In order, therefore, to produce a change of temperature 

 T when the volume is constant, the quantity of heat required 



is -y, and consequently, 



A 



specific heat at constant pressure _ H . , 



specific heat at constant volume H 



T 



COB. Therefore the specific heat at a constant pressure 

 exceeds the specific heat at a constant volume; and this 



