194-198] Specific Heats 169 



CALORIMETRY. 

 Specific Heats of a Perfect Gas. 



196. We now turn to an investigation of the specific heats of a gas, 

 and shall begin by considering the simplest case, namely that of a perfect 

 gas in which the relation between pressure, volume, and temperature is 



(399). 



The equation of energy in this case becomes 



...(400), 



9 



and this may be regarded as the general equation of calorimetry. 



197. Let us first suppose that a quantity d(& of energy in the form of 

 heat is absorbed by the gas, while the volume of the gas is maintained 

 constant. In this case all the heat goes towards raising the temperature of 

 the gas, equation (400) assuming the form 



d<&=NdE ................................. (401). 



Let C v be the specific heat of the gas at constant volume, i.e., the amount of 

 heat required to raise the temperature of a unit mass of gas by one degree, 

 then 



(402)> 



and therefore equation (401) becomes 



198. Next, let us suppose that the absorption of heat takes place at 

 constant pressure. In this case both the volume and temperature will 

 change, but from equation (399) they must change in such a manner that 



T 



= constant. 



v 



If we differentiate this equation logarithmically, we obtain 



d^_dv_ 

 T ~ v ' 



as the relation between dT and dv when the pressure is maintained constant, 

 and using this relation, equation (400) becomes 



d(& = NdE+RNdT ........................ (403). 



The value of d<& is now JC p NmdT where C p is the specific heat at constant 

 pressure. Hence equation (403) leads to the relation 



C p = d ~+^ ........................... (404). 



* Jm dT Jm 



