216 Theory of a Non-Conservative Gas [CH. x 



Specific Heat at Constant Pressure. 



261. To find G p> the specific heat at constant pressure, we suppose that 

 the absorption of heat takes place while the pressure of the gas is maintained 

 constant. The relation dp = will lead to a relation between dT and dv, 

 which must be substituted in equation (514). 



If we assume for p the form obtained in Chapter VI., namely 



, 



it is clear that the resulting equation will be one of extreme complexity, and 

 the results will be so complicated as to be unintelligible. Let us, then, 

 simplify the pressure equation by dropping the cohesion factor and assuming 



the relation 



p=v b RT. ................................ (517), 



leaving aside for the present any discussion of the exact meaning of this 

 procedure. The relation connecting volume and temperature when the 

 pressure is kept constant is now d(vi,T) = Q, and this may be written 



dT _ dv b _ dv 

 ~~ ~~~ dv\' 



Using this value for dv, and writing from equation (503) 



we find that equation (513) becomes 



The value of cftOl is now C p JNmdT, so that 



C - E f dv i 1 v * Vb dv (f(TM ) 

 * JNm 1^(17^) + * NT dv b (/1 (j 



+ #{71 + 3 + z/(//(T) +)}} ............ 



and it is clear from equations (516) and (518) that the quantities C p , O v , C P C V 

 and C p /C v ( = y) are no longer constants when the subsidiary temperatures 

 are taken into account. 



