261-263] Specific Heats 217 



Specific Heats when Subsidiary Temperatures are neglected. 



262. If we neglect subsidiary temperatures, the values of the specific 

 heats assume the simple forms 



C, = il( + 3) .................................... (519), 



The quantities C p , C P C V and 7 accordingly depend on the deviations from 

 Boyle's law. 



If we expand v b as far as the first order of small quantities in the form 



N 

 vi> = =- , where b is the b of Van der Waals' equation, 



v o 



__ _ 

 dv\v b ) ~ N dv ' ' N' 



and equation (520) becomes 



C p = t^( n +V ........................... (521), 



so that as far as the first order of small quantities the quantities C p , C v , and 

 of course also their difference and their ratio, become constants. The value 

 of y is now 



' ' 



These results are exactly those which would be obtained if the molecules 

 possessed no energy except that of the (n + 3) momentoids governed by the 

 principal temperature. 



EXPERIMENTAL VALUES. 



Values of G v . 

 263. With the help of the formula 



it is easy to deduce the value of n, from observations on the value of C v . 

 The value of / is known, to within sufficient accuracy for the present purpose, 

 to be 



/=4'22xl0 7 . 



The value of Rfm has already been tabulated for a number of gases (p. 113). 

 Hence we obtain the following table : 



