1887.] 



Tliermodynamic Properties of Substances. 



51 



Now in this case the following are the forms that the thermo- 

 dynamic equations assume. T is temperature, and is entropy, and 

 e and e are functions to be investigated, c being = dIJdT, where 1 is * 

 the internal energy, and e — dl/dv. 



Then - 



Td<fi = cdT+ (e-t p)dv. 



From this, as de/dT = dcjdv, we have dpJdT — e-fp/T. 



But dp/dT — a by the intrinsic equation, and is a function of v 

 only, . * . e = — b, which is a function of v only, . ' . de/dT = 0, 

 . ' . dejdv = 0, . ' . is c a function of T only, and dl = c dT -\-edv gives — 



I=fcdT +fe dv = 7 + X, 



where 7 is a function of temperature only, and X a function of volume 

 only. 



Similarly, 



Ti0 = cdt + aT dv; 

 . • . dxf) = ~ . dt +• adv, 



where r is a function of temperature and a of volume only. 



Hence we see that c, the specific heat at a constant volume, is a 

 function of the temperature only, and the internal energy and the 

 entropy can be expressed as the sums of two functions, one a function 

 of the temperature only, and the other of the volume only. 



For the specific heat at constant pressure we have — 



= c + oT. 



where a!=dajdv and b'=db/dv, 



C-c = 



Ta' + b' 



In the case of the particular values of a and b that Professor 

 Ramsay has suggested to me, when the intrinsic equation assumes the 

 form — 



_ RT fi 

 ^ ~ v—v v n ' 



E 2 



