Internal Pressure of a Liquid. 195 



We can write the above equation in the form 



where Z = 



L i. 



v 



And if we write I as a linear function o£ the temperature 

 we finally get some such equation as 



K = a + &TlogT + cT, 



where c, however, is an indeterminate integration constant. 

 The problem resolves itself into one quite analogous to that 

 which is being investigated by Nernst, viz. the connexion 

 between heat change and chemical affinity. 



It may be of interest to tabulate briefly the various 

 explicit expressions which have been put forward for K, 

 pointing out the assumptions upon which each rests. 



(a) The Dupre relation (Annates de Chimie et de Physique, 

 1864 seq., and ' Theorie mecanique de la Chaleur ') already 

 discussed, viz. 



K=Z. 



The assumption is that K is independent of temperature. 

 (6) Dupre (I. c.) suggested another relation, viz. 



K=-T|, 



where a x is the coefficient of expansion of the liquid with 



temperature, 

 and /8 „ „ compressibility o£ the liquid at 



constant temperature. 



The above relation may be obtained as follows, assuming an 

 equation of the van der Waals type, viz. 



ET „ 

 p= -K. 



v — b 



On differentiating with respect to temperature, assuming 

 b is constant and further assuming as Dupre did that K is 

 also independent of temperature, one obtains 



(^7 ) =J ^ri — = ™ neglecting p compared with K. 

 02 



