592 RICE ART. L 



methods. Thus by the second equation of (22) 



dp 

 and 



dUt, V, s, r) 



= v{t, p, s, r)*, 



= <^ii, V, r). 



ds 

 Hence by cross-differentiation 



dv(t, p, s, r) _ dajt, p, r) 

 ds dp 



The left-hand side is the quantity — F in Gibbs' text. This 

 equation also appears in Lewis and Randall's book as equation 

 19 of Chapter XXI. 



34. Empirical Relations Connecting a- and t. Degree of Molecular 



Association in Liquids 



We have referred above to the approximately linear relation 

 between surface tension and temperature for many liquids. 

 Also, since surface tension must vanish at or near the critical 

 temperature of a liquid, the relation should then be 



(T = Co 



(■4). 



where o-q is a constant for the liquid and tc the critical tem- 

 perature. Almost 50 years ago Eotvos from a not too rigorous 

 argument suggested that the constant o-o should vary as the 

 number of molecules in unit area of the liquid surface; since 

 the number of molecules per unit volume varies inversely as 

 MV, where M is the molecular weight of the liquid and V the 

 specific volume of the liquid, ao would then vary inversely as 

 (M7)* or directly as (D/M)^, where D is the density of the liquid. 

 About ten years later Ramsay and Shields, in a series of well- 



Note that V is the volume of the whole system. 



