EQUATION AND THE NATURE OF COHESION. 25 



c. Calculation of a from the 'internal latent heal of vaporization. 



This method has already been described l ). There are three for- 

 mulas for the internal latent heat of vaporization from which one 

 might expect to make the calculation but only two of them actually 

 permit that this be done. These formulas are those of Mills, 

 Dieterici and Albertoni. Mills conation is : 



L—E=\il{d>®—W % ) (12) 



Dieterici's equation is 



L— E = CRT Ln e UljD) .(13) 



And Albertoni's is 



L—E = « (rf»/3_Z)V3)__/3 D{d— D)jd ( 14) 



a 



may be determined from these formulas in the following way. 

 If the interna] latent heat represented only the heat necessary to 

 overcome cohesion, then L — E should be equal to the difference 

 in cohesive energy in the liquid and vapor, or L — 2? should equal 

 a(l/v — l// 7 ). As a matter of fact some of the internal heat goes 

 into the molecules so that generally L — E is larger than the diffe- 

 rence of cohesive energy in the liquid and vapor. But as the critical 

 temperature is approached the differences between the molecules in 

 liquid and vapor become less and less and at the critical temperature 

 L — E must be precisely equal to a(ljv — I-/V) and this should be 

 equal to the right hand terms of the three equations just mentioned. 

 Hence we would have from Mills' equation a(l/o — 1//") — ft' 

 (d lli — Z» 1 ' 3 ) ; from Dieterici's we would have: a(l/v—l/V) = C'Rl 

 Ln c {djD) and from Albertoni's: a(l/v— \\V) = x{d' lz — Z> 5/3 )— 

 /3 D{d — -D)jd, in all cases at the critical temperature. Of course at 

 the critical temperature (l/v — \jV) and Ln e {djD) become equal to 

 zero, but the ratio has a definite value and at the limit, the critical 

 temperature, we have respectively from the three equations: 



From Mills 2 ) : 



a = i*.'M*l$dy* (15) 



From Dieterici 3 ) 



a = CET i r, (16) 



!) Mathews: Journal of phys. clieni. , 20, p. 554, 1910. 



2) Mills: Phil. Mag., (6) 22, 97 (1911). 



3) Dieterici: Wied. Ann., 25, 569 (1908). 



