Determining "a" of van der Waals' Equation 157 



difference of opinion as to the value of the coefficient which 

 is given as 1/3 by Young, 1 but as 3/20 by Rayleigh. 2 As 

 will be shown presently, Young's value is to be preferred. 



The value of Si^ 2/3 , the molecular surface tension energy 

 at absolute zero, may be obtained from Eotvos 3 and Ramsay 

 and Shields' 4 rule, $(m<v) 213 -= 2.12 (or 2.ig)(T c T 6). 

 S(w7;) 2/3 divided by N 2/3 , where N is the number of molecules 

 in one gram mol, equals Si; 2/3 . Hence S^ 2 ' 3 

 2.i9(T c - T - - 6)/N 2/3 ; and at absolute zero, where T is 

 zero, S<z; 2/3 = 2.i 9 (T c 6)/N 2/3 == 3.015 X io- 16 (T c 6) ergs. 

 It is assumed that the law holds clear to absolute zero. 



I have used the coefficient 2.19 because I thought it 

 more typical of a non-associating substance, and it is nearer 

 to the value of Eotvos. However, this has given me slightly 

 higher values for "a" than those generally computed, as may 

 be seen in the table. The agreement with other values of 

 "a" seemed on the whole better with this coefficient. It 

 varies slightly with different substances in any case being 

 nearly 2, for- some gases like oxygen, and as high as 2.3 for 

 very complex substances. 2.19 comes close to the mean. 



We have then $V /3 - M 2 K/ 3 ^ = 3.015 X iQ- 16 (T - - 6) 

 ergs. SoM 2 K -= 9.045 X iQ- 16 (T c 6)v . 



The value 6 subtracted from the critical temperature 

 was established for substances having a critical temperature of 

 about 4oo-48o Abs. It would be better perhaps to make 

 it i/8oth of T c . The formula corrected thus would be M 2 K = 

 9.045 X io~ 16 T c i; 79/80 =8.932 X io- 16 T c T; . As this last 

 correction is uncertain, however, I have uniformly subtracted 

 6 from the critical temperature, unless it is specifically 

 stated to the contrary. 



1 Young: "An Essay on the Cohesion of Fluids," Philosophical Trans- 

 actions, 1805. (Collected works, edited by G. Peacock, Vol. I, 1855, p. 418, 

 London.) 



2 Rayleigh: Article on "Capillarity," Encyclopoedia Britannica, xi 

 edition. 



3 Eotvos: Wied. Ann., 27, 458 (1886). 



4 Ramsay and Shields: Zeit. phys. Chcm., 12, 433 (1893). 



