14 THE TRUE VALUE OF a OF VAN DER WAALS' 



in the same proportion between the internal and external pressure 

 at the critical point. In other words it is the energy distribution 

 which is the same in all substances at the critical temperature. At 

 absolute zero, in the solid, the ratio of K, the internal pressure, 

 to P, the external pressure, is infinity. On heating, at first the kinetic 

 energy is used in overcoming cohesion. As the temperature rises 

 the 'external pressure, the vapor pressure, increases and the internal 

 pressure decreases. And at the critical temperature that state is 

 reached in which the ratio of internal to external pressure is always 

 a certain constant, namely 6.5. Certainly some kind of a ratio exists 

 between the internal and external pressure at the critical point, for 

 in helium the external pressure is only 5 atmospheres ; in hydrogen 

 it is 12; in pentane it is 33; and in water it is 200 atmospheres. 

 The internal pressure, or the cohesion of these substances, takes the 

 same order, being lowest in helium, and highest in water. Nor is 

 it likely that the greater or less volume occupied by the molecules 

 in different substances at T r will effect this ratio, for the correction 

 of b applies to both pressures equally and so presumably will 

 not effect their ratio. 



Even in the case of substances which associate, such as water, 

 acetic acid and so on, I consider it not unlikely that this ratio 

 will hold also and that K c , the internal pressure at T„ will also 

 be equal to 6.5 P c Only in these substances it is possible that 

 we have in addition to the cohesional attraction between the mole- 

 cules, such as is found in all substances, an additional attraction, 

 perhaps of a chemical nature, and it is this latter factor which 

 causes their association. In such a case A'., the internal pressure, 

 would be equal not only to a/V c 2 , but to this amount increased 

 by the unknown attraction. At any rate we can regard the matter 

 in this way for the present at least. 



That the ratio K c jP e is approximately or exactly 6.5 in all sub- 

 stances I shall now proceed to show. In the first place it may be 

 recalled that I found that the ratio KJP ( , was equal to SC' , where 

 C' was the constant in Dieterici's equation: L — E = C ' PTLn e (d\D), 

 and S the critical coefficient. *) The values thus found for K c jP r 

 varied from 6.14 — 7. 2 S in some 27 substances, the mean being 

 6.63. This is certainly a wide variation, but the variations were 

 not of a regular character, and they may have been due to the 

 fact that Dieterici's- equation is not exactly true, or that there may 



!) Mathews: Jour. phys. Chein., L><), 592 (1916). 



