EQUATION AND THE NATURE OF COHESION. 15 



be some other complicating circumstances. This value alF c 2 P c is 



(T dP) 

 equal to — — 1. For this fraction van der Waals *) cal- 



( Jr û ' 1 ) ,. 



ciliated for C() 2 the value of 5.7 but this was obtained by the 

 differentiation of Riot's formula for the saturated vapor pres- 

 sure, log P = A -\- Ba! -\- Cfi' , and it has been shown by Mills -) 

 that this gives a value for {dPjdT),. from 10—20% too low. If 

 we increase 5.7 by. 15% it makes 6.5 5. j 



The second method of finding K c /P c is the following: 

 We may find Avhat the ratio (K c -f- P c )/K is from the ratio of 

 the total latent heat of vaporization, L, to the internal latent heat 

 of vaporization, L — E, as the critical temperature is approached. 

 The total heat of vaporization, L, is made up of three parts: 

 (1) the external work done, which is equal to P{V — v): (2), the 

 work done against cohesion, which is equal to a{\Jv — i-jE); 

 and (3), the heat rendered latent by the expansion of the molecules 

 or their change in energy as they pass from the liquid to the vapor, 

 or Z. The internal latent heat is the total heat, L, less the external 

 work, or E, hence we have 



L P{V- -v) + a(l/v - -1/D+JZ (1) 



L — E' a(l/v — l/F)-\ r Z 



Now as the critical temperature is approached Z becomes smaller 

 and smaller and it will vanish before the other two portions of the 

 latent heat vanish, because as the conditions of the vapor and liquid 

 become more nearly alike there will be less and less difference 

 between the molecules in the two states. Since they are already 

 under great internal forces, they will be less affected as the critical 

 temperature is neared by the difference in internal pressure in liquid 

 and vapor than are the cohesion and pressure energies. Hence as 

 the critical temperature is approached the limiting value of the 

 ratio Lj{L — E), which at the critical temperature has the inde- 

 terminate form 0/0, will be 



L-E=^~\P ' (2) 



The value of this fraction should be in all cases 7.5/G.5, or 

 1.154, if a/F c 2 = 6.5 P c . I have computed the value of this ratio 



!) Van der Waai. s: Proceedings, Amsterdam Academy, 3. 583 1 11)01). 

 2 ) Mills: Jour. pays. Cliem., 8, 593, (1904). 



