Do Molecules Attract, Etc. 525 



size in liquid and vapor, or do not in other ways gain energy. 1 

 I believe the internal latent heat of vaporization consists of 

 at least three parts, not two as is often stated, these three 

 parts are : (i) the heat consumed in expanding against external 

 pressure, or E; (2), the heat consumed in overcoming molec- 

 ular cohesion, or A; (3), heat consumed in increasing internal 

 molecular potential energy by expanding the molecule, or 

 increasing its energy of rotation, or I. This last factor is 

 often overlooked. If L is the total latent heat of vaporiza- 

 tion the expression should be : L E I == A. And if mole- 

 cules attract inversely as the square of the distance we should 

 have (I, E I)/(V^ VDJ - /. 



There are two principal reasons why it cannot be assumed 

 that all the internal latent heat of vaporization goes to in- 

 creasing the potential energy by separating the molecules 

 against the force of their molecular cohesions. The first of 

 these reasons is that the value "b," of van der Waals' equa- 

 tion, has to be taken larger in the vapor than in the liquid 

 for some distance below the critical point. And there are 

 good reasons for thinking that "6" represents the real volume 

 of the molecules. The second reason is the value a/V 2 re- 

 presenting cohesion in van der Waals' equation. A third 

 reason has been given by Tyrer. 



To show that the molecules actually do expand in passing 

 from the liquid to the vapor, I have calculated the value of 

 "6" for pentane, and benzene using Young's data. I have 

 also calculated several others of his substances, but as the 

 result is similar in them to that in these two, I give only the 

 latter in Table 2, which shows the value of b in cc in the liquid 

 and vapor for gram molecular quantities b V - RT/- 

 (P + a/V 2 ). 2 



1 A similar objection to Mills' conclusion has been raised by Professor 

 Tyrer: Phil. Mag., [6] 23, 112 (1912). 



2 Since sending this paper to the publisher I have found that the value of 

 "a" is larger than assumed here. This change requires be and b-v both to be 

 larger. At 150 bv should be about 127 cc and at 40 only 14. The relation 

 between b e and bv is not greatly changed, but the difference between them 

 becomes greater. 



