Do Molecules Attract, Etc. 529 



to account for doubling the volume of b between o Abs. and 

 T c . Van der Waals 1 himself only assumed the constancy 

 of the molecular volume "6" for simplicity, an'd has now 

 definitely adopted the idea of a change in volume of the 

 molecules. He has obtained, by making certain assumptions, 

 the following expression for the change of il b, " the molecular 

 volume: (b b )/(V - - b) = = i - - (b -- b Y/(b g b }\ In 

 this equation b g and b are the limiting values of b ; b g at low 

 vapor pressures, and b under high pressure; the actual value 

 under any temperature and pressure is "b." Van der Waals 

 assumes that in liquids at low temperatures, b g == 2b . Both 

 probability and direct observation lead, therefore, to the 

 conclusion that the molecules expand on passing from the 

 liquid to the vapor state. 



It is clear that if the molecules do thus expand against- 

 the great force of atomic affinity, or intra-molecular cohesion, 

 some heat must be absorbed. The quantity thus absorbed 

 will probably be greatest at low temperatures, where there is a 

 maximum difference in cohesive pressure between the liquid 

 and the vapor, and will diminish rapidly near the critical 

 temperature, since the volumes of the molecules in the two 

 states approach each other and become equal at the critical 

 temperature. As we near the critical temperature, therefore, 

 the value of I will become very small, and the equation L - 

 E == A will become very nearly true. 



The second reason why the internal latent heat of 

 vaporization can not be assumed to go altogether to increas- 

 ing the distance between the molecules is the fact that the 

 internal pressure, the cohesive pressure, is inversely pro- 

 portional to the square of the volume. For, assuming as be- 

 fore that all the latent heat goes toward separating the mole- 

 cules, if a/V 2 is the cohesive pressure per unit surface then the 

 cohesive energy in the liquid will be a/V^ and in the vapor, 

 a/V,,; and the difference in their cohesive energies will be 



1 Van der Waals: "The Liquid State and the Equation of Condition," 

 Proc. Roy. Acad. Sci. Amsterdam (English Translation), 6, 123 ,(1903)- 



