The Internal Pressures of Liquids 613 



2. Derivation of "a" from the Surface Tension by Eotvos 



Law 



By the law of Eotvos the surface-tension energy TV* /3 is 

 equal to C(T C T). The surface-tension energy is a linear 

 function of the temperature counting downward from the 

 critical temperature. The derivation of TV* /3 and N 1/3 TV 2/3 

 has already been given on page 607. 



a. What is C of Eotvos? 



Eotvos found that C varied between 2.27 and 2.34 as is 

 shown in Table 4, but he believed the variation to be acci- 

 dental and that C should be constant for all substances. It 

 has since been shown that C is not constant. What C is may 

 be shown as follows : 



Since the surface energy decreases uniformly with an in- 

 crease of the kinetic energy of the molecules, and is accordingly 

 a linear function of the temperature, one of the constitutents 

 of C must be the gas constant R; and since there are onlyN 2/3 

 molecules in the surface, where N is the number in a gram mol, 

 R must be R for a gram mol divided by N 1/3 . The remainder 

 of C should be 1 / 3 the ratio of the internal to the external pres- 

 sure at the critical temperature as that is the point of depart- 

 ure. Young has shown that the surface-tension pressure is 1 / 3 

 the cohesive pressure; and the greater the external pressure 

 the less important the internal pressure will be. Hence C, I 

 thought, must equal K C R/3P C N 1/3 . While the foregoing rea- 

 soning was not entirely convincing the result turned out to 

 be correct, I believe, as will presently be shown. I have 

 uniformly taken N as 6.21 X io 23 and R as 8.321 X io 7 . 



(8) TVl /s = K c R(Tc T) / 3 PcN 1/3 . 

 Since K c == a/V* we have 



(9) TVl /3 = aR(T c T) / 3 V'P C N 1/3 

 (io) a = 3 T c V c N 1/3 rv; /3 / (T c T)S, 



since RT C /V C P C = S, and R == SV C P C /T C . 



Formula (io) gives the second method of computing "a." 



