Determining "a" of van der Waals' Equation 159 



With the values thus found for four of the most carefully 

 investigated non-associating substances, the value of the real 

 molecular volume, or b c , at the critical temperature was com- 

 puted by substituting in van der Waals' equation, with the 

 following result : 



By substituting the values of M 2 K derived in the fore- 

 going manner from the surface tension, b c turns out to be the 

 same fraction of V c for the three best investigated, normal 

 substances, ether, pentane and iso-pentane, a result antici- 

 pated from van der Waals' reduced, characteristic equation. 

 V c is, therefore, 2.074^. The value thus obtained for b c , 

 namely V 72.074, is very close to that calculated by van 

 der Waals from a value of "a" obtained from the coefficient 

 of compressibility. He thus obtained the value V c == 2.036^ 

 Other estimates of b c made by him bring it about 2.08. This 

 value of b c , moreover, is inherently probable, the value of b c 

 necessarily being close to V c /2, and presumably a little less 

 than this. 



We may now, with this value of b c fixed, calculate by 

 substitution in van der Waals' equation the value of the 

 coefficients in the formulas given on page 154 in place of those 

 derived when "a" and "b" were considered constant. 



The following relationships were obtained : 2 



1 a/P c = 6.284V, 2 ; in place of a/P c = 3V C 2 . 



2 V^ = 2.074^; in place of V c = $b c . 



3 p c = a/27.026 c 2 ; in place of P c = a/2jb c 2 . 



4 T c == 7.769a/27.02R6 c ; in place of T c = 8a/2jRb c . 



5 b c + RT C /P C = 4-243 V c ; in place of b c + RT C /P C = 3 V C . 



6 P C V C /T C == R2.074/7.769 = 21.92; in place of P C V C /T C - 3 R/8 * 



30.80. 



7 RT C /P C V C = 3-75- 



1 Van der Waals: Proc. Roy. Acad. Sci., Amsterdam, 3, 583 (1901). 



2 Compare with van der Waals: Proc. Roy. Acad. Sci., Amsterdam, 13, 

 (1912). 



