30 THE TRUE VALUE OF a OF VAN DER WAALS' 



van La All's values are incorrect. These values are compared in 

 Table 2 column 7. 



/'. Computation of a from Van der Waals equation when b is 

 separately determined by means of a modified ('rompions equation. 



I will here simply call attention to this method without calcu- 

 lating the values as they are the same as the values calculated from 

 the latent heat in other ways. Here, however, we make the calcu- 

 lation from the total latent heat and not from the internal latent 

 heat as in Mills' and Dieterici's equations. 



Crompton's equation is: 



L= 2BTlM f {d/D) 



From this equation Mills gets the result that T{dPjdT) r = 

 %BT/F e . Since T c (dPjdT) c is equal to P c -f ajV c 2 , which is equaJ 

 to ll2\.j{V r - — b c ) it is clear that in place of 2 we should have 

 Vcji^'c — ^)- From the latent heat we may hence calculate b c and 

 from the value of b c thus found we may get a by substituting 

 in van der Waals' equation at the critical temperature. I have 

 computed pentane at 170° by this method. The result was that 

 V c jb c came out 2.016. Tins gives a of 20.S4 X 1()12 dvnes for 

 a gram mol. This agrees closely with a determined for pentane 

 in other ways as shown in table 2. In the case of octane the 

 agreement is not so good, in ^-octane at 220° b,. is found to be 

 only r c /1.89 whereas /'./2.02 is required. This value of r/1.89 

 for b r would give for a, 43.25 X10 12 which is nearly that given 

 by Dieterici's equation from the internal latent heat and much 

 higher than most of the other methods. I have not calculated any 

 other substances but I suppose they would agree very well on the 

 whole with the calculation from Mills' and Dieterici's equations. 

 It will in this respect bear out the other computations. 



From this equation combined with Dieterici's we have at once 

 Kl(F—h) = l/#+ a/BT c /', = l/tf+ C'. For many substances 

 S is about 3.75 and C' is 1.733 so that l/S -f C = 2. 



Putting this equation of Crompton's in this form makes it more 



easily understood. As is shown later on, Log a = JL' (V c — b,)Jb c . 



K'V C 

 From this we get for the value of VJiV^—bX , — ^— • The equa- 

 ' ,K ' c ' b r Loga l 



tion thus becomes: L = {K'V c \b c Log a) BT 'lM e {djD). In a perfect 



