756 



III. The values of nk and hk at the critical point. 



In consequence of the variability — not only of a, but also of b 



— it is exceedingly difficult, if not impossible, to separate the two 

 constants of v. d. Waals's equation of state. For large volumes 

 only the quantity RTh,, — a can be calculated, so that nothing would 

 be left but to calculate the corresponding \'b\\\q oï b ïov Siw arbitrarily 

 assumed value of a. 



Fortunately there is a circumstance — at least for H, — which 

 enables us to separate the values of a and b, i.e. this circumstance 



that very probably the ratio — is constant at all temperatures -. hence 



a 



that a and b vary equally with T, or that a varies together with h. 



Kamert.ingh Onnes^) recently found: 



974 



Tk ^ 33°,18 ahs. ; pk = — 12,816 atm. \ dk= ^ 0,0310. 



76 



From this we calculate: 



RTk 0,0036618X33,18 0,121499 ^^,,^,^ 



hv — —^— ~ — ~-^- rrr 0,0011850. 



p/c 8x12,816 102,528 



This is still to be multiplied by {1 -\- a) (1 — b) = 1 —{b — a) at 

 0° C, i.e. by 1—5,9.10-4 = 0,99941. Because of this bk becomes: 



Z)fczr: 1184,3 X 10-^ ....... (I) 



expressed in the normal volume at 0° C. Further: 



27 27 



ak — RTk X bkX— = 0,00014398 X — = 0,00048592 : X . 



oX oA 



27 / 7 A' . ^ 

 In this the correction quantity X = with y = 



' ' 8y— iVy+»y 



— (1 _|_004 1 ^7\) : 2 = 0,6152 {\/Tk being =5,760) has the value 

 6,885 X (0,3809)' = 0,9988. Hence ak becomes = 0,0004865. But 

 this must now be multiplied by f0,9994)' = 0,9988, as we have 

 taken the uncorrected values for RTk and bk- In consequence of 

 this we get: 



or still better with h—"k would be more plausible than with v-Vs. For then (for 

 ft-'/s) the attraction would be in inverse ratio with the molecule surface. I had, 

 indeed, considered this last possibility before. Then tht- quantity b would vary 

 directly with T, and a would simply follow the variations of ö — on account of 

 the proportionality with b—^ls 



There are other advantages connected with the supposition a •.• i';—-/». Forv = oo 

 a would at the same time with b approach a limiting value a,;, and for v = Vq 

 the lowest limiting value Uq would be in the same relation to ak as (bk : bQ)V3, 

 which numerically leads to very good results. 



1) These Proc. Vol. XX p. 178—184. 



