124 Transactions of the Boyal Society of South Africa. 
§ 2. The van der Waals ''a" as a Function of the Temperatuee. 
Following KuENEN, we shall, as a first approximation, regard the a of 
the equation — 
^+|.)(f-*)=ET (2) 
as a function of T only, and as a quantity which is independent of T. 
By applying well-known thermodynamical relationships we easily 
obtain — 
t'^'' -vvfT'^'- 
(3) 
where 2h is the vapour-pressure at temperature T, and i\ and are the 
specific volumes of the respective phases of the complex on the same 
isothermal. Integration between any two temperatures gives— 
Tjr\Tjrj ¥-tTi?-i^.)'^T ... (4) 
As experimental substance Isopentane was selected, for which the 
saturation data have been determined with great accuracy by Young,"'' 
Pcm.^ mm. Hg.~~| 
From these data the integrand of (4) was evaluated in — - — ^-^ — J 
units. These figures are given in column A of Table I. Integration was 
performed by means of a large-scale drawing on millimetre paper. The 
critical temperature was taken for the lower limit, and for the integration 
constant was written — 
For isopentane this becomes- 
3 X 250 1 5 X (4-266) ^ _ rcm.^ mm. Hg 
460-8 ^ o(j 
Column B of Table 1. gives the values obtained for the right-hand side 
of (4), and in the other columns are given values of a and of log a as 
functions of T. 
The last column of the table and Fig. 1 show conclusively that log a 
is a linear function of T, so that we may write — 
a = £"-/3T (6) 
* S. Young : Proc. Phys. Soc. 13 (1895), p. 602. 
