56 OUTLINES OF PHYSICAL CHEMISTRY
and from these three equations we can deduce the characteristics of the critical state, v u p u t 1? expressed in terms of a, b, and b :
a
��„ pressure . . p x =
��27 b*
��„ „ temperature . . t x = ^ . ^.
For carbon dioxide, the critical temperature thus calculated (32*5°) approximates fairly closely to that experimentally found by Andrews (31°). For the pressure and volume the agreement is not quite so good (61*2 and
The constants a and b and the critical temperature of other substances have also been established by calculation in quite a satisfactory manner.
The Theory of the Corresponding States. — If in Van der Waals's equation we put
p = irp l9 v = <pv ] and t = 0t,,
that is to say, if we consider the actual pressure p as a fraction n of the critical pressure p u and in the same way the volume and temperature as fractions, </> and 0, of the critical volume and temperature ; and if at the same time we express a and b in terms of p x and v x :
& = ?'a = 27^ l & 2 = 3 i ? l V:
then after some simple transformations we obtain
(t + ^ 2 ) (3^-1) = 80.
1 Van der Waals's equation gives a very good qualitative interpre- tation of the facts observed by Andrews. From the quantitative point of view the interpretation is not quite so good. The reader will gain a good idea of this inexactitude by calculating the values of p, for a given temperature, which correspond to different values of v, and describing the isotherm thus determined beside the experi-
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