Page:Outlines of Physical Chemistry - 1899.djvu/76

 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 =  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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