If the reduced pressure of a gas is given, we can easily calculate its actual pressure
by using p = prpc, and likewise for the volume and temperature. van der Waals, who
first tried this procedure, hoped that gases confined to the same reduced volume, Vr,
at the same reduced temperature, Tr, would exert the same reduced pressure, pr.
The hope was largely fulfilled (Fig. 1.21). The illustration shows the dependence of
the compression factor on the reduced pressure for a variety of gases at various
reduced temperatures. The success of the procedure is strikingly clear: compare this
graph with Fig. 1.14, where similar data are plotted without using reduced variables.
The observation that real gases at the same reduced volume and reduced temperature
exert the same reduced pressure is called the principle of corresponding states.
The principle is only an approximation. It works best for gases composed of spherical
molecules; it fails, sometimes badly, when the molecules are non-spherical or
polar.