
234 The Principles of Thermodynamics
vdW pressure is always greater than the ideal gas pressure. In the interesting
cases where both the parameters are non-vanishing, it can go both ways. Let
us compute the difference in the pressures
P
ideal
−P
vdW
=
RT
V
−
RT
V −b
+
a
V
2
= −
RTb
V (V −b
+
a
V
2
(12.23)
It is easy to see that the ratio r = (a(V −b)/RTV b) determines the required
answer, i.e P
ideal
> P
vdW
if r > 1, the two pressures equal if r = 1 and P
ideal
< P
vdW
if r < 1. The constant b for many known gases is very small compared to 10
L, so we can approximate r to just (a)/(RTb). It should be appreciated that
this is not the same as ignoring b in the vdW pressure formul ...