
The van der Waals Equation 239
The important conclusion that follows is that all maxima occur at V
r
≥ 1 and that all
minima occur at V
r
≤ 1. This further has the very important consequence that P
max
r
is always positive. On the other hand, P
min
r
can be positive or negative depending on
whether
˜
V
r
is greater than
2
3
or lesser than it, while still being lesser than 1. These
points will assume significance while discussing the issue of negative pressures in
vdW systems.
For pressures above P
max
r
as well as for pressures below P
min
r
, the cubic equation
determining the intersection of a vdW isotherm with P
r
= const. has only one root.
This can be checked by applying ...