
The Critical Point 269
For this purpose, it is useful to recast eqn.(13.9) in the form
2p −8t + 3v p−3v
3
=0 (13.30)
Using this, it is easy to see that in the vicinity of the critical point
C
P
−C
V
=8R
1
p −3v
2
1
2+3v
(13.31)
Approaching along the critical isochore:
Along this line v=0,p=4t(in fact this is true even if one is not in the vicinity
of T
c
). Hence C
P
−C
V
t
−1
. For the ideal vdW case, since C
V
remains finite by
choice, one concludes that C
P
t
−1
. If an additional exponent
α
is introduced via
C
P
(t) → t
−
α
, one concludes that for approach along the critical isochore
α
=1.
Approaching along the critical isobar:
Along the critical isobar p=0, v
3
= −8t/3. It should ...