Rewriting Van der Waals Eqn. of State
3
2
v
v
v
0
kT
a
ab
b
P
P
P
(1)
For
c
T
T
3 solutions
1
2
3
(v
, v
, v
)
for fixed
P, T
c
T
T
3 solutions coalesce at
v
v
c
i.e. for
,
C
C
P
P
T
T
LHS of Eqn. (1) is
3
C
v
v
But
3
3
2
2
3
v v
v 3v v
3v v v
c
c
c
c
(2)
Comparing (1) and (2)
From (iii) and (ii) dividing
Then
2
3
2
and
3
3
( )
3
3
3
( )
27
27
8
(
)
27
c
c
c
c
c
c
c
c
c
c
c
kT
b
i
b
v
b
P
a
ab
a
v
ii
P
P
b
b
ab
a
v
iii
T
P
bk
Define
reduced variables
/
,
/
,
/
c
c
c
P
P
P
T
T
T
Universal from
1
2
8
3
1
3
(3)
P
T
Law of Corresponding States
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Figure Caption:
The liquid gas coexistence curves of many fluids can be virtually superimposed when
the temperature and density are scaled by their corresponding critical values
c
T
and
c
.
Plots of this
kind are manifestations of the “law of corresponding states”.
This plot from Guggenheim (1945) played
an important role in the development of the theory of critical phenomena by showing that the data cannot
be fitted with a quadratic curves van der Waals theory implies, but require the cubic shown here, which
corresponds to the fact that the orderparameter exponent
1/ 3
and
not
1/2 as van der Waals theory
implies.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Chakabarti
 mechanics, Statistical Mechanics, tc, van der, Critical phenomena, Van der Waals Eqn.

Click to edit the document details