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Lecture 2
1
Equations of State – How far can we push it?
(16.3,16.4)
Consider the vdW equation of state:
()
2
a
P
Vb
R
T
V
⎛⎞
+−
=
⎜⎟
⎝⎠
( )
22
P
Va
V
bR
T
V
=
32
0
RT
a
ab
V
V
PP
P
−+
+
−
=
( )
Cubic equation in V
3 roots
→
0
PV
RT
bP V
aV
ab
+
−
=
Fig. 16.7
Figure shows that below the critical
point, liquid and gaseous phase of CO
2
can coexist.
c
So, at a given T<T , as you compress the gas,
(G
A) you reach a point where V will change
with essentially no increase in P (A
D), until
all of the gas liquifies.
Then, further compression
requires a hug
→
→
e increase in P (D
L).
→
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2
P vs. V for vdW equation
Fig. 16.8a
2
2
At
:
0
Inflection point in curve
c
c
c
T
T
PP
T
VV
∂∂
==
c
For T<T
undulating curve reflects
3 roots of our cubic equation in V.
But at the critical point, T
c
, the three roots become degenerate:
()
3
32
2
3
03
3
0
cc
c
c
V
V
V
V
−=
→
−
+
−
=
Equate with
0
RT
a
ab
Vb
V
V
P
⎛⎞
−+
+
−
=
⎜⎟
⎝⎠
Lecture 2
3
Equating the two equations gives the following three relations:
23
33
c
cc
c
c
RT
aa
b
Vb
V
V
P
PP
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This note was uploaded on 04/01/2012 for the course CHEM 444 taught by Professor Gruebele,m during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Gruebele,M
 Physical chemistry, pH

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