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Lecture 5 – September 9, 2008
Virial Expansions
Empirical Treatment of Real Gasses
Consider the Compression Factor, Z
RT
V
p
Z
=
For the case of a perfect gas, Z = 1
For the case where finite size effects matter,
V
p
is larger than expected for an ideal gas so Z > 1
For the case where attractive interactions are important,
V
p
is smaller than expected for an ideal
gas so Z < 1
Quantifying these Effects, the van der Waals Equation of State
(1)
Molecular Volume correction to the perfect gas law:
b
V
RT
p
−
=
where b = molar volume = m
3
/mol
(accounts for repulsions)
(2)
Attractive Interactions
2
ideal
V
a
p
p
−
=
, where
a = attractive interactions which reduce pressure units = pressure x volume
2
(3)
Putting the two together yields the van der Waals Equation of State
2
V
a
b
V
RT
p
−
−
=
valid for
b
V
>>
or
(
)
RT
b
V
V
a
p
2
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
2
V
a
V
b
1
V
RT
p
−
⎟
⎠
⎞
⎜
⎝
⎛
−
=

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