PHYS 445 Lecture 33  Nonideal classical gases
33  1
© 2001 by David Boal, Simon Fraser University.
All rights reserved; further resale or copying is strictly prohibited.
Lecture 33  Nonideal classical gases
What's Important:
•
nonideal classical gases
•
virial coefficient
Text
: Reif
Nonideal classical gases
The previous two lectures on phase transitions have dealt with quantized spins on a
lattice.
We now move to the continuum problem of phase transitions in a nonideal
gas  that is, a gas of interacting particles.
The total energy for a broad category of interaction models can be expressed as
H
=
K
+
U
= (1/2
m
)
Σ
i
p
i
2
+
Σ
j
≠
k
u
jk
(
r
jk
)
(33.1)
where the momentum dependence is contained in the kinetic energy term and the
coordinate dependence is in the potential energy term (
of course, there exist situations
in which the interactions are momentumdependent too
).
For example, the "612" LennardJones potential is of the form
u
(
r
)
=
u
o
R
r
12

2
R
r
6
where
u
o
and
R
are parameters.
This potential is strongly repulsive at short range, and
weakly attractive at long range.
Because of the separation of the Hamiltonian into
position and momentum components, the partition function factors as well:
Z
=
1
N
!
1
h
3
N
e

ß
(
K
+
U
)
d
3
p
1
..
∫
d
3
p
N
d
3
r
1
..
d
3
r
N
=
1
N
!
1
h
3
N
e

ß
2
m
(
p
1
2
+
..
p
N
2
)
d
3
p
1
...
∫
d
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 Spring '08
 DavidBoal
 Physics, Energy, nonideal classical gases

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