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Physics 404  Spring 2011
Homework 11 Solutions
Question 1
Kittel+Kromer, Chpater 10, Problem 1
a)
We know the Helmholtz free energy of the vdW gas:
F
vdW
=

Nτ
±
log
²
n
Q
(
V

Nb
)
N
³
+ 1
´

N
2
a
V
(1)
The entropy can be found from
σ
=

∂F
∂τ
µ
µ
µ
µ
V
(2)
=
N
±
log
²
n
Q
(
V

Nb
)
N
³
+ 1
´
+
Nτ
±
N
n
Q
(
V

Nb
)
(
V

Nb
)
N
dn
Q
dτ
´
(3)
Using
n
Q
=
(
mτ
2
π
¯
h
2
)
3
/
2
we obtain
σ
=
N
±
log
²
n
Q
(
V

Nb
)
N
³
+
5
2
´
(4)
b)
The energy U can be obtained from F by diﬀerentiation w.r.t.
τ
or simply using
F
=
U

τσ
:
U
=
F
+
τσ
(5)
=

Nτ
±
log
²
N
Q
(
V

Nb
)
N
³
+ 1
´

N
2
a
V
+
τ
×
N
±
log
²
n
Q
(
V

Nb
)
N
³
+
5
2
´
(6)
=
3
2
Nτ

N
2
a
V
(7)
which is the ideal gas energy plus the vdW correction for attractive interactions.
Question 2
Kittel+Kromer, Chpater 10, Problem 2 We will use the CC equation
dp
dT
=
L
T
Δ
V
(8)
together with the ideal gas law Δ
V
≈
τ/p
. Here we have an approximate equality since the
volume of the liquid phase is not exactly zero, but it is negligible compared to the volume
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