CH353M
Homework assignment 3 (
due Friday Oct. 14
)
1.
(
5
) Derive the expression for
pv
CC for a material with the following equation of state:
2
Va
b
P
c
T
=+ +
,
where
a
,
b
,
and
c
are constants.
2
2
2
2
PV
V
P
P
V
cT
cT
CCT
TT
b
V
ba b
P c
T
∂∂
−=
=
−
=
−
++
2 (20).
One mole of a gas occupies one half of a container that is separated from the rest
of the container by a partition. The initial volume of the gas is
V
and its temperature is
T
.
After the partition is removed, the gas expands irreversibly and occupies the volume 2
V
.
The equation of state of the gas is
2
(/
)
(
)
PaV Vb R
T
+−
=
and its heat capacity
V
C
is temperatureindependent.
A.
What is the temperature of the gas after expansion?
We have
dU =
V
C
n dT + [T
V
P
T
∂
∂
P] dV
Using
P = RT/(Vb) – a/V
2
we find
22
VV
RT
RT
a
dV
dU
C dT
dV
C dT
a
VbVbV
V
=+
−+
−−
Integrating this,
11
((
2
) (
1
)
)
0
(2)
(1)
V
UCT
T
a
∆=
−
−
−
=
or, using V(2)=2V(1)=2V,
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View Full DocumentT(2)=T(1)
2
V
a
CV
B.
What is the change of the entropy of the gas in this process?
Use
VV
V
CC
PR
d
V
dS
dV
dT
dT
TT
V
b
T
∂
=+
=
+
∂−
∆
S=R ln((2Vb)/(Vb)) +
/(2
)
ln
V
V
Ta C
V
C
T
−
C.
In the class, we have derived the relationship
()
/
constant
CRC
PV
+
=
between the
pressure and the volume of an ideal gas undergoing a reversible adiabatic process,
in which it receives no heat from the surroundings. Derive an analogous
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 Spring '08
 LIM
 Physical chemistry, pH

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