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ChE 359 Homework #2
Solutions prepared by Chris Singer
1.
(10 points) Suppose two objects
A
and
B
, with heat capacities
C
A
and
C
B
and
initial temperatures
T
A
and
T
B
are brought into thermal contact.
If
C
A
>
C
B
, state
whether the equilibrium temperature
T
would be closer to
T
A
or
T
B
, and justify
your choice.
When two objects are brought into thermal contact, but are
otherwise isolated from the surroundings, both objects will have the same
temperature at equilibrium.
Since they are isolated, there is no net change in
the energy of the total system:
dU
tot
=
dU
A
+
dU
B
=
0
, or
Δ
U
A
+
Δ
U
B
=
0
.
The
change in energy of A is given by the heat capacity:
Δ
U
A
=
C
A
dT
T
A
T
∫
=
C
A
T
−
T
A
( )
.
The
change
in
energy
of
B
is
given
by
the
heat
capacity:
Δ
U
B
=
C
B
dT
T
B
T
∫
=
C
B
T
−
T
B
( )
.
Thus, we substitute back into our expression to get:
C
A
T
−
T
A
( ) +
C
B
T
−
T
B
( ) =
0
, which we can rearrange to get an expression for the
equilibrium
temperature:
T
=
C
A
T
A
+
C
B
T
B
C
A
+
C
B
.
If
C
A
>
C
B
,
we
can
make
the
assumption:
T
≈
C
A
T
A
+
C
B
T
B
C
A
=
T
A
+
C
B
T
B
C
A
≈
T
A
, so the equilibrium temperature
would be closer to
T
A
.
2.
(25 points) Two moles of an ideal gas undergo an irreversible isothermal
expansion from
V
1
=
100 L
to
V
2
=
300 L
at
T
=
300 K
.
a.
(5 points) List the natural variables that govern this process, and the
fundamental thermodynamic equation for a property that is a function of
these variables.
The variables that are specified/controlled at the system
boundary are
T
,
V
, and
N
.
Thus, the fundamental thermodynamic
equation
corresponding
to
these
natural
variables
is
F T
,
V
,
N
( )
,
or
dF
=
−
SdT
−
PdV
+
μ
j
dN
j
j
=
1
M
∑
b.
(5 points) During this process process, state whether this property would
stay the same, increase, or decrease, and justify your choice.
During this
process, we want to maximize entropy and minimize free energy.
Thus,
the
Helmholtz
free
energy
would
decrease
during
this
process.
Also this can be seen from
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This note was uploaded on 02/09/2011 for the course CHE 359 taught by Professor Cynthialo during the Spring '10 term at Washington University in St. Louis.
 Spring '10
 CynthiaLo
 Equilibrium, Mole, Kinetics

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