HW 4 Solutions
CH 353: Physical Chemistry I (54655)
Spring 2008
Bersuker
(10 points)
I.
An ideal gas containing 2.5 moles for which
2
/
3
,
R
C
m
V
=
undergoes the following reversible
cyclical process from an initial state characterized by
450
=
T
K and
00
.
1
=
p
bar:
(a) It is expanded reversibly and adiabatically until the volume doubles.
You can calculate the final temperature of an adiabatic expansion via
630
.
1
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
γ
i
f
i
f
V
V
T
T
, giving
K.
We can thus calculate the initial and final pressure and volume using the ideal gas
equation
m
3
, with
283
=
f
T
V
2
10
25
.
9
/
−
×
=
=
i
i
i
P
nRT
185
.
0
2
=
=
i
f
V
V
m
3
, leading to
314
.
0
=
i
f
f
i
T
T
=
i
f
V
V
p
p
bar.
Clearly the adiabatic process has
q
equal to zero.
.
0
Thus
.
0
since
0
equality.
Clausius
the
and
zero
is
heat
reversible
the
since
0,
J
10
68
.
8
)
450
283
(
2
K
mol
J
314
.
8
5
5
.
2
J
10
5.21
K)
450
K
283
(
2
K
8.314Jmol
3
mol
5
.
2
3
1

1

,
3
1
1
,
=
Δ
=
=
Δ
=
Δ
×
−
=
−
×
×
×
=
Δ
=
Δ
×
−
=
−
×
×
×
=
Δ
=
=
Δ
total
gs
surroundin
m
p
m
V
S
q
S
S
T
nC
H
T
nC
w
U
(b) The pressure is increased in an isothermal reversible compression until
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 Spring '08
 Bersuker
 Physical chemistry, Mole, pH, NC, mol

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