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Dec. 3, 2010
PHYS 2101
HW#14
WileyPlus Problem Solutions
1
HW #14 Solutions – or at least most of them…
(USING BOOK VALUES 9
th
Edition in problems; problem # indicated by [])
1) [20CQ4] From the information, “
An ideal monatomic
gas at initial temperature T
0
(in kelvins) expands
from initial volume V
0
to volume 2V
0
by each of the five processes indicated in the TV diagram”
, we
know that
C
V
=
3
2
R
,
C
P
=
C
V
+
R
=
5
2
R
, and
γ
=
C
P
V
=
5
3
[NOTE: this is a
T

V
diagram, not
p

V
]
(a) In an isothermal expansion,
Δ
T
=
T
f
−
T
0
=
0
.
The only process in which the temperature remains
constant is
AE.
(b) In an isobaric expansion, the pressure (
p
) remains constant.
From the ideal gas law,
pV
=
nRT
, this
means that
T
0
V
0
=
T
f
V
f
⇒
T
f
=
T
0
V
0
2
V
0
( )
=
2
T
0
. The process in which the temperature increases by a factor
of 2 is
AC.
(c) In an adiabatic expansion,
Q
= 0.
In Section 19.11, we know for an adiabatic process,
p
0
V
0
=
p
f
V
f
[Eqn. 19–53] and
T
0
V
0
−
1
=
T
f
V
f
−
1
[Eqn. 19–55].
Here
T
0
V
0
−
1
=
T
f
2
V
0
( )
−
1
, or
T
f
=
T
0
1
2
( )
−
1
=
T
0
1
2
( )
5
3
−
1
≅
0.63
T
0
.
The process in which the temperature decrease by this factor is
AF.
(d) In general, the entropy change of a reversible gas process is given by [see Eqn. 20–4]:
Δ
S
gas
,
reversible
=
nR
ln
V
f
V
0
⎛
⎝
⎜
⎞
⎠
⎟
+
nC
V
ln
T
f
T
0
⎛
⎝
⎜
⎞
⎠
⎟
.
In this case,
Δ
S
gas
,
reversible
=
nR
ln
V
f
V
0
⎛
⎝
⎜
⎞
⎠
⎟
+
3
2
ln
T
f
T
0
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
=
nR
ln
2
V
0
V
0
⎛
⎝
⎜
⎞
⎠
⎟
T
f
T
0
⎛
⎝
⎜
⎞
⎠
⎟
3
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
nR
ln
2
T
f
T
0
⎛
⎝
⎜
⎞
⎠
⎟
3
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
is never negative (the entropy never decreases; it either remains
the same
AF
, or increases
AE
,
AD
,
AC
,
AB
).
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