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12. The connection between molar heat capacity and the degrees of freedom of a diatomic gas is given by
setting
f
= 5 in Eq. 2051. Thus,
C
V
=
5
2
R
,
C
p
=
7
2
R
, and
γ
=
7
5
. In addition to various equations from
Chapter 20, we also make use of Eq. 214 of this chapter. We note that we are asked to use the ideal
gas constant as
R
and not plug in its numerical value. We also recall that isothermal means constant
temperature, so
T
2
=
T
1
for the 1
→
2 process. The statement (at the end of the problem) regarding
“permo
le”maybetakentomeanthat
n
may be set identically equal to 1 wherever it appears.
(a) The gas law in ratio form (see Sample Problem 201) as well as the adiabatic relations Eq. 2054
and Eq. 2056 are used to obtain
p
2
=
p
1
µ
V
1
V
2
¶
=
p
1
3
,
p
3
=
p
1
µ
V
1
V
3
¶
γ
=
p
1
3
1
.
4
,
T
3
=
T
1
µ
V
1
V
3
¶
γ
−
1
=
T
1
3
0
.
4
.
(b) The energy and entropy contributions from all the processes are
•
process 1
→
2
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 Fall '08
 SPRUNGER
 Physics, Heat

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