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Homework #8 Solutions
#1
463
The internal energy change of hydrogen gas during a heating process is to be
determined using an empirical specific heat relation, constant specific heat at average
temperature, and constant specific heat at room temperature.
Analysis
(
a
) Using the empirical relation for
)
(
T
c
p
from Table A2c and relating it to
)
(
T
c
v
,
(
)
3
2
)
(
dT
cT
bT
R
a
R
c
T
c
u
u
p
+
+
+

=

=
where a = 29.11, b = 0.1916 10
2
, c = 0.4003 10
5
, and d = 0.8704 10
9
.
Then,
(
)
[
]
(
)
kJ/kg
6194
=
=
D
=
D
=



+




=

+

+
+
+


=
+
+
+

=
=
D



kg/kmol
2.016
kJ/kmol
12,487
kJ/kmol
12,487
)
200
800
)(
10
8704
.
0
(
)
200
800
)(
10
4003
.
0
(
)
200
800
)(
10
1961
.
0
(
)
200
800
)(
314
.
8
11
.
29
(
)
(
)
(
)
(
)
(
)
(
4
4
9
4
1
3
3
5
3
1
2
2
2
2
1
4
1
4
2
4
1
3
1
3
2
3
1
2
1
2
2
2
1
1
2
2
1
3
2
2
1
M
u
u
T
T
d
T
T
c
T
T
b
T
T
R
a
dT
dT
cT
bT
R
a
dT
T
c
u
u
u
(
b
) Using a constant
c
p
value from Table A2b at the average temperature of 500 K,
kJ/kg
6233
=

⋅
=

=
D
⋅
=
=
200)K
K)(800
kJ/kg
(10.389
)
(
K
kJ/kg
10.389
1
2
avg
,
K
500
@
avg
,
T
T
c
u
c
c
(
c
) Using a constant
c
p
value from Table A2a at room temperature,
kJ/kg
6110
=

⋅
=

=
D
⋅
=
=
200)K
K)(800
kJ/kg
(10.183
)
(
K
kJ/kg
10.183
1
2
avg
,
K
300
@
avg
,
T
T
c
u
c
c
#2
4120
The compression work from
P
1
to
P
2
using a polytropic process is to be
compared for neon and air.
Assumptions
The process is quasiequilibrium.
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 Summer '08
 thermo

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