788
An insulated cylinder initially contains air at a specified state. A resistance heater
inside the cylinder is turned on, and air is heated for 15 min at constant pressure. The
entropy change of air during this process is to be determined for the cases of constant and
variable specific heats.
Assumptions
At specified conditions, air can be treated as an ideal gas.
Properties
The gas constant of air is
R
= 0.287 kJ/kg.K
(Table A1).
Analysis
The mass of the air and the electrical work done during this process are
(
)
(
)
(
)
(
)
(
)(
)
kJ
180
s
60
15
kJ/s
0.2
kg
0.4325
K
290
K
/kg
m
kPa
0.287
m
0.3
kPa
120
in
e,
in
e,
3
3
1
1
1
=
=
D
=
=
⋅
⋅
=
=
t
W
W
RT
P
m
V
The energy balance for this stationary closed system can be expressed as
)
(
)
(
1
2
1
2
in
e,
out
b,
in
e,
energies
etc.
potential,
kinetic,
internal,
in
Change
system
mass
and
work,
heat,
by
nsfer
energy tra
Net
out
in
T
T
c
h
h
m
W
U
W
W
E
E
E
p

@

=
D
=

D
=

43
42
1
43
42
1
since
D
U
+
W
b
=
D
H
during a constant pressure quasiequilibrium process.
(
a
) Using a constant
c
p
value at the anticipated average temperature of 450 K, the final
temperature becomes
Thus,
(
)(
)
K
698
K
kJ/kg
1.02
kg
0.4325
kJ
180
K
290
in
e,
1
2
=
⋅
+
=
+
=
p
mc
W
T
T
Then the entropy change becomes
(
)
(
)(
)
kJ/K
0.387
K
290
K
698
ln
K
kJ/kg
1.020
kg
0.4325
ln
ln
ln
1
2
avg
,
0
1
2
1
2
avg
,
1
2
sys
=
˜
˜
ˆ
⋅
=
=
˜
˜
ˆ

=

=
D
T
T
mc
P
P
R
T
T
c
m
s
s
m
S
p
p
Ã
(
b
)
Assuming variable specific heats,
(
)
kJ/kg
706.34
kg
0.4325
kJ
180
kJ/kg
290.16
in
e,
1
2
1
2
in
e,
=
+
=
+
=

=
m
W
h
h
h
h
m
W
From the air table (Table A17, we read
s
2
o
= 2.5628 kJ/kg·K corresponding to this
h
2
value.
Then,
(
)
(
)(
)
kJ/K
0.387
K
kJ/kg
1.66802
2.5628
kg
0.4325
ln
1
2
0
1
2
1
2
sys
=
⋅

=

=
˜
˜
ˆ
+

=
D
o
o
o
o
s
s
m
P
P
R
s
s
m
S
Ã
792
One side of a partitioned insulated rigid tank contains an ideal gas at a specified
temperature and pressure while the other side is evacuated. The partition is removed, and
the gas fills the entire tank. The total entropy change during this process is to be