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Homework # 9
Solutions
#1 560
Air is expanded in an adiabatic turbine. The mass flow rate of the air and the
power produced are to be determined.
Assumptions
1
This is a steadyflow process since there is no change with time.
2
The
turbine is wellinsulated, and thus there is no heat transfer.
3
Air is an ideal gas with
constant specific heats.
Properties
The constant pressure specific heat of air at the average temperature of
(500+150)/2=325°C=598 K is
c
p
= 1.051 kJ/kg·K (Table A2
b
). The gas constant of air is
R
= 0.287 kPa
⋅
m
3
/kg
⋅
K (Table A1).
Analysis
(
a
) There is only one inlet and one exit, and thus
m
m
m
=
=
2
1
. We take the
turbine as the system, which is a control volume since mass crosses the boundary. The
energy balance for this steadyflow system can be expressed in the rate form as
out
in
energies
etc.
potential,
kinetic,
internal,
in
change
of
Rate
(steady)
0
system
mass
and
work,
heat,
by
nsfer
energy tra
net
of
Rate
out
in
0
E
E
E
E
E
4
4
4
3
4
4
2
1
43
42
1
=
=
D
=

ä
˜
˜
ˆ

+

=
˜
˜
ˆ

+

=
+
˜
˜
ˆ
+
=
˜
˜
ˆ
+
2
)
(
2
2
2
2
2
2
1
2
1
2
2
2
1
2
1
out
out
2
2
2
2
1
1
V
V
T
T
c
m
V
V
h
h
m
W
W
V
h
m
V
h
m
p
The specific volume of air at the inlet and the mass flow rate are
/kg
m
2219
.
0
kPa
1000
K)
273
K)(500
/kg
m
kPa
287
.
0
(
3
3
1
1
1
=
+
⋅
⋅
=
=
P
RT
v
kg/s
36.06
=
=
=
/kg
m
0.2219
m/s)
)(40
m
2
.
0
(
3
2
1
1
1
V
A
m
Similarly at the outlet,
/kg
m
214
.
1
kPa
100
K)
273
K)(150
/kg
m
kPa
287
.
0
(
3
3
2
2
2
=
+
⋅
⋅
=
=
P
RT
m/s
78
.
43
m
1
/kg)
m
4
kg/s)(1.21
06
.
36
(
2
3
2
2
2
=
=
=
A
m
V
(
b
) Substituting into the energy balance equation gives
kW
13,260
=
˜
ˆ

+

⋅
=
˜
˜
ˆ

+

=
2
2
2
2
2
2
2
1
2
1
out
/s
m
1000
kJ/kg
1
2
m/s)
78
.
43
(
m/s)
40
(
)K
150
K)(500
kJ/kg
051
.
1
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This note was uploaded on 09/04/2009 for the course CHEM 2300 taught by Professor Thermo during the Summer '08 term at University of Utah.
 Summer '08
 thermo

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