Naik, Sameer V.
Fall 2009
1000
Solution for Special Problem 25
Given:
- Water executing Carnot heat engine cycle
Find:
- Pressure, temperature, specific volume, specific internal energy, specific enthalpy at all
four states within the cycle
- Heat transfer and work (kJ) for each process in the cycle
- Thermal efficiency (%) of the cycle
- P-v diagram
System:
Assumptions:
- Carnot cycle executed in a closed piston-cylinder device
- Negligible changes in KE and PE
Basic Equation(s):
Q
W
U
KE
PE
−
= Δ
+ Δ
+ Δ
1
cycle
C
thermal
H
H
W
T
Q
T
η
=
=
−
Solution:
(a) At state 1, we have water at 40 bar and 15% quality.
Using Table A-3:
(
)
(
)
3
3
3
3
3
1
1
m
m
m
1.2522
10
0.15 0.04978
1.2522
10
0.008532
kg
kg
kg
f
g
f
v
v
x
v
v
−
−
=
+
−
=
×
+
−
×
=
(
)
(
)
1
1
kJ
kJ
kJ
1082.3
0.15 2602.3
1082.3
1310.3
kg
kg
kg
f
g
f
u
u
x
u
u
=
+
−
=
+
−
=
(
)
(
)
1
1
1
kJ
kJ
kJ
1087.3
0.15 1714.1
1344.42
kg
kg
kg
f
g
f
f
fg
h
h
x
h
h
h
x h
=
+
−
=
+
=
+
=
At state 2, we have saturated vapor at 40 bar.
Using Table A-3:
3
2
m
0.04978
kg
g
v
v
=
=
,
2
kJ
2602.3
kg
g
u
u
=
=
,
2
kJ
2801.4
kg
g
h
h
=
=
Process 2-3 is adiabatic.
Applying energy balance, we have:
23
23
23
q
w
u
−
= Δ

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