HOMEWORK SET 7a
8.105
A piston/cylinder has ammonia at 2000 kPa, 80
o
C with a volume of 0.1 m
3
. The
piston is loaded with a linear spring and outside ambient is at 20
o
C, shown in Fig.
P8.71. The ammonia now cools down to 20
o
C at which point it has a quality of
10%. Find the work, the heat transfer and the total entropy generation in the
process.
CV
Ammonia out to the ambient,
both
1
Q
2
and
1
W
2
Energy Eq.5.11:
m(u
2
−
u
1
) =
1
Q
2
−
1
W
2
Entropy Eq.8.37:
m(s
2
- s
1
) =
1
Q
2
/ T
ambient
+
1
S
2 gen
Process:
P = A + BV
=>
1
W
2
=
∫
P dV = ½ m(P
1
+ P
2
) (v
2
- v
1
)
State 1:
Table B.2.2
v
1
= 0.07595 m
3
/kg,
u
1
= 1421.6 kJ/kg,
s
1
= 5.0707 kJ/kg K
m = V
1
/v
1
= 0.1/0.07595 = 1.31665 kg
State 2:
Table B.2.1
v
2
= 0.001638 + 0.1
×
0.14758 = 0.016396 m
3
/kg
u
2
= 272.89 + 0.1
×
1059.3 =378.82 kJ/kg
s
2
= 1.0408 + 0.1
×
4.0452 = 1.44532 kJ/kg K
1
W
2
= ½ m(P
1
+ P
2
)( v
2
- v
1
)
= ½
×
1.31665 (2000 + 857.5)( 0.016396 – 0.07595)
=
- 112 kJ
1
Q
2
= m(u
2
−
u
1
) +
1
W
2
= 1.31665 (378.82 – 1421.6) –112
= - 1484.98 kJ
1
S
2 gen
= m(s
2
−
s
1
) – (
1
Q
2
/ T
amb
)
= 1.31665 (1.44532 – 5.0707) –
–1484.98
293.15
= – 4.77336 + 5.0656 =
0.292 kJ/K
P
v
1
2
2
1
T
s
P
2

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