5-82
5-105 A cylinder equipped with a set of stops for the piston is initially filled with saturated liquid-vapor
mixture of water a specified pressure. Heat is transferred to the water until the volume increases by 20%.
The initial and final temperature, the mass of the liquid when the piston starts moving, and the work done
during the process are to be determined, and the process is to be shown on a P-v diagram.
Assumptions The process is quasi-equilibrium.
Analysis (a) Initially the system is a saturated mixture at 125 kPa pressure, and thus the initial temperature
is
T1
Tsat @125 kPa
106.0qC
The total initial volume is
V1
m f v f mgv g
2 u 0.001048 3 u 1.3750
4.127 m 3
H2O
5 kg
Then the total and specific volumes at the final state are
V3
v3
1.2V1
V3
m
1.2 u 4.127
4.953 m 3
5 kg
4.953 m 3
0.9905 m 3 /kg
P
Thus,
P3
v3
½°
¾ T3
0.9905 m /kg °¿
300 kPa
3
2
373.6qC
(b) When the piston first starts moving, P2 = 300 kPa and V2 =
V1 = 4.127 m3. The specific volume at this state is
v2
V2
m
4.127 m 3
5 kg
3
1
v
0.8254 m 3 /kg
which is greater than vg = 0.60582 m3/kg at 300 kPa. Thus no liquid is left in the cylinder when the piston
starts moving.
(c) No work is done during process 1-2 since V1 = V2. The pressure remains constant during process 2-3
and the work done during this process is
Wb
³
3
2
P dV
P2 V 3 V 2 ·
¸
¸
© 1 kPa ˜ m ¹
§
300 kPa 4.953 4.127 m 3 ¨¨
1 kJ
3
247.6 kJ
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