HOMEWORK SET 3
4.35
A piston cylinder contains 1 kg of liquid water at 20
o
C and 300 kPa. There is a
linear spring mounted on the piston such that when the water is heated the
pressure reaches 3 MPa with a volume of 0.1 m
3
.
a) Find the final temperature
b) Plot the process in a P-v diagram.
c) Find the work in the process.
Solution:
Take CV as the water. This is a constant mass:
m
2
= m
1
= m ;
State 1: Compressed liquid, take saturated liquid at same temperature.
B.1.1:
v
1
= v
f
(20) = 0.001002 m
3
/kg,
State 2:
v
2
= V
2
/m = 0.1/1 = 0.1 m
3
/kg and P = 3000 kPa
from B.1.3
=> Superheated vapor
close to T = 400
o
C
Interpolate:
T
2
=
404
o
C
Work is done while piston moves at linearly varying pressure, so we get:
1
W
2
=
∫
P dV = area = P
avg
(V
2
−
V
1
) =
1
2
(P
1
+ P
2
)(V
2
- V
1
)
= 0.5 (300 + 3000)(0.1
−
0.001) =
163.35 kJ
T
C.P.
v
2
1
300 kPa
P
C.P.
v
T
300
20
2
1
4.47
Consider a piston cylinder with 0.5 kg of R-134a as saturated vapor at -10
°
C. It is now
compressed to a pressure of 500 kPa in a polytropic process with n = 1.5. Find the
final volume and temperature, and determine the work done during the process.
Solution:
Take CV as the R-134a which is a control mass.
m
2
= m
1
= m

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