This preview shows pages 1–3. Sign up to view the full content.
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 Pv 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 R134a 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 R134a which is a control mass.
m
2
= m
1
= m
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Process:
Pv
1.5
= constant
until
P = 500 kPa
1: (T, x)
v
1
= 0.09921 m
3
/kg,
P = P
sat
= 201.7 kPa
from Table B.5.1
2: (P, process)
v
2
= v
1
(P
1
/P
2
)
(1
/1.5)
= 0.09921
×
(201.7/500)
2/3
=
0.05416
Given (P, v) at state 2 from B.5.2 it is superheated vapor at
T
2
= 79
°
C
Process gives P = C v
1.5
,
which is integrated for the work term, Eq.(4.4)
1
W
2
=
∫
P dV =
m
1  1.5
(P
2
v
2
 P
1
v
1
)
=
2
 0.5
×
(500
×
0.05416  201.7
×
0.09921) =
7.07 kJ
4.56
The refrigerant R22 is contained in a piston/cylinder as shown in Fig. P4.56, where
the volume is 11 L when the piston hits the stops. The initial state is
−
30
°
C, 150
kPa with a volume of 10 L. This system is brought indoors and warms up to 15
°
C.
a.
Is the piston at the stops in the final state?
b
.
Find the work done by the R22 during this process.
Solution:
This is the end of the preview. Sign up
to
access the rest of the document.
This homework help was uploaded on 04/10/2008 for the course ME 235 taught by Professor Borgnakke during the Spring '07 term at University of Michigan.
 Spring '07
 Borgnakke

Click to edit the document details