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Assignment #8
PROBLEM 8.1
PROBLEM STATEMENT:
A thermodynamic cycle using air as the working fluid in a
closed system is outlined below. The specific heats of air can be assumed constant
throughout the cycle with values taken at the initial conditions. The four processes
that make up the cycle are:
Process 12:
Air at standard conditions (State 1: 1 atm, 298 K)
is heated at constant volume to state 2, where
Process 23:
The air at State 2 is expanded isobarically to
State 3, where
Process 34:
The air is expanded isentropically until it returns
to pressure P
1
at State 4.
Process 41:
The air is compressed isobarically to return it to State 1.
(a) Sketch the
diagrams of this cycle. Pay special attention to the
relative slopes of the process lines.
(b) Find the
numerical value
of the power cycle efficiency of this heat engine.
GIVEN:
Air, P
1
= 1 atm, T
1
= 298 K
Process 12: Constant volume to P
2
=10P
1
Process 23: Constant pressure (isobaric) to v
3
=3v
2
Process 34: Constant entropy (isentropic) to P
4
=P
1
Process 41: Constant pressure (isobaric) to v
1
FIND:
ASSUMPTIONS:
Ideal gas, constant specific heats.
GOVERNING RELATIONS:
1.
For constant specific heats,
2.
For an ideal gas, R = c
P
– c
V
and k = c
P
/ c
V
3.
Ideal gas equation,
4.
PT relation for isentropic process, constant specific heats:
5.
Thermal efficiency,
QUANTITATIVE SOLUTION:
a).
The P  v diagram can be derived from the known processes. For the
T  s diagram, note that for the constant volume process,
and for the isobaric process,
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steeper than the isobaric processes. The diagrams for this cycle are shown
below.
Ts diagram
P
2
3
1
3v
1
P
1
10P
1
v
1
4
v
4
dv = 0
dP = 0
ds = 0
Pv diagram
T
3
dP = 0
ds = 0
dv = 0
2
4
dP = 0
1
s
v
b).
The temperature of each state can be found in terms of T
1
. Also, the
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 Spring '07
 Dr.Kinne

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