Chemical Engineering 2300 / Thermodynamics I
Spring 2013
Solution to Homework Assignment 12 (Lectures 1
‐
25)
Prof. Geof Silcox
Due Tuesday, 2013 April 23, by 17:00
Problem 1 (10 points)
An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression
process, air is at 95 kPa and 27 C, and 750 kJ/kg of heat is transferred to the air during
the constant
‐
volume heat
‐
addition process. Assuming constant specific heats,
determine (a) the pressure and temperature at the end of the heat
‐
addition process, (b)
the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for
the cycle. Approximate answers: (a) 4000 kPa, 2000 K: (b) 400 kJ/kg; (c) 60 percent; (d)
500 kPa.
Solution
From Table A
‐
2 at 300 K, C
v
= 0.718 kJ/(kg K), k = 1.400. The process is sketched at
below on a P
‐
v diagram.
a) Find T
3
and P
3
. We start with the isentropic compression from 1 to 2:
K
2
.
689
8
300
v
v
T
T
or
v
v
T
T
4
.
0
1
k
2
1
1
2
1
k
2
1
1
2
From the ideal gas law,
kPa
1746
300
2
.
689
95
8
T
T
rP
P
1
2
1
2
.
P
v
2
1
3
4
w
in
w
out
q
out
q
in
TDC
BDC
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View Full DocumentFor an ideal gas with constant C
v
,
q
in
= C
v
(T
3
‐
T
2
).
Then
K
1734
2
.
689
718
.
0
750
T
C
q
T
2
v
3
3
.
From the ideal gas law,
kPa
4392
300
1734
95
8
T
T
rP
P
1
3
1
3
.
b) Find the net work leaving the engine (w
net,out
). From an energy balance over the
cycle,
w
net,out
= q
in
‐
q
out
.
We start with the isentropic expansion from 3 to 4:
K
7
.
754
8
1
1734
v
v
T
T
or
v
v
T
T
4
.
0
1
k
4
3
3
4
1
k
4
3
3
4
.
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 Spring '08
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 Chemistry, kPa, Qin, mean effective pressure

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