4
How to improve the efficiency
of a heat engine.
Increase T
h
This requires high temperature materials
Decrease T
c
This requires efficient heat transfer.
.
Cogeneration
Use of waste heat
This power plant in Denmark uses the waste heat to heat green
houses nearby.
Refrigerators
Coefficient of performance
COP- the heat removed from the
cold source divided by the work
done.
cc
hc
QQ
COP
wQQ
==
−
c
hc
T
COP
TT
=
−
The maximum Carnot COP
since
c
h
hc
Q
Q
TT
=
Refrigerator
1 Compressor – gas is compresses and heated
2 Heat exchange coils - the heat is released
from the gas and exhausted outside of the
refrigerator.
3 Expansion valve – The pressure is decreased
after going through the valve. The gas is cooled
4 Cooling coils- Heat is absorbed from within the
refrigerator. The gas is heated.
The refrigerator uses a liquid with a low
boiling point. The evaporation takes up heat
from the refrigerator and the condensation of
the gas releases the heat outside the refrigerator.
1
2
3
4
Refrigerator
A freezer is kept at a temperature of 0
o
F. What is the maximum
COP for a Carnot refrigerator with output temperature of 85
o
F. If the
electrical energy use is 500kWh/year how much heat is removed in
one year, assume 90% conversion of electrical energy to work.
T
c
= ( 0 -32)(5/9) +273=255 K
T
h
=(85-32)(5/9)+273=302 K
c
hc
T
COP
TT
=
−
255
302
54
255
.==
−
3
60min 60
0.9(500 10 )
min
s
WxWhr
hr
⎛⎞⎛⎞
=⋅
⎜⎟⎜⎟
⎝⎠⎝⎠
9
1.62 10= xJ
c
Q
COP
w
=
(
9 9
5.4 1.62 10 8.7 10== =
c
xQCOPw x x J
Heat removed
COP
Work
Heat
Summary
• The second law of thermodynamics limits the efficiency
of heat engines to less than 100%
• The Carnot cycle is a reversible cycle taking in heat at
high T and exhausting heat at low T.
• The maximum efficiency of a heat engine working
between two temperatures is the Carnot efficiency that
depends only on the ratio of the absolute temperatures.
• Refrigerators and heat pumps are heat engines run in
reverse.
• The maximum coefficient of performance is determined
by a Carnot cycle.
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