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COF HP =
𝑄𝐻
𝑄𝐻
𝑇𝐻
=
==
𝑊 𝑄𝐻 −𝑄𝐿
𝑇𝐻 −𝑇𝐿
QH=25
W
Ql
46
 H.E CAR =
𝑊 𝑄𝐻−𝑄𝐿
𝑇𝐿
=
= =1 𝑄𝐻
𝑄𝐻
𝑇𝐻
QH
W
Ql
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= W/QH1 = (QH1QL1)/QH1
= W/QH1 =0.6 (THTO)/TH
W=0.6 QH1 *(TH- TO)/TH
COP= QL2/W =QL2/ (QH2QL2) QL2/W =0.6 TL/ (TOCOP=
TL)
W= QL2*(TO- TL)/0.6 TL
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COP= QL/W =QL/ (QH- QL)
C.O.P)C =TL/ (TH- TL)= 261/27
=7.1
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Ex. A heat engine operates between two reservoirs at
800°C and 20°C. One–half of the work output of the
heat engine is used to drive a Carnot heat pump that
removes heat from the cold surroundings at 2°C and
transfers it to a house maintained at 22°C. If the house
is losing heat at a rate of 17 kW, determine the
minimum rate of heat supply to the heat engine
required to keep the house at 22°C.
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Ex. A refrigerator should remove 400 kJ from some food. Assume the refrigerator works
in a Carnot cycle between −15◦C and 45◦C with a motor compressor of 400 W. determine:
a) The rate of heat removed from the cycle (kW)?
b) The time required in minutes does it take if this is the only cooling load?
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Example 6-5
A heat pump is to be used to heat a building during the winter. The building is
to be maintained at 21oC at all times. The building is estimated to be losing
heat at a rate of 135,000 kJ/h when the outside temperature drops to -5oC.
Determine the minimum power required to drive the heat pump unit for this
outside temperature.
Q Lost
21 oC
Win
Q H
Q L
HP
-5 oC
The heat lost by the building has to be supplied by the heat pump.
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58
kJ
 =Q

Q
H
Lost = 135000
h
Q H
TH
=
Q H − Q L TH − TL
(21 + 273) K
=
(21 − ( −5)) K
= 1131
.
COPHP =
Using the basic definition of the COP
COPHP =
Q H
Wnet , in
Q H
COPHP
135,000 kJ / h 1h 1 kW
=
1131
.
3600s kJ / s
= 3.316 kW
Wnet , in =
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62
Q#2
Two Reversible heat engines operate in series as shown in the figure. If both
engines have the same thermodynamic efficiency and the heat input to the first
engine is 1000 kW, determine: a) The temperature of the intermediate thermal reservoir, T2 (K).
b) The total work generated by both engines (kW).
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Q#6
Water enters a condenser as a saturated vapor at 42oC and leaves as saturated liquid
at the same temperature. The mass flow rate 𝑚 = 0.0167 kg/s. The heat is
removed using a refrigeration cycle operating between low temperature TL= 42oC
and high temperature TH = 65oC. The refrigeration cycle has a coefficient of
performance half of Carnot coefficient of performance (𝛽 = 0.5𝛽𝑐𝑎𝑟𝑛𝑜𝑡 ). Find the
rate of work into the refrigeration cycle
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Example 6-3
An inventor claims to have invented a heat engine that develops a thermal
efficiency of 80 percent when operating between two heat reservoirs at 1000 K
and 300 K. Evaluate his claim.
TH = 1000 K
WOUT
HE
QL
TL
TH
300 K
= 1−
1000 K
= 0.70 or 70%
 th , rev = 1 −
QH
TL = 300 K
The claim is false since no heat engine may be more efficient than a Carnot
engine operating between the heat reservoirs.
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Example 6-4
An inventor claims to have developed a refrigerator that maintains the
refrigerated space at 2oC while operating in a room where the temperature is
25oC and has a COP of 13.5. Is there any truth to his claim?
TH = 25oC
QH
Win
R
QL
TL = 2oC
QL
TL
=
QH − QL TH − TL
(2 + 273) K
=
(25 − 2) K
= 1196
.
COPR =
The claim is false since no refrigerator may have a COP larger than the COP for
the reversed Carnot device.
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