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Reversed carnot problems solution and notes
Safety Management And Environmental Engineering (University of Cebu)
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A reversed Carnot refrigeration system has a maximum temperature of 220 0C and
1.
minimum temperature of 20 0C.
COPc =(20+273)/(220-20) = 1.465
Find the COP heating and cooling.
COPH = COPc + 1 = 2.465
COPH = (220+273)/200 = 2.465
A reversed Carnot refrigeration cycle has an evaporator temp of -10 0 C and
2.
condenser temp of 300C. If compressor power is 10kw, find the heat rejected in
the condenser.
COPc = T1/(T2-T1) = Qa/W
Qa = 10(263)/40 =65.75 kw
W = Qr - Qa
Qr = 75.75
kw
A reversed Carnot refrigeration system rejects 1000 kw of heat at 65 0C while
3.
0
receiving heat at -20
C. Determine: COP cooling and heating, power required,
Refrigerating effect in Tons of refrigeration
COPc = 253/85 = 2.976
COPh = 3.976
2.976 = Qa/(1000 - Qa)
COP = Qa/(Qr - Qa)
Qa = 748.49 kw
W = Qr - Qa
= 251.51 kw
RE = Qa = 748.49 kw /3.516 = 212.88 TR
4.
A reversed Carnot refrigeration system has a refrigerating COP of 4. find
Tmax/Tmin, If the work input is 6 kw, find RE
COPc = T1/(T2 - T1)
5.
(T2 - T1)/T1 = 1/COPc
T2/T1 - 1
= 1/4
T2/T1 = 5/4
A reversed Carnot engine absorbs 40000 kw from a heat sink. The temp of the heat
sink is -200C and the temp of the heat reservoir is 70 0C. Determine the power
required of the engine.
COPc = 253/90 = Qa/W
6.
reversed
W = 40000/(253/90) = 1422.98 kw
Carnot
refrigeration
system
has
an
evaporator
temp
of
-50C
and
0
condenser temp of 45 C. Find the performance factor if it will operate in a heat
pump.
COPh = (45+273)/50
= 6.36
A carnot heat pump uses thermal reservoirs at -20 0C and 500C. How much power
7.
does this pump consume to produce 100kw heating effect.
Qr = 100 kw
W = 21.67
8.
COPc = Qa/W
COPc = (Qr - W)/W
253/70 = (100 - W)/W
kw
A reversed carnot cycle is used for cooling. The input work is 12 kw while the
COP is 3.8. Calculate RE. 12.97 Tons
COP = Qa/W
Qa = RE = 3.8(12)/3.516 = 12.97 TR
A carnot refrigerator operates in a room in which the temp is 250C and consumes
9.
3 kw of power when operating. If the food compartment of the refrigerator is to
be
maintained
at
30C.
Determine
the
rate
of
heat
removal
from
the
food
compartment. 37.64kw
COP = 276/22
10.
A
reversed
= QA/3
QA = 37.64 kw
carnot
cycle
that
operates
between
-20C
and
compressor power. Find the tons of refrigeration needed. 66.7
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500C
needs
45
kw
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Find the performance factor of a heat pump that operates between -4 0C and 300C.
11.
8.91
12.
A heat pump has a compressor power of 10 kw and heat rejected of 50 kw to the
low temp region. Find the temp of the low region if the temp of the high region
is 400C.
-22.60C
A heat pump operates between 360F and 1200F. If heat added from the low temp
13.
region is 500 BTU/min, find the HP needed for the compressor. 1.7
QR = 500 BTU/min /42.42 = 11.78 hp
COPc = (36 + 460/(120 - 36) = 5.9
COPh = 6.9 = QR/W
W = 1.7 kw
A refrigerator operates between 360F and 1200F. If heat added from the high temp
14.
region is 500 BTU/min, find the HP needed for the compressor. 1.996 kw
Qa = 500/42.2 = 11.78 hp
COPc = 5.9 = Qa/W
W = 11.78/5.9 = 1.996 kw
A heat pump operates between -40 C and 280C. If the compressor power needed is 6
15.
kw, find the kJ/min added from the low temp source. 3386.25
COPc = 269/32 = 8.41
COPh = QR/W
COPh = 9.41
QR = 9.41(6) = 56.46 kw = 56.46 kJ/s (60) = 3387.6 kJ/min
A refrigerator operates between -40 C and 280C. If the compressor power needed
16.
is 6 kw, find the kJ/min added from the low temp source.
COPc = 269/32 = 8.41
COPc = Qa/W
COPh = 9.41
Qa = 8.41(6) = 50.46
kw = 50.46 kJ/s (60) =
kJ/min
A reversed carnot cycle refrigerator operates between -40 C and 280C. If the
17.
compressor power needed is 6 kw, find the kJ/min added from the low temp source.
3026.25
18.
A reversed carnot cycle has a refrigerating COP of 3. Determine the ration Th/T L
3/2
19.
A reversed carnot cycle is used for heating and cooling. The work supplied is 10
kw, if COP for cooling is 3, determine T2/T1, TR, COP heating.
20.
A reversed carnot cycle is used for refrigeration and rejects 1000 kw of heat at
600C while receiving heat at -200C. Determine COP, power required, RE
A reversed carnot cycle rejects 830 BTU/lb as heat at a temp of 1140 0F. The
21.
cycle receives heat at a temp of 140 0F. Calculate S for the rejection process,
net work
Qr=830 BTU/lb
W = (T2 - T1)S
22.
COPh = (1140+460)/1000) = 1.6= 830/W
W = 518.75 BTU/lb
s = 518.75/1000 = 0.51875 BTU/lb-R
SM mall uses carnot refrigeration cycle that operates at an evaporator temp of
200C and condenser temp of 600C. Cooling water enters the condenser at 90
gal/min where the temp increases from 23 0C to 390C. Find the brake power needed
to drive the compressor if compressor eff. is 85%. (1 gal = 3.785 kg) 81.89 hp
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COPc =293/40 = 7.325
510.2139 hp
COPh = 8.325
COPh = Qr/W
Qr = 90(3.785)/60[(4.19)(16)]=380.6196 kw Qr=
W = 510.2139/8.325 = 61.286 hp
Wb = 61.286/0.85
72.101 hp
COPh = Qr/W
Wb = W/0.85
23.
nc = W/Wb
One of the Computer company in the US uses carnot heat pump to be used for
heating its office and maintaining it at 250C during the winter.. The average
outdoor temp outside office is 40C. The office is estimated to lose heat at a
steady rate of 120,000 kJ. Find the energy needed for the compressor, in kJ
8456.4
24.
One of the Computer company in Cebu City uses carnot refrigeration system
to be
0
used for cooling its office and maintaining it at 5 C during summer.. The
average outdoor temp outside office is 340C. The office is estimated to gain
heat at a steady rate of 50,000 kJ. Find the energy needed for the compressor,
in kJ
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