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Unformatted text preview: 5.49 A large heat pump should upgrade 4 MW of heat at 65°C to be delivered as heat at 145°C. What is the minimum amount of work (power) input that will drive
this? For the minimum work we assume a Camot heat pump and Q1. = 4 MW. Q H TH 273.15 +145 '3HP=. =THTL= 14565 =5'227
Win
Q
BREF=BHPl =—=4.227
Win Now we can solve for the work win = QL/ﬂREF = 4/4227 = 0.946 MW This is a domestic or
small ofﬁce building
size AI’C unit. much
smaller than the 4 MW
in this problem. 5.57 Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10°C. Assume the refrigerator works in a Carnot cycle between —8°C and 35°C with a motorcompressor of 660 W. How much
time does it take if this is the only cooling load?
Solution: (1V. Water in tray. We neglect tray mass. Energy 1341.: ml:u2 — u1)=1Q2 — 1W2
Process : P = constant + Po
1W2 =1 P ‘W = Pom(V2 — V1) 1% = 111012 — 1L11l+1wz = 111012 — 111) Tb]. 13.1.1 : h] = 41.99 lil"lig, Tb]. B.1.5 :32 =  333.5 3mg
1Q2 = 0.25 kg (3334 — 41.99 } kl’kg =  93.343 1:] Consider now reﬁ'igerator
QL QL TL 233 — 3
B w _QHQL_ THTL_35(3)_ 6.15 QL 1Q: 93.343
[3  [3 = 616 =15.24kJ For the motor to transfer that amount of energy the time is found as W=Jurdt=9lr3t w 15.24x1000
=—= 4s . 600 25°
W At: Comment: We neglected a baseload of the refrigerator so not all the 650 W are
available to make ice= also our coefﬁcient of perfomiance is very optimistic and
ﬁnally the heat transfer is a transient process. All this means that it will take much
more time to make icecubes. 5.83
A house is cooled by a heat pump driven by an electric motor using the inside as
the lowtemperature reservoir. The house gains energy in direct proportion to the temperature difference as anin = K(TH  TL). Determine the minimum electric
power to drive the heat pmnp as a function of the two temperatures. Solution: Refrigerator CUP: [3 : {EL"Win 3 TLJ'CI‘ H  TL} ; Heat gain must be removed: QL = anin = K[TH  TL) Solve for required work and substitute in for B o Wm = (ED"ﬂ 2 KU‘H — TL) x (TH  TL).“1'L . 2;
WmEKCTH' L) ’TL 5.97
Hydrogen gas is used in a Carnot cycle having an efﬁciencyr of 60% with a low
temperature of 300 K. During the heat rejection the pressure changes from 90 kPa
to 120 kPa. Find the high and low temperature heat transfer and the net cycle
work per unit mass of hydrogen. Solution:
As the efﬁciencyr is known, the high temperature is found as
TL
1] =05 =1—T— =>TH=TL.='(1 0.6): ?50K
H Now the volume ratio needed for the heat transfer, T3 = T4 = TL, is 1.3 v4 = (RT3 .5 P3 ) 1" (RT4I' P4 ) = P4_" P3 = 120 .r' 90 = 1.333
so from Eq.'}".9 we have with R = 4.1243 ﬁ'om Table A5
qL = RTL ln (v3."'v4 ) = 355.95 kakg
Using the efﬁciency from Eq.7.4 then
qH= qL (1  0.6) = 889.9 kakg
The net work equals the net heat transfer
w = qH  qL = 533.9 kakg ...
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 Fall '08
 Sherif

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