%3Cp%20class%3D%22MsoNormal%22%3EIf%26nbsp%3Ba%26nbsp%3Bbuilding%26nbsp%3Bloses%
ID: 2993488 • Letter: #
Question
%3Cp%20class%3D%22MsoNormal%22%3EIf%26nbsp%3Ba%26nbsp%3Bbuilding%26nbsp%3Bloses%26nbsp%3Bheat%26nbsp%3Bat%26nbsp%3Bthe%26nbsp%3Brate%26nbsp%3Bof%26nbsp%3B17%2C000%26nbsp%3BBtu%3D(h*F)%26nbsp%3B(9000%26nbsp%3BW%3DK)%0Atemperature%26nbsp%3Bdifference%26nbsp%3Bfrom%26nbsp%3Bindoors%26nbsp%3B(72%26nbsp%3BF%2C%26nbsp%3B228C)%26nbsp%3Bto%26nbsp%3Boutdoors%2C%26nbsp%3Bwhat%26nbsp%3Bis%0Athe%26nbsp%3Blowest%26nbsp%3Boutdoor%26nbsp%3Btemperature%26nbsp%3Bat%26nbsp%3Bwhich%26nbsp%3Ba%26nbsp%3BCarnot%26nbsp%3Bheat%26nbsp%3Bpump%26nbsp%3Bcan%26nbsp%3Bmaintain%26nbsp%3Bthe%0Ainterior%26nbsp%3Btemperature%26nbsp%3Bof%26nbsp%3Bthe%26nbsp%3Bbuilding%3F%26nbsp%3BThis%26nbsp%3Bheat%26nbsp%3Bpump%26nbsp%3Bhas%26nbsp%3Ba%26nbsp%3Bnominal%26nbsp%3Bpower%26nbsp%3Binput%2C%26nbsp%3Bwhen%26nbsp%3Bit%0Ais%26nbsp%3Brunning%2C%26nbsp%3Bof%26nbsp%3B80%26nbsp%3BkW.%26nbsp%3B(Note%26nbsp%3Bthat%26nbsp%3Bthe%26nbsp%3Bheat%26nbsp%3Bpump%26nbsp%3Bcontrols%26nbsp%3Bthe%26nbsp%3Bindoor%26nbsp%3Btemperature%26nbsp%3Bby%0Acycling%26nbsp%3Bon%26nbsp%3Band%26nbsp%3Boff%3B%26nbsp%3Bbut%26nbsp%3Bwhen%26nbsp%3Bit%26nbsp%3Bis%26nbsp%3Bon%2C%26nbsp%3Bit%26nbsp%3Balways%26nbsp%3Bdraws%26nbsp%3B80%26nbsp%3BkW.)%3C%2Fp%3E%3Cp%26nbsp%3Bclass%3D%22MsoNormal%22%3E%3Co%3Ap%3E%3C%2Fo%3Ap%3E%3C%2Fp%3EExplanation / Answer
Let Tc be outside temp.
input power= W = 80kW
in a carnot cycle(heat pump ) , W = Qh - Qc and Qh/W = Qh/(Qh-Qc) = Th/(Th-Tc)
=> Qh = W x Th/(Th-Tc) = 80kW x Th/(Th-Tc)
Qc = 9000 (Th-Tc) = 9kW (Th-Tc )
Th = interior temp = 228 C = 501 K
=> Qh = 80 kW (501/(501-Tc))
Qc = 9kW(501-Tc)
Qh-Qc=W => 80 kW (501/(501-Tc)) - 9kW(501-Tc) = 80kW
=> 80 (501) - 9 (501-Tc)^2 = 80 (501-Tc)
=> 80 (501) -9 (Tc^2) - 9 (501^2) + 9 (1002 Tc) = 80 (501) - 80 (Tc)
=> 9(Tc^2) -90098 Tc + 2259009 = 0
=> Tc = 25.13 K or Tc = 9985.75 K
therefore min temp. = 25.13 K
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.