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Heat pump problem

  1. Oct 25, 2014 #1
    1. The problem statement, all variables and given/known data
    A)What is the coefficient of performance of an ideal heat pump that extracts heat from 11∘C air outside and deposits heat inside your house at 30∘C?
    B) If this heat pump operates on 2000W of electrical power, what is the maximum heat it can deliver into your house each hour?
    2. Relevant equations
    COP = QH/W
    COPideal = TH/(TH-TL)

    3. The attempt at a solution
    TH = 30 + 270 = 300
    TL = 11 + 270 = 281

    COPideal = 300/(300-281) = 16
    that part came up right
    for the second part
    W = 2000 J/s

    COP = QH/W
    QH = COP(W) = 16 (2000 J/s) = 32000 J/s
    32000 J/s (3600 s/ h) = 115200000 J/h
    i rounded to 2 sig figs because thats what the question wanted but it was wrong. What mistake did I make?
     
  2. jcsd
  3. Oct 26, 2014 #2

    rude man

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    why are you using oK = oC + 270 when it's oK = oC + 273?
    Even though to 2 sig. digits it worked out OK. I would still round off at the end of calculations rather than in the middle somewhere.
    I suppose to 2 sig. digits the answer is 1.2e8 J.

    Otherwise I see nothing wrong with what you did.
     
    Last edited: Oct 26, 2014
  4. Oct 26, 2014 #3
    Thanks! it wouldnt take 1.2e8 so i tried 1.1e8 and it took that for some reason
     
  5. Oct 26, 2014 #4

    rude man

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    1.1e8 is a truncation. 1.2e8 is the correct answer to 2 significant digits. Complain! :smile:
     
  6. Oct 26, 2014 #5
    worth a shot. thanks!
     
  7. Oct 26, 2014 #6

    rude man

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    Oops, don't complain yet! Redoing the numbers, it's 1.1e8 after all:
    COP = 303/19 = 15.947
    W = 15.947 x 2000 x 3600 = 1.148e8 which to 2 sig # is 1.1e8.
    (Although I suppose you could argue 1.148 ~ 1.15 which to 2 sig digits is 1.2.)

    Again, note that K = oC + 273.15 or 273 for short. Don't use 270 ever.
     
  8. Oct 26, 2014 #7
    ahh yea i gotta get out of the habit of rounding too soon. This one is very close
     
  9. Oct 26, 2014 #8

    haruspex

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    Hmm.. I get ((30+273)/(30-11))*2000*3600=1.148...e8
     
  10. Oct 27, 2014 #9

    rude man

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    Please see my post #6. I believe we have concordance.
     
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