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Heat pump work done

  1. Nov 7, 2011 #1

    I am trying this question from Physics gre prepbook

    A heat pump is to extract from an outdoor environment at 7oC and heat the
    environment indoors to 27 celcius. for each 15000 J of heat delivered indoors, the smallest
    amount of work that must be supplied to the heat pump is approximately

    a)500 J
    b)1000 J
    c)1100 J
    d)2000 J
    e) 2200 J

    this is how I did my work.

    [tex]T_c = (7+273) K[/tex]

    [tex]T_h=(27+273) K[/tex]

    the highest possible efficiency is that of carnot engine


    let the [itex]\eta[/itex] be the efficiency of this pump . then

    [tex]\eta \leqslant \frac{1}{15}[/tex]

    [tex]\because \; \eta=\frac{W_{eng}}{|Q_h|}[/tex]

    [tex]\therefore \; \frac{W_{eng}}{|Q_h|} \leqslant \frac{1}{15}[/tex]

    [tex]Q_h=15000 J\;\Rightarrow \; W_{eng}\leqslant \frac{15000}{15}[/tex]

    [tex]W_{eng} \leqslant 1000 [/tex]

    which suggests that W has some maximum value but the problem is talking about the
    minimum value of W. is something wrong ?
  2. jcsd
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