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Heating Your Kitchen with Your Refrigerator

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data

    How long would a 3.50 kW space heater have to run to put into a kitchen the same amount of heat as a refrigerator (coefficient of performance = 3.13) does when it freezes 1.46 kg of water at 21.4°C into ice at 0°C?

    m=1.46 kg
    c_water=4186 J/kg
    Delta T= 21.4°C
    L_fusion= 3.34x10^5 J/kg
    COP= 3.13
    P= 3.50 kW

    2. Relevant equations

    Q_c = m x c_water x Delta T + m x L_f

    COP = Q_c/W

    P = W/t

    3. The attempt at a solution

    I plugged everything into the equation for the heat and got 618427 J. Then I divided that by the coefficient of performance to get that work = 197581 J. Then, I divided that by 3500 W for the power and found that t = 56.45 s. And apparently that's not the answer. I'm not sure where I went wrong!
  2. jcsd
  3. Apr 24, 2013 #2


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    Science Advisor
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    Gold Member

    You computed the work done to transfer an amount of heat. Where did that heat go?
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