Heating Your Kitchen with Your Refrigerator

[2001]

Homework Statement

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

Homework Equations

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

COP = Q_c/W

P = W/t

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!

 

[haruspex]

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