An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes

Question

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 degree C and rejects heat to a room at a temperature of 25.4 degree C. Suppose that liquid water with a mass of 72.8 kg at 0.0 degree C is converted to ice at the same temperature. Take the heat of fusion for water to be L_f = 3.34 Times 10^5 J/kg. How much heat |Q_H| is rejected to the room? Express your answer in joules to four significant figures. How much energy E must be supplied to the device? Express your answer in joules.

Explanation / Answer

We can define E as the work needed and knowing that k=Qcooling/W being and that Qheating=Qcooling+W, k the coefficient of performance that for a fridge is k=Tcold/(Thot-Tcold) so in kelvins we get that k=273.15/25.4=10.732 and with that in mind we can proceed to say that W*k=Qcooling so Qheat=Wk+W so W=Qheat/(k+1)=2.476*10^6 so E=2.476*10^6 Joules

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