A refrigerator keeps its freezer compartment at -10 deg C. It is located in a ro

Question

A refrigerator keeps its freezer compartment at -10 deg C. It is located in a room where the temperature is 20 deg C. The coefficient of performance (heat pump in cooling mode) is 4.69. How much work (J) is required to freeze one 26-g ice cube? Assume that we put 26 g of water into the freezer. The initial temperature of the water is 20 deg C. The final temperature of the ice cube is ?10 deg C. The refrigerator removes the heat from the freezer compartment, maintaining its temperature at about -10 deg C.

Explanation / Answer

The mass of the ice cube m = 26g = 26*10^-3 kg The coefficeint of performance CP = 5.2 The initial temperature of the water Ti = 20C the final temperature of the ice Tf =- 10C SO the amount heat removed from water to freeze ice is Q = mcw ?T + mLf + mcice ?T = (26*10^-3 kg)[ (4186J/kg C)(20) + 333*10^3 J/kg + (2100J /kg C)(10)] = 11380.72 J The coefficient of performance CP = Q/W Therefore work done W = CP Q = (5.2)(11380.72) = 59179.74 J

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