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

Question

A refrigerator keeps its freezer compartment at -10degrees C. It is located in a room where the temperature is 20 degrees C. The coefficient of performance (heat pump in cooling mode)is 5.20. 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 temperatureof the water is 20 degrees C. The final temperature of the ice cube is -10degrees C. The refrigerator removes the heat from the freezer compartment, maintaining its temperature at about -10degrees 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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