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What is the maximal coefficient of performance of a refrigerator which cools down 10 kg of...

What is the maximal coefficient of performance of a refrigerator which cools down 10 kg of water (and then ice) to -6?C. Upper heat source of this refrigerator is surroundings at constant temperature 21?C. Initially water is in equilibrium with surroundings. What is maximal coefficient of performance of heat pump operating in the same configuration. Specific heat of water, specific heat of ice, and latent heat of fusion are equal to 4.19KJ/kg/K, 2.1KJ/kg/K and 335 KJ/kg, respectively.

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Answer #1

Water temperature = T1 = - 6 C = 267 K

Surroundings temperature = T2 = 21 C = 294 K

Maximum COP of Refrigerator= T1 / (T2 - T1) = 267 / (294-267) = 9.88

Maximum COP of a Heat pump operating between same temperature conditions is

COP of heat pump = T2 / T2 - T1 = 294 / (294-267) = 10.88

Since here we are asked to find the maximum COP of refrigerator and heat pump with given values of temperature, we should follow Carnot approach. There is nothing to do with Specific heat values given in the problem for finding Maximum COP's of refrigerator and heat pump.

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