Question

A Carnot refrigerator transfers heat from its inside (5.63 oC) to the room air outside (22.0...

A Carnot refrigerator transfers heat from its inside (5.63 oC) to the room air outside (22.0 oC). (a) Find the coefficient of performance of the refrigerator. (b) Determine the magnitude of the minimum work needed to cool 5.84 kg of water from 22.0 to 5.63 oC when it is placed in the refrigerator.

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Homework Answers

Answer #1

Inside temperature = TC = 5.63 oC = 278.63 K

Outside temperature = TH = 22 oC = 295 K

COP = 17.02

Mass of water = m = 5.84 kg

Initial temperature of water = T1 = 22 oC

Final temperature of water = T2 = 5.63 oC

Specific heat of water = Cw = 4186 J/(kg.K)

Heat to be removed to cool the water = QC

QC = mCw(T1 - T2)

QC = (5.84)(4186)(22 - 5.63)

QC = 400184.95 J

Work done to cool the water by the refrigerator = W

W = 23512.63 J

a) Coefficient of performance = 17.02

b) Magnitude of work needed to cool 5.84 kg of water from 22oC to 5.63oC when placed in the refrigerator = 23512.63 J

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