The most effective refrigerator or air conditioner is one that removes the great

Question

The most effective refrigerator or air conditioner is one that removes the greatest amount of energy from the cold reservoir in exchange for the least amount of work. Thus, for these devices we define the coefficient of performance (COP) in terms of |qc|: COP (cooling) = |qc|/W A good refrigerator should have a high COP, typically 5 or 6. Suppose that a refrigerator has a COP of 5.5. When the refrigerator is running, its power input is 450 W. A glass of water (250 g) at a temperature of 20 degree C is placed in the freezer compartment. How long would it take the water to freeze at 0 degree C assuming that the operation of the refrigerator results only in energy being extracted from the water?

Explanation / Answer

given COP= 5.5 = QC/W

QC= 450*5.5 J/sec =2475 J/sec

water at 20 deg.c need to loose sensible heat up to 0 deg.c which is =mass*specific heat* temperature difference=

250*4.184*20= 20920 joules

since water needs to be frozen by supplying latent heat of fusion whose value is =334 J/gm

heat to be removed for freezing ice= 334*250 joules=83500 joules

total heat needs to be removed =sensible heat + heat due to fusion = 20920+83500 joules=104420 joules

time required= heat to be removed/ heat input rate= 104420/2475 sec =42.2 sec

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