A refrigerator is to cool 50 kg of water from 250C to 50C. The specific heat of water is 4.2 kJ/kgK. If the COP of the refrigerator is 2.0 and has a power input of 500 W, find the time taken to cool the water.

700 minutes

Explanation:

Heat loss by water = Heat gained by the refrigerator

ΔT = IVt

But, power = IV

ΔT = Gt

G = (P x COP)

Thus,

( - ) = (P x COP) x t

where is the mass of water, is the specific heat of water, ΔT = ( - ) is the change in temperature, P is the power of the refrigerator in kilowatts and t is the time taken.

= 50 kg, = 4.2 kJ/(kg K), = 250 (523 K), = 50, P = 500W (0.5 KW), COP = 2.0 KW

( - ) = (P x COP) x t

50 x 4200 x (523 - 323) = (0.5 x 2.0) x t

50 x 4.2 x 200 = t

42000 = t

⇒ t = 42000

      = 42000 s

   t  = 700 minutes

The time taken to cool the water is 700 minutes.

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