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Q.

A metal cylinder of 5 kg is heated electrically by a 20 W heater in a room 20oC. The cylinder temperature rises uniformly to 30oC in 5 minute and finally becomes constant at 45oC. Assuming that the rate of heat loss is proportional to the excess temperature over the surroundings.

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a

the rate of loss of heat of cylinder to surrounding at 25oC is 4 W

b

the rate of loss of heat of cylinder to surrounding at 45oC is 20 W

c

the rate of loss of heat of cylinder to surrounding at 25oC is 8 W

d

the rate of loss of heat of cylinder to surrounding at 45oC is zero

answer is A.

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Detailed Solution

Troom =20∘Cmcylinder =5kg            P=20WSince temperature becomes constant at 45°C⇒Power lost at 45°C = 20 WFrom Newton's law of cooling∴ dQdtT=45∘C=20=K(45−20)⇒ K=45Since temperature rises uniformly to 30°C thus, at 25°C,dQdt=k(25−20)=4W
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