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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