A metal cylinder of very high conductivity and mass 0.5 kg is heated electrically by a 12 W heater in a room at 1 5 ∘ C . The cylinder temperature rises to 2 5 ∘ C in 5 min and finally becomes constan

Question

A metal cylinder of very high conductivity and mass 0.5 kg is heated electrically by a 12 W heater in a room at 1 5 ∘ C . The cylinder temperature rises to 2 5 ∘ C in 5 min and finally becomes constant at 4 5 ∘ C . Assuming that the rate of heat loss is proportional to the excess temperature over the surroundings

TestHub · Accepted Answer

In the final state, dt dQ e ​ ​ = k ( 45 − 15 ) = 12 . K = 5 2 ​ ; at 2 0 ∘ C , dt dQ e ​ ​ = k ( 20 − 15 ) = 5 2 ​ × 5 = 2 watt . m.s. dt dT ​ = 12 − 5 2 ​ ( T − 15 ) ⇒ m.s. dt dT ​ = 18 − 5 2 ​ T . m.s. ∫ 15 25 ​ 18 − 5 2 ​ T d T ​ = ∫ 0 300 ​ d t ⇒ s = ℓ l n ( 2 3 ​ ) 240 ​ J / k g − ∘ C .

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JEE Advanced 2027 (Class 12)