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Question

A thermally insulated piece of metal is heated by supplying a constant power P. Due to this, the temperature of the metal starts varying with time as T= at^1/4 + To(T not)

The heat capacity of the metal as a function of temperature is

(1) 4PT³/a^4

(2) 4P(T-To)³/a^4

(3) 4PT²/a³

(4) 4P(T - To)²/a³

Joshi sir comment

P = dQ/dt = mcdT/dt

or mcdT = Pdt

or mc = Pdt/dT

or mc = Pd/dT[(T-T₀)⁴/a⁴]

here mc is heat capacity

now solve

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