A current carrying wire heats a metal rod. The wire provides a constant power P to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod change with the (t) as $T\left(t\right)=T_0\left(1+\beta t^{1/4}\right)$ where $\beta$ is a constant with appropriate dimension of temperature. the heat capacity of metal is :

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