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) inthe metal rod changes with time (t) as
$$T(t) = T_0 (1 + \beta t^{\frac{1}{4}}),$$
where $$\beta$$ is a constant with appropriate dimension while $$T_0$$ is a constant with dimension of temperature. The heat capacity of the metal is,