A thermally insulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at constant power $P$. This leads to an increase in the absolute temperature $T$ of the metal with time $t$ as $T\left(t\right)= T_0{\left[1 +a\left(t - t_0\right)\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$, where $a$, $t_0$ and $T_0$ are constants. The heat capacity $C_{\mathrm{P}}\left(T\right)$ of the metal is