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

• A
  $\frac{4 P (T(t) - T_0)^3}{\beta^4 T_0^4}$
• B
  $\frac{4 P (T(t) - T_0)}{\beta^4 T_0^2}$
• C
  $\frac{4 P (T(t) - T_0)^4}{\beta^4 T_0^5}$
• D
  $\frac{4 P (T(t) - T_0)^2}{\beta^4 T_0^3}$