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(t)=T_(0)(1+betat^(1//4))` where `beta` is a constant with appropriate dimension of temperature. the heat capacity of metal is :

Options

A. `(4P(T(t)-T_0))/(beta^4 T_0^2)`
B. `(4P(T(t)-T_0)^2)/(beta^4 T_0^3)`
C. `(4P(T(t)-T_0)^4)/(beta^4 T_0^5)`
D. `(4P(T(t)-T_0)^3)/(beta^4 T_0^4)`