$A$ 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:

Which of the following statements is $NOT$ true?

What is the heat capacity of a substance?

On what does the value of heat capacity depend?

The $S.I.$ unit of specific heat capacity is

The figure below shows the variation of specific heat capacity $(C)$ of a solid as a function of temperature $(T)$. The temperature is increased continuously from $0$ to $500 \ K$ at a constant rate. Ignoring any volume change,which of the following statement$(s)$ is (are) correct to a reasonable approximation?
$(A)$ The rate at which heat is absorbed in the range $0-100 \ K$ varies linearly with temperature $T$.
$(B)$ Heat absorbed in increasing the temperature from $0-100 \ K$ is less than the heat required for increasing the temperature from $400-500 \ K$.
$(C)$ There is no change in the rate of heat absorption in the range $400-500 \ K$.
$(D)$ The rate of heat absorption increases in the range $200-300 \ K$.