Two substances $A$ and $B$ of the same mass are heated at a constant rate. The variation of temperature $\theta$ of the substances with time $t$ is shown in the figure. Choose the correct statement.

Which of the following statements is $NOT$ true?

The specific heat of a substance at temperature $T^{\circ}C$ is given by $C = \alpha T^2 + \beta T + \gamma$. The amount of heat required to raise the temperature of a mass $m \, g$ of the substance from $0^{\circ}C$ to $T_o^{\circ}C$ is .......

The thermal capacity of $100 \,g$ of aluminum (specific heat $= 0.2 \,cal / g ^{\circ} C$) is ............ $cal / ^{\circ} C$.

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 $200-300 \ K$.

On what factors does the required amount of heat depend to heat a given substance?