The specific heat $C$ of a solid at low temperature shows temperature dependence according to the relation $C = D T^{3}$,where $D$ is a constant and $T$ is the temperature in Kelvin. $A$ piece of this solid of mass $m \ kg$ is taken and its temperature is raised from $20 \ K$ to $30 \ K$. The amount of heat required in the process in energy units is

  • A
    $5 \times 10^{4} D m$
  • B
    $(33 / 4) \times 10^{4} D m$
  • C
    $(65 / 4) \times 10^{4} D m$
  • D
    $(5 / 4) \times 10^{4} D m$

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On which factor does the required amount of heat depend to increase the temperature of a substance?

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 $200-300 \ K$.

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