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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, the following statement$(s)$ is (are) correct to a reasonable approximation.$Image$
$(A)$ 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 absorbtion in the range $400-500 \ K$.
$(D)$ the rate of heat absorption increases in the range $200-300 \ K$.
$( A , B , C , D )$
$(A,C)$
$(A,B,D)$
$(A,C,D)$
Solution
$q=m C T $
$\frac{d q}{d t}=m c \frac{d T}{d t}$
$R =$ rate of absortion of heat $=\frac{ dq }{ dt } \propto C$
$(i)$ in $0-100 k$
$C$ increases, so $R$ increases but not linearly
$(ii)$ $\Delta q=m C \Delta T$ as $C$ is more in ( $400 k-500 k)$ then $(0-100 k)$ so heat is increasing.
$(iii)$ $C$ remains constant so there no change in $R$ from ( $400 k-500 k$ )
$(iv)$ $C$ is increases so $R$ is increases in range $(200 k-300 k)$
