Question

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 $500K$ at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to reasonable approximation

• A. the rate at which heat is absorbed in the range $0-100K$ varies linearly with temperature $T$
• B. heat absorbed in increasing the temperature from $0-100K$ is less than the heat required for increasing the temperature from $400-500K$
• C. there is no change in the rate of heat absorption in the range $400-500K$
• D. the rate of heat absorption increases in the range $200-300K$

Answer 1

Answer: (C), (D)

$$\begin{gathered} Q=mCT \\ Rightarrow\frac{dQ}{dt}=mc\frac{dT}{dt} \end{gathered}$$
R = rate of absortion of heat $=\frac{dQ}{dt}\propto C$
(i) in 0 - 100 K C increase, so R increases but not linearly
(ii) $\Delta$Q = mC$\Delta$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 increases in range(200 K - 300K)