Heat and Thermodynamics 6 Question 19
24. 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. lgnoring any volume change, the following statement(s) is (are) correct to reasonable approximation.
(2013 Adv.)
(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 $200-300 K$
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Answer:
Correct Answer: 24. (c, d)
Solution:
- $Q=m C T \Rightarrow \frac{d Q}{d t}=m c \frac{d T}{d t}$
$R=$ rate of absortion of heat $=\frac{d Q}{d t} \propto C$
(i) in $0-100 K C$ increase, so $R$ increases but not linearly
(ii) $\Delta Q=m C \Delta T$ as $C$ is more in $(400 K-500 K)$ then
$$ (0-100 K) \text { so heat is increasing } $$
(iii) $C$ remains constant so there no change in $R$ from $(400 K-500 K)$
(iv) $C$ is increases so $R$ increases in range $(200 K-300 K)$
