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. [2013]

Question

Smart Achievers · Accepted Answer

(2, 3, 4)

$(1) As we know, Q = m c Δ T$

$\Rightarrow \frac{d Q}{d t} = m c \frac{d T}{d t}$ or, $\frac{d Q}{d t} \propto C$ i.e., rate of heat absorption $\propto C$ .

In the range 0 to 100K from the graph, C increases with temperature but not linearly therefore the rate at which heat is absorbed varies with temperature. But not linearly.

(2) As the value of C is greater in the temperature range 400-500K, the heat absorbed in increasing the temperature from 0-100K is less than the heat required for increasing the temperature from 400-500K.

(3) From the graph the value of C does not change in the temperature range 400-500K, therefore there is no change in the rate of heat absorption in this range.

(4) As the value of C increases from 200-300K, the rate of heat absorption increases in the range 200-300K.

Solution

1 The rate at which heat is absorbed in the range 0–100 K varies linearly with temperature T.

2 Heat absorbed in increasing the temperature from 0–100 K is less than the heat required for increasing the temperature from 400–500 K.

3 There is no change in the rate of heat absorption in the range 400–500 K.

4 The rate of heat absorption increases in the range 200–300 K.

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