JEE Advance - Physics (2013 - Paper 2 Offline - No. 10)

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.

JEE Advanced 2013 Paper 2 Offline Physics - Heat and Thermodynamics Question 24 English

The rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T.
Heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400-500 K.
There is no change in the rate of heat absorption in the range 400-500 K.
The rate of heat absorption increases in the range 200-300 K.

Explanation

JEE Advanced 2013 Paper 2 Offline Physics - Heat and Thermodynamics Question 24 English Explanation

According to definition of specific heat capacity,

$$C = {{\Delta Q} \over {m\Delta T}}$$

$$ \Rightarrow \Delta Q = mC\Delta T$$ $$\therefore$$ $${{\Delta Q} \over {\Delta t}} = mC{{\Delta T} \over {\Delta t}}$$

Rate of heat absorbed $$R = {{\Delta Q} \over {\Delta t}}$$

$$ \Rightarrow {{\Delta Q} \over {\Delta t}} \propto C$$

(a) In 0-100 K,

C increases with T but not linearly. So R increases but not linearly.

(b) As $$\Delta Q = mC\Delta T$$

$$Q = m\int {C\Delta T} $$

= m area under C-T curve

From the graph it is clear that area under C-T is more in 400-500 K than in 0-100 K.

Therefore, heat absorbed in 0-100 K is less than in 400-500 K.

(c) In 400-500 K,

C remains constant so there is no change in R.

(d) In 200-300 K,

C increases so R increases.

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