JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Heat & Thermodynamics

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.

(A)the rate at which heat is absorbed in the range $0 - 100 K$ varies linearly with temperature $T$ .✓ Correct
(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.✓ Correct
(C)there is no change in the rate of heat absorption in the range $400 - 500 K$ .✓ Correct
(D)the rate of heat absorption increases in the range 200-300 K.✓ Correct

Answer: (A), (B), (C), (D)

Solution

Given

\frac{d T}{d t} = constant

, the rate of heat absorption is

\frac{d H}{d t} = m C \frac{d T}{d t}

.

(A) In 0-100 K, C varies linearly with T, so

\frac{d H}{d t}

varies linearly with T. ✓

(B) Heat absorbed =

H = m \int C d T

= area under the C-T curve. Area from 0-100 K (

A_{1}

) < Area from 400-500 K (

A_{2}

). ✓

(C) In 400-500 K, C is constant, so

\frac{d H}{d t}

is constant (no change). ✓

(D) In 200-300 K, C increases, so

\frac{d H}{d t}

increases. ✓

Note: The official answer key lists both "ABCD" and "BCD" as accepted answers.

JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · One or more correct options

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JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Heat & Thermodynamics

Solution

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