JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Heat & Thermodynamics

Two different metal bodies

A

and

B

of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

(A) $\frac{3}{8}$ ✓ Correct
(B) $\frac{8}{3}$
(C) $\frac{4}{3}$
(D) $\frac{3}{4}$

Answer: (A)

Solution

Since both bodies receive heat at the same rate and have equal mass, we have

\frac{d Q _{A}}{d t} = \frac{d Q _{B}}{d t}

. Using

d Q = m c d T

, we get

m_{A} c_{A} \frac{d T _{A}}{d t} = m_{B} c_{B} \frac{d T _{B}}{d t}

. Since

m_{A} = m_{B}

, we have

\frac{c _{A}}{c _{B}} = \frac{d T _{B} / d t}{d T _{A} / d t}

. From the graph, body A's temperature rises from 0 to 120°C in 3 time units, giving

\frac{d T _{A}}{d t} = \frac{120}{3} = 40

. Body B's temperature rises from 0 to 90°C in 6 time units, giving

\frac{d T _{B}}{d t} = \frac{90}{6} = 15

. Therefore,

\frac{c _{A}}{c _{B}} = \frac{15}{40} = \frac{3}{8}

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Heat & Thermodynamics

Solution

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