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Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \mathrm{~K}$ .The piston $\mathrm{A}$ is free to move, while that of $\mathrm{B}$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $\mathrm{A}$ is $\mathrm{30 \mathrm{~K}}$ , then the rise in temperature of the gas in $\mathrm{ \mathrm{B}}$ is.
Option: 1
$30 \mathrm{~K}$

Option: 2
$18 \mathrm{~K}$

Option: 3
$50 \mathrm{~K}$

Option: 4
$42 \mathrm{~K}$

Answers (1)

best_answer

For cylinder A. For cylinder B
$\mathrm{dQ}=\mathrm{nC}_{\mathrm{pd}} \mathrm{d}_{1}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}_{2}$
$\mathrm{\Rightarrow nCpdT_{1}= nCvdT_{2}}$

From (I) and (II)

$\mathrm{c}_{\mathrm{v}} \mathrm{dT}_{2}=\left(\mathrm{c}_{\mathrm{v}}+\mathrm{R}\right) 30$
$\therefore \quad \mathrm{dT}_{2}=\frac{\left(\mathrm{c}_{\mathrm{v}}+\mathrm{R}\right) 30}{\mathrm{c}_{\mathrm{v}}}$

For diatomic gas $\mathrm{c}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$

$\therefore \quad \mathrm{dT}_{2}=42 \mathrm{~K}$ .

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Shailly goel

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