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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}.

Posted by

Shailly goel

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