A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gas

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12.Kinetic Theory of Gases

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A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left $(L)$ and right $(R)$ halves. The $rms$ speed of the molecules in $L$ part is equal to the mean speed of molecules in the $R$ part. Then the ratio of the mass of a molecules in $L$ part to that of a molecules in $R$ part is

A

$\frac{3}{2}$

B

$\frac{\pi }{4}$

C

$\frac{2}{3}$

D

$\frac{3\pi }{8}$

Solution

$\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}_{\mathrm{L}}}}=\sqrt{\frac{8 \mathrm{RT}}{\pi \mathrm{M}_{\mathrm{R}}}}$

$\frac{M_{L}}{M_{R}}=\frac{3 \pi}{8}$

Standard 11

Physics

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