Question

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

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{\pi }}{2}$
• C. $\frac{\sqrt{2}}{3}$
• D. $\frac{3\pi }{8}$

Answer 1

The correct option is D $\frac{3\pi }{8}$

The rms speed of the left part is given by
$V_{rms}=\sqrt{\frac{3kT}{m_L}}$

The average speed of the right part is given by
$V_{avg}=\sqrt{\frac{8kT}{\pi m_R}}$

Equating them,
$\sqrt{\frac{3kT}{m_L}}$ = $\sqrt{\frac{8kT}{\pi m_R}}$
$\Rightarrow \frac{m_L}{m_R}=\frac{3\pi }{8}$