Q. 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 molecule in $L$ part to that of a molecule in $R$ part is
A) $\sqrt{\frac{3}{2}}$
B) $\sqrt{\pi/4}$
C) $\sqrt{2/3}$
D) $3\pi/8$
Explanation
(d) Root means square velocity of molecule in left part
$v_{rms} = \sqrt{\frac{3KT}{m_{L}}}$
Mean or average speed of molecule in right part
$v_{av} = \sqrt{\frac{8}{\pi}\frac{KT}{m_{R}}}$
According to problem $\sqrt{\frac{3KT}{m_{L}}} = \sqrt{\frac{8}{\pi}\frac{KT}{m_{R}}}$
$\Rightarrow \frac{3}{m_{L}} = \frac{8}{\pi\ m_{R}}\ \Rightarrow \frac{m_{L}}{m_{R}} = \frac{3\pi}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.