Question

A vessel is partitioned in two equal halves by a fixed dia thermic 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. $3\pi/8$

Answer 1

Answer: (D)

$3\pi/8$

Answer 2

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 $\sqrt{\frac{3KT}{m_{L}}} = \sqrt{\frac{8}{\pi}\frac{KT}{m_{R}}}$

⇒ $\frac{3}{m_{L}} = \frac{8}{\pi m_{R}}$ ⇒ $\frac{m_{L}}{m_{R}} = \frac{3\pi}{8}$.