Question

Figure shows a vessel partitioned by a fixed diathermic separation. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left pat equals the mean speed of the molecules in the right part. Calculate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.

• A. $\frac{3\pi }{8}$
• B. $\frac{5\pi }{8}$
• C. $\frac{7\pi }{8}$
• D. $\frac{9\pi }{8}$

Answer 1

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

Let $M_1$ and $M_2$ be the molecular masses.
Temperature on both sides are same (diathermic wall)
$(V_{rms}{)}_1=(V_{av}{)}_2$
$\sqrt{\frac{3RT}{M_1}}=\sqrt{\frac{8RT}{\pi M_2}}\Rightarrow \frac{M_1}{M_2}=\frac{3\pi }{8}$