Question

Figure shows a vessel partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part 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.

Answer 1

The leftside of the container has a gas having a molecular weight = $M_1$, and right part has molecular weight = $M_2$.

The temperature of both left and right chambers are equal since the separator is diathermic

$\frac{\sqrt{3RT}}{\sqrt{M_1}}=\frac{\sqrt{8RT}}{\sqrt{\pi M_2}}$

$\Rightarrow \frac{3RT}{M_1}=\frac{8RT}{\pi M_2}$

$\Rightarrow \frac{M_1}{\pi M_2}=\frac{3}{8}$

$\Rightarrow \frac{M_1}{M_2}=\frac{3\pi }{8}$ = 1.1775 = 1.18