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

Let the temperature of gas in both the chambers be T.
Let the molar mass of gas in the left chamber and right chamber be M_​1 and M₂, respectively.
Let mass of gas in the left and right chamber be m₁ and m₂, respectively. Then,

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\[ v_{rms}  = \sqrt{\frac{3kT}{m_1}} = \sqrt{\frac{8kT}{\pi m_2}}\] 

\[                 \Rightarrow 3 m_1    =   \frac{8 m_2}{3 . 14}\] 

\[                 \Rightarrow \frac{m_2}{m_1} = 1 . 18\]