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.

Options

A. `(2pi)/(7)`
B. `(3pi)/(8)`
C. `(3pi)/(10)`
D. `(pi)/(3)`

Answer

B

Explanation

The seprator is diathermal it means the temperature of gas on both parts of vessel should be equal , let this common temperature is `T`.
hence rms speed of the gas in left part
`v_(rms) = sqrt((3kT)/(m_1))` ..(i)
`m_(1)` is the mass of a molecules in left part.
Similarly the mean speed of a molecules of the gas in right aprt
`v_(mean) = sqrt((8kT)/(pim_2))`..(i)
`m_(2)` is the mass of a molecules in right part
as per question
`r_(rms_=v_(men) impliessqrt((3kT)/(pi_1)) = sqrt((8kT)/(pi m_(2)))`
Hence `(m_1)/(m_2) = (3 pi)/(8)`.