A vessel is partitioned in two halves by a fixed diathermic separator. Two different 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 :
Answer & explanation
Correct answer: option 4
rms velocity of molecule in left part : vrms
vrms = \(\sqrt{\frac{3KT}{m_L}}\)
Average speed of molecule is right part : vavg
vavg = \(\sqrt{\frac{8KT}{\pi m_R}}\)
According to question : \(\sqrt{\frac{3KT}{m_L}}\) = \(\sqrt{\frac{8KT}{\pi m_R}}\)
\(\frac{3}{m_L} = \frac{8}{\pi m_R}\)
\(\Rightarrow \frac{m_L}{m_R} = \frac{3\pi}{8}\)