Solution:
Solution
Given,
Partition has hole of diameter $$d$$, Mean pressure between both sections is equal.
Boltzmann constant $${{K}_{B}}$$
At constant pressure, Mean Free path $$\lambda \ \alpha \ \sqrt{{{K}_{B}}T}$$
Mean free path in $${{1}^{st}}$$ section $${{\lambda }_{I}}=\sqrt{{{K}_{B}}\times 150}$$
Mean free path in $${{2}^{nd}}$$ section $${{\lambda }_{II}}=\sqrt{{{K}_{B}}\times 300}$$
$$\dfrac{{{\lambda }_{I}}}{{{\lambda }_{II}}}=\dfrac{\sqrt{{{K}_{B}}\times 150}}{\sqrt{{{K}_{B}}\times 300}}=0.707$$
Hence, $$\dfrac{{{\lambda }_{I}}}{{{\lambda }_{II}}}\cong 0.7$$
