Question

A container is divided into two equal parts I and II by a partition with a small hole of diameter d. The two partitions are filled with same ideal gas, but held at temperatures $T_I=150$K and $T_{II}=300$K by connecting to heat reservoirs. Let ${\lambda }_I$ and ${\lambda }_{II}$ be the mean free paths of the gas particles in the two parts such that $d>>{\lambda }_I$ and $d>>{\lambda }_{II}$. Then ${\lambda }_I/{\lambda }_{II}$ is close to.

• A. $0.25$
• B. $0.5$
• C. $0.7$
• D. $1.0$

Answer 1

The correct option is C $0.7$

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 ${\lambda }_{II}=\sqrt{K_B\times 300}$

$\frac{{\lambda }_I}{{\lambda }_{II}}=\frac{\sqrt{K_B\times 150}}{\sqrt{K_B\times 300}}=0.707$

Hence, $\frac{{\lambda }_I}{{\lambda }_{II}}\cong 0.7$