If the molecular radius of hydrogen gas is $0.5 \ \mathring A$,then the mean free path of hydrogen gas molecules at $0 \ ^\circ C$ temperature and $1 \ atm$ pressure is ........ $\mathring A$. (Given $k_B = 1.38 \times 10^{-23} \ J \ K^{-1}$)

The mean free path for a gas,with molecular diameter $d$ and number density $n$,can be expressed as:

$A$ molecule is travelling in air at $300 \, K$ and $1 \, atm$, and the radius of the molecule is $0.6 \times 10^{-10} \, m$. Calculate the approximate mean free path of the molecule. (The number density is $2.44 \times 10^{25} \, \text{molecules}/m^3$)

The internal energy of real gases is determined by which of the following?

In the van der Waals equation $\left( P + \frac{a}{V^2} \right)(V - b) = RT$,what do $a$ and $b$ represent?

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