Consider a gas for which the diameter of molecules is $\sigma$. The gas is at a pressure $P$ and temperature $T$,and $N_a$ is Avogadro's number. What is the mean free path along the $x$-axis?

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 $k_B = 1.38 \times 10^{-23} \ J \ K^{-1}$)

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at $2.0 \; atm$ and temperature $17\,^{\circ} C$. Take the radius of a nitrogen molecule to be roughly $1.0 \; \mathring{A}$. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of $N_{2} = 28.0 \; u$).

On increasing the number density of a gas in a vessel,the mean free path of the gas:

The value of $C_p - C_v = 1.00 R$ for a gas in state $A$ and $C_p - C_v = 1.06 R$ in another state $B$. If $P_A$ and $P_B$ denote the pressure and $T_A$ and $T_B$ denote the temperature in the two states,then:

The change in volume $V$ with respect to an increase in pressure $P$ has been shown in the figure for a non-ideal gas at four different temperatures ${T_1}, {T_2}, {T_3}$ and ${T_4}$. The critical temperature of the gas is