For a van der Waals gas,if $P_c, V_c$,and $T_c$ are the critical pressure,volume,and temperature respectively,then the value of $P_cV_c/T_c$ is:

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

Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} C$ and pressure $1.01 \times 10^{5} Pa$. Assume the molecular diameter $d = 0.3 nm$ and the gas is ideal. Given Boltzmann constant $k = 1.38 \times 10^{-23} J K^{-1}$. (Result in $nm$)

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion,the average time of collision between molecules increases as $V^q$,where $V$ is the volume of the gas. The value of $q$ is $\left( \gamma = \frac{C_P}{C_V} \right)$.

What is the effect of a decrease in the number of molecules per unit volume on the mean free path?

The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of gas $B$. If number densities of the gases $A$ and $B$ are $n_A$ and $n_B$, respectively, then the correct option is :