The mean free path of a molecule of diameter $5\times10^{-10} \ m$ at the temperature $41^{\circ}C$ and pressure $1.38\times10^{5} \ Pa$ is given as . . . . . . $m$. (Given $k_{B}=1.38\times10^{-23} \ J/K$).

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

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 $nm$)

What is free path? And what is mean free path?

We have $0.5 \, g$ of hydrogen gas in a cubic chamber of size $3 \, cm$ kept at $NTP$. The gas in the chamber is compressed keeping the temperature constant until a final pressure of $100 \, atm$ is reached. Is one justified in assuming the ideal gas law in the final state? (Hydrogen molecules can be considered as spheres of radius $1 \, \mathring{A}$).

An ideal gas in a closed container is slowly heated. As its temperature increases,which of the following statements are true?
$(A)$ The mean free path of the molecules decreases.
$(B)$ The mean collision time between the molecules decreases.
$(C)$ The mean free path remains unchanged.
$(D)$ The mean collision time remains unchanged.