According to kinetic theory of gases,
A. The motion of the gas molecules freezes at $0^\circ$C.
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
D. Average kinetic energy per molecule per degree of freedom is $\dfrac32 k_BT$ (for monoatomic gases).
Choose the most appropriate answer from the options given below
Answer: (B) B and C only
A: False. Molecular motion stops only at absolute zero, not at $0^\circ$C.
B: True. $\lambda = \dfrac{1}{\sqrt2\pi d^2 n}$ decreases as the number density $n$ increases.
C: True. $\lambda = \dfrac{k_BT}{\sqrt2\pi d^2 P}$ increases with $T$ at constant $P$.
D: False. The energy per degree of freedom is $\dfrac12 k_BT$; $\dfrac32 k_BT$ is the total for a monoatomic molecule.
B and C only.
Solution by Sreeraj P, M.Sc Physics