According to kinetic theory of gases, A. The motion of the gas… | JEE Main 2022 (27 Jun, Shift 2)

Q13JEE Main 2022 · 27 JUN · SHIFT 2Medium

Mean Free Path & Real Gases

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 $\frac{3}{2} k_B T$ (for monoatomic gases). Choose the most appropriate answer from the options given below:

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Answer: (b)

A: false; molecular motion does not stop at $0^\circ$ C (KE $\propto T$ in kelvin, 273 K here).
B: true; $\lambda = \dfrac{1}{\sqrt{2}\,n\pi d^2}$ decreases as $n$ increases.
C: true; at constant $P$ , $\lambda = \dfrac{kT}{\sqrt{2}\pi d^2P} \propto T$ .
D: false; energy per degree of freedom is $\dfrac{1}{2}k_BT$ ; $\dfrac{3}{2}k_BT$ is the total for a monoatomic molecule.
So the answer is (b) B and C only.

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Mean Free Path & Real Gases question from JEE Main 2022 (27 Jun, Shift 2)

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