Kinetic Theory

JEE Main level, single correct, medium

84 of 168

Question 84 of 168

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0∘C0^{\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 32kBT\dfrac{3}{2}{k}_{B}T (for monoatomic gases).
Choose the most appropriate answer from the options given below

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Answer: (B) B and C only

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0K0K.
B. The mean free path decreases on increasing the number density of the molecules.
C. The mean free path increases on increasing the volume. Now if temperature is increased by keeping the pressure constant the volume should increase that is mean free path increases.
Mean free path λ=12πd2n\lambda =\dfrac{1}{\sqrt{2}\pi {d}^{2}n}, here, n=NVn=\dfrac{N}{V}
⇒λ=12πd2NV\Rightarrow \lambda =\dfrac{1}{\sqrt{2}\pi {d}^{2}\dfrac{N}{V}}
Using, PV=NKTPV=NKT
⇒λ=KT2πd2P\Rightarrow \lambda =\dfrac{KT}{\sqrt{2}\pi {d}^{2}P}
D. Average kinetic energy per molecule per degree of freedom is 12kBT\dfrac{1}{2}{k}_{B}T.
Thus, B and C only.

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