Kinetic Theory

JEE Main level, single correct, medium

50 of 168

Question 50 of 168

Consider a sample of oxygen behaving like an ideal gas. At 300K300K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
(Molecular weight of oxygen is 32gmol−1;R=8.3JK−1mol−132g{mol}^{-1};R=8.3J{K}^{-1}{mol}^{-1})

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Answer: (C) 3π8\sqrt{\dfrac{3\pi }{8}}

vrms=3RTM{v}_{rms}=\sqrt{\dfrac{3RT}{M}}
vavg=8πRTM{v}_{avg}=\sqrt{\dfrac{8}{\pi }\dfrac{RT}{M}}
vrmsvavg=3π8\dfrac{{v}_{rms}}{{v}_{avg}}=\sqrt{\dfrac{3\pi }{8}}

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