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JEE Main 2021 (24 Feb, Shift 2) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from JEE Main 2021 (24 Feb, Shift 2)

Q71JEE Main 2021 · 24 FEB · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

The root mean square speed of molecules of a given mass of a gas at 27∘^\circC and 1 atmosphere pressure is 200 ms−1{}^{-1}. The root mean square speed of molecules of the gas at 127∘^\circC and 2 atmosphere pressure is x3\frac{x}{\sqrt{3}} ms−1{}^{-1}. The value of x will be _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 400

  1. vrms=3RTMv_{rms} = \sqrt{\dfrac{3RT}{M}} depends only on TT, not on pressure.
  2. v2v1=400300=23\dfrac{v_2}{v_1} = \sqrt{\dfrac{400}{300}} = \dfrac{2}{\sqrt{3}}
  3. v2=200×23=4003 m s−1v_2 = 200 \times \dfrac{2}{\sqrt{3}} = \dfrac{400}{\sqrt{3}}\text{ m s}^{-1}
  4. So x=400x = 400.
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