Kinetic Theory · JEE Preparation Physics

The root mean square speed of gas molecules is v at pressure P and temperature T. If the pressure is doubled keeping the temperature constant, the ne…

Practice question from Kinetic Theory (JEE Preparation Physics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-3A0430

The root mean square speed of gas molecules is vv at pressure PP and temperature TT. If the pressure is doubled keeping the temperature constant, the new root mean square speed will be:

  1. A.vvCorrect answer
  2. B.2v\sqrt{2}v
  3. C.2v2v
  4. D.v/2v/\sqrt{2}

Solution

The root mean square speed of an ideal gas depends only on its temperature, given by vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}}. Since the temperature TT remains constant, the rms speed does not change, even if the pressure is doubled (the density doubles accordingly, keeping vrmsv_{rms} constant).

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