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KCET2023PhysicsKinetic Theory of Gases

The speed of sound in an ideal gas at a given temperature T is v . The rms speed of gas molecules at that temperature is v_ rms . The ratio of the velocities v and v_ rms for helium and oxygen gases are X and X^ . respectively. Then, X X^ is equal to

Options

  1. A21 5
  2. B5 21
  3. C5 21
  4. D21 5

Correct answer

B. 5 21

Step-by-step solution

The speed of sound at a given temperature is given by v_ sound = r R T M v_ rms = 3 R T M For oxygen molecules; v₀ v_ rms = r₀ R T M 3 R T M = r₀ 3 For helium molecules; v_ He v_ rms = r_ He R T M 3 R T M = r_ He 3 (r_ Be = 5 3 , r_ O = 7 5 ) x^ x = 5 9 7 15 = 25 21 = 5 21

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