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Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases

In a gas, the rms speed of oxygen molecules is v . If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the new rms speed will be

Options

  1. A2v
  2. Bv 2
  3. Cv
  4. D4v

Correct answer

A. 2v

Step-by-step solution

The initial rms speed of oxygen molecules is given by: v = 3RT M where M is the molar mass of O₂ molecules. When the temperature is doubled, the new temperature is T' = 2T . When oxygen molecules dissociate into oxygen atoms, the molar mass becomes half, so M' = M 2 . The new rms speed v' is given by: v' = 3RT' M' = 3R(2T) M 2 v' = 4 3RT M = 2 3RT M v' = 2v

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