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

For a gas at absolute temperature T , the mean square speed of its molecules is proportional to

Options

  1. A1 T
  2. BT
  3. CT
  4. DT^2

Correct answer

B. T

Step-by-step solution

The mean square speed of gas molecules is given by the square of the root mean square speed. The root mean square speed is v_ rms = 3RT M Squaring both sides, the mean square speed is v_ rms ^2 = 3RT M Alternatively, from the kinetic theory of gases, the average translational kinetic energy of a molecule is 1 2 m v^2 = 3 2 k_B T This gives v^2 = 3 k_B T m Therefore, the mean square speed is directly proportional to the absolute temperature T .

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