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

Imagine a container is evacuated such that only one molecule of a gas remains inside. Let v_a and v_ rms denote the average speed and the rms speed of the gas respectively.

Options

  1. Av_a < v_ rms
  2. Bv_a = v_ rms
  3. Cv_a > v_ rms
  4. Dv_ rms is undefined

Correct answer

B. v_a = v_ rms

Step-by-step solution

For a single molecule, let its speed be v . The average speed of the gas is given by v_a = v_i N . Since there is only one molecule, N = 1 , which gives v_a = v . The root mean square speed is given by v_ rms = v_i^2 N . For N = 1 , v_ rms = v^2 = v . Therefore, v_a = v_ rms .

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