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

Determine the rms speed of hydrogen molecules within a sample of hydrogen gas at 300 K . Also, find the temperature at which the rms speed is twice this calculated speed.

Options

  1. A1930 m s ⁻¹ , 1200 K
  2. B3860 m s ⁻¹ , 2400 K
  3. C1930 m s ⁻¹ , 600 K
  4. D965 m s ⁻¹ , 1200 K

Correct answer

A. 1930 m s ⁻¹ , 1200 K

Step-by-step solution

The root mean square speed of gas molecules is given by: v_ rms = 3RT M For hydrogen gas ( H ₂ ), M = 2 10⁻³ kg mol ⁻¹ . Substituting T = 300 K and R = 8.314 J mol ⁻¹ K ⁻¹ : v_ rms = 3 8.314 300 2 10⁻³ v_ rms = 3.7413 10^6 1934 m s ⁻¹ 1930 m s ⁻¹ Let T' be the temperature at which the rms speed is twice the initial speed. Thus: v_ rms ' = 2 v_ rms 3RT' M = 2 3RT M Squaring both sides: 3RT' M = 4 ( 3RT M ) T' = 4T T' = 4 300 = 1200 K

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