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AP EAMCET201923 Apr 2019Morning ShiftPhysicsKinetic Theory of GasesActual

Three closed vessels (A, B ) and (C ) are at the same temperature (T ) and contain gases. Vessel (A ) contains only ( O ₂, B ) contains only ( N ₂ ) and ( C ) contains a mixture of equal quantities of ( O ₂ ) and ( N ₂ ). If the rms speed of ( O ₂ ) molecules in vessel (A ) is (v₁ ) and that of ( N ₂ ) molecules in vessel (B ) is (v₂ ) then the rms speed of ( O ₂ ) molecules in vessel ( C ) is

Options

  1. A( ( v₁+v₂ 2 ) )
  2. B(v₁ )
  3. C( (v₁ v₂ ) )
  4. D( v₁ 2 )

Correct answer

B. (v₁ )

Step-by-step solution

Key Idea Root mean square velocity of any gas is given by (v_ rms = 3 R T M ) Where, (M= ) molecular weight. As, rms speed of any gas is depends on the temperature of gas and molecular weight of gas. In a mixture of gases (say ( N ₂ ) and ( O ₂ ) ) at a constant temperature, rms speed is independent to the quantity (moles) of gas present in the gas mixture. So, in this problem the rms speed of ( O ₂ ) in vessel (C ) is (v₁ ). Hence, the correct option is (b).

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