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MHT CET202521 Apr 2025Evening ShiftPhysicsKinetic Theory of GasesActual

The temperature of an ideal gas is increased from 100 K to 400 K. If ' x ' is the R.M.S. velocity of its molecules at 100 K, it becomes

Options

  1. Ax 4
  2. B2 x
  3. C3 x
  4. D4 x

Correct answer

B. 2 x

Step-by-step solution

The root mean square velocity follows v_ rms = 3RT M , showing v_ rms T . Given v₁ = x at T₁ = 100 K , the velocity at T₂ = 400 K is determined by the ratio v₂ v₁ = T₂ T₁ . Substituting values yields v₂ x = 400 100 = 4 = 2 , so v₂ = 2x . The RMS velocity becomes 2x .

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