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KVPY2016PhysicsKinetic Theory of Gases

A container is divided into two equal part I and II by a partition with a small hole of diameter d. The two partitions are filled with same ideal gas, but held at temperature T _ I =150 ~K and T _ II =300 ~K by connecting to heat reservoirs. Let _ I and _ II be the mean free paths of the gas particles in the two parts such that d > _ I and d > _ II . Then _ I / _ II is close to -

Options

  1. A0.25
  2. B0.5
  3. C0.7
  4. D1.0

Correct answer

C. 0.7

Step-by-step solution

As dimension of hole is very small than mean path, then at equilibrium effusion rate of gas in both direction must be equal. For this P ₁ T ₁ = P ₂ T ₂ Mean free path T P array c ₁ ₂ = T₁ T₂ P₂ P₁ T₁ T₂ T₂ T₁ ₁ ₂ = T₁ T₂ = 150 300 =0.7 array

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