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JEE MainPhysicsKinetic Theory of Gases

Samples of the same ideal gas are kept in two separate containers. The ratio of the collision frequency of the gas molecules in the first container to that in the second container is 2 . If the ratio of the absolute temperature of the gas in the first container to that in the second container is 4 , then the ratio of their pressures is

Options

  1. A1
  2. B4
  3. C8
  4. D2

Correct answer

B. 4

Step-by-step solution

The collision frequency of an ideal gas is given by Z = 2 d^2 n v Since the number density n = P kT and the average speed v = 8kT m , we can write the proportionality as: Z P T T P T For the same gas in two different states, the ratio of their collision frequencies is: Z₁ Z₂ = P₁ P₂ T₂ T₁ We are given that Z₁ Z₂ = 2 and T₁ T₂ = 4 . Substituting these values: 2 = P₁ P₂ 1 4 2 = P₁ P₂ 1 2 P₁ P₂ = 4 Answer: 4

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