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JEE MainPhysicsKinetic Theory of Gases

An open vessel containing air at 27^ C is heated until the average translational kinetic energy of the remaining air molecules becomes 1.5 times its initial value. Assuming ideal gas behaviour, the fraction of the original mass of air that has escaped the vessel is

Options

  1. A2 3
  2. B1 3
  3. C1 2
  4. D1 4

Correct answer

B. 1 3

Step-by-step solution

The average translational kinetic energy of gas molecules is directly proportional to the absolute temperature ( E T ). Initial temperature, T₁ = 27^ C = 300 K Since the kinetic energy becomes 1.5 times, the new temperature T₂ is: T₂ = 1.5 300 K = 450 K For an open vessel, the pressure and volume remain constant. According to the ideal gas law ( PV = nRT ), the number of moles is inversely proportional to the absolute temperature: n₁ T₁ = n₂ T₂ Let n₁ be the initial number of moles and n₂ be the final number of mol

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