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JEE MainPhysicsKinetic Theory of Gases

Two separate vessels contain Helium (molar mass 4 g mol ⁻¹ ) and Neon (molar mass 20 g mol ⁻¹ ) respectively. The first vessel contains a mass m of Helium at pressure P and volume V . The second vessel contains a mass 2m of Neon at pressure 2P and volume V 2 . The ratio of the average translational kinetic energy per molecule of Helium to that of Neon is:

Options

  1. A2:5
  2. B1:1
  3. C2:1
  4. D5:2

Correct answer

A. 2:5

Step-by-step solution

The average translational kinetic energy per molecule of a gas is directly proportional to its absolute temperature T , since K = 3 2 k_BT . From the ideal gas equation, PV = nRT = m M RT , the temperature can be expressed as T = PVM mR . For Helium in the first vessel: T₁ = P V 4 m R = 4PV mR For Neon in the second vessel: T₂ = (2P) ( V 2 ) 20 (2m) R = PV 20 2mR = 10PV mR The ratio of the average translational kinetic energy per molecule of Helium to that of Neon is equal to the ratio of their temperatures: K₁ K₂

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