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JEE MainPhysicsKinetic Theory of Gases

Two separate flasks contain equal masses of helium gas and oxygen gas at the same room temperature. The ratio of the total kinetic energy of the helium gas to the total kinetic energy of the oxygen gas is : (Given : Molar mass of helium = 4 g/mol , Molar mass of oxygen = 32 g/mol )

Options

  1. A3 : 5
  2. B8 : 1
  3. C5 : 24
  4. D24 : 5

Correct answer

D. 24 : 5

Step-by-step solution

The total kinetic energy of a bulk gas is given by E = n f 2 RT , where n is the number of moles and f is the degrees of freedom. Let the mass of each gas be m . For helium (a monoatomic gas), f = 3 and the number of moles n_ He = m 4 . Total kinetic energy of helium, E_ He = ( m 4 ) ( 3 2 ) RT = 3m 8 RT . For oxygen (a diatomic gas), f = 5 and the number of moles n_ O ₂ = m 32 . Total kinetic energy of oxygen, E_ O ₂ = ( m 32 ) ( 5 2 ) RT = 5m 64 RT . Taking the ratio of their total kinetic energies: E_ He E_ O ₂

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