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JEE MainPhysicsKinetic Theory of Gases

A closed container holds a mixture of Helium (a monatomic gas) and Oxygen (a diatomic gas) in thermal equilibrium. Which of the following statements is correct regarding the properties of the two gases?

Options

  1. AThe average total kinetic energy per molecule is the same for both gases.
  2. BThe root mean square speed of the molecules is the same for both gases.
  3. CThe average translational kinetic energy per unit mass is the same for both gases.
  4. DThe average translational kinetic energy per molecule is the same for both gases.

Correct answer

D. The average translational kinetic energy per molecule is the same for both gases.

Step-by-step solution

In thermal equilibrium, both gases in the mixture are at the same temperature T . The average translational kinetic energy per molecule for any gas depends only on its absolute temperature and is given by 3 2 k_BT . Since both gases are at the same temperature, their average translational kinetic energies per molecule are identical. The average total kinetic energy per molecule depends on the degrees of freedom ( f ), given by f 2 k_BT . Helium is monatomic ( f=3 ) and Oxygen is diatomic ( f=5 ), so their total kin

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