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JEE MainPhysicsKinetic Theory of Gases

Equal moles of Helium gas and Oxygen gas are kept in separate closed containers at the same temperature. Which of the following statements correctly compares their average translational kinetic energies per molecule and their average total kinetic energies per molecule?

Options

  1. ATheir average translational kinetic energies are equal, but the average total kinetic energy of Oxygen is grea
  2. BBoth their average translational kinetic energies and their average total kinetic energies are equal.
  3. CTheir average total kinetic energies are equal, but the average translational kinetic energy of Helium is grea
  4. DBoth the average translational kinetic energy and the average total kinetic energy of Oxygen are greater than

Correct answer

A. Their average translational kinetic energies are equal, but the average total kinetic energy of Oxygen is grea

Step-by-step solution

According to the kinetic theory of gases, the average translational kinetic energy per molecule for any gas is 3 2 k_B T , which depends only on the absolute temperature. Thus, since both gases are at the same temperature, their average translational kinetic energies are equal. However, the total kinetic energy per molecule depends on the degrees of freedom f , and is given by f 2 k_B T . Helium is a monatomic gas with f = 3 , so its average total kinetic energy per molecule is 3 2 k_B T . Oxygen is a diatomic gas

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