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JEE MainPhysicsKinetic Theory of Gases

A monoatomic gas A and a rigid diatomic gas B are found to have the exact same average kinetic energy per molecule. The ratio of the absolute temperature of gas A to the absolute temperature of gas B is :

Options

  1. A3 : 5
  2. B1 : 1
  3. C5 : 3
  4. D5 : 3

Correct answer

C. 5 : 3

Step-by-step solution

The average kinetic energy per molecule of an ideal gas is given by f 2 k_ B T , where f is the number of degrees of freedom. For a monoatomic gas A , the degrees of freedom f_ A = 3 . For a rigid diatomic gas B , the degrees of freedom f_ B = 5 . Given that the average kinetic energies per molecule are equal: 3 2 k_ B T_ A = 5 2 k_ B T_ B Solving for the ratio of their absolute temperatures: 3 T_ A = 5 T_ B T_ A T_ B = 5 3 Answer: 5 : 3

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