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JEE MainPhysicsKinetic Theory of Gases

A mixture of two unknown ideal gases A and B is kept in a closed vessel in thermal equilibrium. If the ratio of the average total kinetic energy per molecule of gas A to that of gas B is 5:6 , which of the following could be the structural nature of gas A and gas B respectively?

Options

  1. ADiatomic and non-linear polyatomic
  2. BNon-linear polyatomic and diatomic
  3. CMonoatomic and diatomic
  4. DDiatomic and monoatomic

Correct answer

A. Diatomic and non-linear polyatomic

Step-by-step solution

For an ideal gas in thermal equilibrium at temperature T , the average total kinetic energy per molecule is given by f 2 kT , where f is the number of degrees of freedom. Since both gases are in the same vessel, they are at the same temperature T . The ratio of their average kinetic energies per molecule is: E_A E_B = f_A 2 kT f_B 2 kT = f_A f_B Given that E_A E_B = 5 6 , we have f_A = 5 and f_B = 6 . A gas with 5 degrees of freedom is typically a rigid diatomic gas, while a gas with 6 degrees of freedom is a non-l

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