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JEE MainPhysicsKinetic Theory of Gases

A gaseous mixture consists of 2 moles of helium (He) and 3 moles of nitrogen ( N ₂ ) in thermal equilibrium at a temperature T . The ratio of the total translational kinetic energy of the mixture to the total internal energy of the mixture is

Options

  1. A7 : 5
  2. B3 : 5
  3. C1 : 1
  4. D5 : 7

Correct answer

D. 5 : 7

Step-by-step solution

The translational kinetic energy is associated with 3 degrees of freedom for all types of gas molecules. Total translational kinetic energy of the mixture: E_ trans = (n₁ + n₂) 3 2 R T = (2 + 3) 3 2 R T = 15 2 R T The total internal energy depends on the total degrees of freedom ( f=3 for monoatomic He and f=5 for diatomic N ₂ at normal temperatures). Total internal energy of the mixture: E_ int = n₁ 3 2 R T + n₂ 5 2 R T E_ int = 2 3 2 R T + 3 5 2 R T = 3 R T + 15 2 R T = 21 2 R T The required ratio is: E_ trans E_

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