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JEE MainPhysicsKinetic Theory of Gases

A gaseous mixture consists of a monoatomic gas and a diatomic gas. If the effective molar specific heat of the mixture at constant volume is 21 10 R , the ratio of the number of moles of the monoatomic gas to that of the diatomic gas is :

Options

  1. A3:2
  2. B2:3
  3. C3:5
  4. D5:3

Correct answer

B. 2:3

Step-by-step solution

Let n₁ and n₂ be the number of moles of the monoatomic and diatomic gases, respectively. The molar specific heat at constant volume for a monoatomic gas is C_ v₁ = 3 2 R , and for a diatomic gas it is C_ v₂ = 5 2 R . The effective molar specific heat of the mixture at constant volume is given by: C_ v,mix = n₁ C_ v₁ + n₂ C_ v₂ n₁ + n₂ Substitute the given values: 21 10 R = n₁ ( 3 2 R ) + n₂ ( 5 2 R ) n₁ + n₂ Dividing both sides by R and cross-multiplying: 2.1(n₁ + n₂) = 1.5 n₁ + 2.5 n₂ 2.1 n₁ + 2.1 n₂ = 1.5 n₁ + 2.

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