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Kinetic Theory of Gases appeared 26 times across 3 years — 3% of Physics. This question is from Degrees of Freedom and Specific Heat of Gas Mixtures.

Year 2026 2025 2024 Total
Questions 6 11 9 26
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N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

Solution & Explanation

Related Formula

The equivalent degrees of freedom feq for a mixture of gases is:

feq = (n₁ f₁ + n₂ f₂)/(n₁ + n₂)

where:

  • n₁, n₂ are the number of moles of each gas.
  • f₁, f₂ are the respective degrees of freedom of each gas.
Core Logic

For the given gases:

  • Polyatomic gas:
  • Moles, n₁ = N
  • Degrees of freedom, f₁ = 6
  • Monoatomic gas:
  • Moles, n₂ = 2
  • Degrees of freedom, f₂ = 3

    • We want the mixture to behave as a diatomic gas. For a diatomic gas:

  • Equivalent degrees of freedom, feq = 5
Step 1: Solve for N

Substitute the values into the degrees of freedom mixture formula:

5 = ((N)(6) + (2)(3))/(N + 2) 5(N + 2) = 6N + 6 5N + 10 = 6N + 6 10 - 6 = 6N - 5N N = 4
Pattern Recognition

Diatomic equivalent degree of freedom is 5. Since the monoatomic degrees of freedom (3) and polyatomic degrees of freedom (6) bracket 5, you can use the weighted ratio method to find the molar proportions directly.

Chapter Mix

Class 11 Physics: Kinetic Theory of Gases

Reference Study Guides

Kinetic Theory Of Gases

More Kinetic Theory of Gases Previous-Year Questions — Page 6

Q31 jee_main_2024_31_jan_morning Kinetic Energy Of Gas Molecules
The parameter that remains the same for molecules of all gases at a given temperature is :
  • A. kinetic energy
  • B. momentum
  • C. mass
  • D. speed

Solution

Related Formula
KE = (f)/(2)kT
Core Logic

The average translational kinetic energy of any gas molecule depends only on the absolute temperature of the gas and is independent of the nature or mass of the gas.

For 1 mole of any ideal gas, the average translational kinetic energy is (3)/(2)RT. Therefore, at a given temperature, the kinetic energy parameter is uniform across all ideal gases.

Pattern Recognition

Temperature is directly proportional to average translational kinetic energy. If T is constant, KE is constant for all gases regardless of mass.

Chapter Mix

Class 11 Physics: Kinetic Theory

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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)