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Kinetic Theory of Gases appeared 26 times across 3 years — 3% of Physics. This question is from Mixture of Gases.

Year 2026 2025 2024 Total
Questions 6 11 9 26
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If three moles of monoatomic gas (γ = (5)/(3)) is mixed with two moles of a diatomic gas (γ = (7)/(5)), the value of adiabatic exponent γ for the mixture is:

Solution & Explanation

Related Formula
fmixture = (n₁ f₁ + n₂ f₂)/(n₁ + n₂) γmixture = 1 + 2fmixture
Core Logic

For a monoatomic gas, degrees of freedom f₁ = 3. Moles n₁ = 3. For a diatomic gas, degrees of freedom f₂ = 5. Moles n₂ = 2. We can compute the equivalent degrees of freedom for the mixture using a weighted average.

Step 1: Calculate Equivalent Degrees of Freedom
fmixture = (n₁ f₁ + n₂ f₂)/(n₁ + n₂) fmixture = (3(3) + 2(5))/(3 + 2) = (9 + 10)/(5) = (19)/(5)
Step 2: Calculate Adiabatic Exponent
γmixture = 1 + 2fmixture γmixture = 1 + (2)/((19)/(5)) = 1 + (10)/(19) = (29)/(19) ≈ 1.52
Pattern Recognition

Alternatively, you can compute Cv and Cₚ for the mixture: Cv,mix = n₁ Cv1 + n₂ Cv2n₁ + n₂, and γmix = Cp,mixCv,mix. Both methods yield identical results rapidly.

Chapter Mix

Class 11 Physics: Kinetic Theory of Gases Class 11 Physics: Thermodynamics

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%)