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

Year 2026 2025 2024 Total
Questions 6 11 9 26
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The ratio of vapour densities of two gases at the same temperature is (4)/(25) , then the ratio of r.m.s. velocities will be: [cite: 59-61]

Solution & Explanation

Related Formula

The root-mean-square (r.m.s.) velocity of gas molecules is given by:

vrms = √((3RT)/(M))

Since molecular weight M is directly proportional to the vapour density (ρ), the r.m.s. velocity is inversely proportional to the square root of its vapour density:

vrms1vrms2 = √((ρ₂)/(ρ₁))
Core Logic

Given the ratio of vapour densities :

(ρ₁)/(ρ₂) = (4)/(25)

Therefore, the ratio of their r.m.s. velocities is:

vrms1vrms2 = √((25)/(4)) = (5)/(2)
Pattern Recognition

R.M.S. velocity changes inversely with the square root of mass or density. Whenever a density ratio is given, simply invert the fraction and take the square root to immediately find the velocity ratio.

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

More Kinetic Theory of Gases Questions — jee_main_2025_28_jan_evening

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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%)