Schooling · Class 11 · Physics · Kinetic Theory · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-II
Kinetic Theory: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A gas consists of a large number of…
- Pressure of a gas equals one-third…
- Temperature is directly proportional…
- The root-mean-square (rms) speed of…
- The equipartition theorem states…
- Monatomic gases have 3 translational…
- Mean free path λ is the average…
- Formulas and facts
- P V = N kB T
- Pressure from kinetic theory
- ⟨KE⟩ = (3/2) kB T
- v_rms = √(3 R T / M)
- Equipartition
- Cv = (f/2) R
- For monatomic gas (f = 3): Cv =…
- Worked examples
- Finding rms speed of nitrogen at…
- Average kinetic energy of a helium…
- Molar heat capacity of oxygen
- Watch out for
- Forgetting to convert molar mass…
- Confusing average speed with rms…
- Assuming diatomic molecules have…
- Writing pressure as P = ρ v̄²…
- Using Celsius directly in kinetic…
What this chapter is about
Kinetic theory explains the behaviour of gases by treating them as collections of a very large number of tiny molecules in constant random motion. Instead of describing a gas only through measurable quantities like pressure, volume and temperature, this chapter connects these bulk properties to the microscopic motion of individual molecules. You learn how pressure arises from countless molecular collisions with container walls, and how temperature is a measure of the average kinetic energy of molecules.
Key ideas
- A gas consists of a large number of molecules moving randomly in all directions; intermolecular forces are negligible except during brief collisions.
- Pressure of a gas equals one-third the product of its density and the mean of the squared molecular speeds: P = (1/3) ρ v̄², where v̄² is the mean square speed.
- Temperature is directly proportional to the average translational kinetic energy of molecules: (1/2) m v̄² = (3/2) kB T, where kB is Boltzmann's constant.
- The root-mean-square (rms) speed of molecules is v_rms = √(3 kB T / m) = √(3 R T / M), with M being molar mass.
- The equipartition theorem states that each quadratic term (degree of freedom) in the energy expression of a molecule contributes (1/2) kB T to its average energy.
- Monatomic gases have 3 translational degrees of freedom; diatomic gases (at moderate temperatures) have 3 translational and 2 rotational, giving 5 degrees of freedom.
- Mean free path λ is the average distance a molecule travels between successive collisions: λ = 1 / (√2 π d² n), where d is molecular diameter and n is number density.
Formulas and facts to remember
- Ideal gas equation in molecular form: P V = N kB T, where N is the number of molecules and kB = 1.38 × 10⁻²³ J K⁻¹.
- Pressure from kinetic theory: P = (1/3) (N/V) m v̄² = (1/3) ρ v̄².
- Mean translational kinetic energy per molecule: ⟨KE⟩ = (3/2) kB T.
- Root-mean-square speed: v_rms = √(3 R T / M), with R = 8.314 J mol⁻¹ K⁻¹ and M in kg mol⁻¹.
- Equipartition: each degree of freedom contributes (1/2) kB T per molecule or (1/2) R T per mole.
- Molar heat capacity at constant volume: Cv = (f/2) R, where f is the number of degrees of freedom.
- For monatomic gas (f = 3): Cv = (3/2) R ≈ 12.5 J mol⁻¹ K⁻¹; γ = Cp/Cv = 5/3.
- For diatomic gas (f = 5 at moderate T): Cv = (5/2) R ≈ 20.8 J mol⁻¹ K⁻¹; γ = 7/5 = 1.4.
- Mean free path: λ = kB T / (√2 π d² P).
Common mistakes
- Forgetting to convert molar mass from g mol⁻¹ to kg mol⁻¹ when using R in SI units → always express M in kg mol⁻¹ for consistency.
- Confusing average speed with rms speed; they differ by a numerical factor → use the correct formula for each quantity.
- Assuming diatomic molecules have only 3 degrees of freedom like monatomic ones → include 2 rotational degrees at room temperature for diatomic gases.
- Writing pressure as P = ρ v̄² instead of P = (1/3) ρ v̄² → remember the factor of one-third from averaging over three perpendicular directions.
- Using Celsius directly in kinetic theory formulas → always convert temperature to kelvin before substituting.
Quick revision
- Pressure arises from molecular collisions; P = (1/3) ρ v̄².
- Temperature measures average translational KE: (3/2) kB T per molecule.
- rms speed ∝ √T and ∝ 1/√M; lighter molecules move faster at the same temperature.
- Equipartition: each degree of freedom adds (1/2) kB T energy per molecule.
- Monatomic Cv = (3/2) R; diatomic Cv = (5/2) R at room temperature.
- Mean free path decreases when pressure rises or molecular size increases.