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Kinetic Theory

NCERT Class 11 Physics Chapter 12

Kinetic Theory for Class 11 Physics, JEE and NEET: ideal gas, pressure and temperature from molecular motion, rms speed, equipartition and mean free path.

6 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part II (Class 11), Chapter 12 “Kinetic Theory”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.5 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Molecular nature of matter

    The atomic hypothesis, Dalton and Avogadro, and how far apart molecules are in solids, liquids and gases.

    Class 11 only NCERT Section 12.2 12 min read 5 solved examples 6 practice questions

  2. Behaviour of gases

    PV = μRT = NkB T, Avogadro’s hypothesis, real versus ideal gases and Dalton’s law of partial pressures.

    NCERT Section 12.3 12 min read 6 solved examples 6 practice questions

  3. Kinetic theory of an ideal gas

    Assumptions, pressure P = (1/3)nm⟨v⟩, kinetic meaning of temperature, rms speed and solved examples.

    NCERT Section 12.4 16 min read 6 solved examples 6 practice questions

  4. Law of equipartition of energy

    Degrees of freedom, ½kB T per mode, and energy of monatomic and diatomic molecules.

    NCERT Section 12.5 12 min read 5 solved examples 6 practice questions

  5. Specific heat capacity from kinetic theory

    Cv, Cp and γ for monatomic, diatomic and polyatomic gases; 3R for solids.

    NCERT Section 12.6 12 min read 4 solved examples 6 practice questions

  6. Mean free path

    Derivation of l = 1/(√2 nπd), collision time, and how l depends on size, density and pressure.

    NCERT Section 12.7 16 min read 5 solved examples 6 practice questions

Key formulas in this chapter

Molecular nature of matter

  • 1 Å = 10 m = 0.1 nm
  • Molecules per m3 in a gas: n = P/(kB T)
  • Average spacing ≈ n−1/3

Behaviour of gases

  • PV = μRT = NkB T
  • P = kB nT (n = N/V)
  • P = ρRT/M
  • kB = 1.38 × 10−23 J K−1; R = NA kB = 8.314 J mol−1 K−1
  • μ = M/M0 = N/NA
  • P = P + P + … (Dalton)

Kinetic theory of an ideal gas

  • P = (1/3)nm⟨v2⟩ = (1/3)ρ⟨v2⟩
  • ½ m ⟨v2⟩ = (3/2) kB T
  • E = (3/2) N kB T; PV = (2/3)E
  • vrms = √(3kB T/m) = √(3RT/M0)

Law of equipartition of energy

  • Energy per active quadratic term = ½ kB T
  • ε = (f/2) kB T per molecule; U = (f/2) RT per mole
  • f = 3 (monatomic), 5 (rigid diatomic or linear), 6 (rigid non-linear), 7 (vibrating diatomic)

Specific heat capacity from kinetic theory

  • Cv = (f/2)R; Cp = Cv + R (f = all energy modes; U = (f/2)RT per mole)
  • Cv = (3/2)R, Cp = (5/2)R, γ = 5/3 (monatomic)
  • Cv = (5/2)R, Cp = (7/2)R, γ = 7/5 (rigid diatomic)
  • Cv = (3 + f)R, Cp = (4 + f)R (non-linear polyatomic; here f = vibrational modes only)
  • Cp − Cv = R (any ideal gas)
  • γ = 1 + 2/f (f = all energy modes)
  • C = 3R (classical solid, per mole of atoms, neglecting thermal expansion)

Mean free path

  • τ = 1/(nπd⟨v⟩) (other molecules at rest)
  • l = ⟨v⟩τ = 1/(nπd) (other molecules at rest)
  • l = 1/(√2 nπd) (all molecules moving)
  • τ = 1/(√2 nπd⟨v⟩) (all molecules moving)
  • l = kB T/(√2 πd2P) (ideal gas, n = P/(kB T))
  • collisions per second = ⟨v⟩/l = 1/τ

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