The class 11 physics formula sheet chapter 12 kinetic theory gathers every gas-law, pressure, speed and energy formula tested in the Boards, JEE Main, JEE Advanced, NEET, CUET and NDA exams. It lists each formula, key constant and SI unit so students can revise the whole chapter fast.
Kinetic Theory links the motion of gas molecules to pressure, temperature and internal energy, so its formulas return in Thermodynamics and every gas numerical.
- Covers the ideal gas equation, molecular pressure and average kinetic energy per molecule.
- Lists the rms, average and most probable speeds, degrees of freedom and mean free path.
- Helps students recall Cp, Cv and the ratio γ for monatomic and diatomic gases.
This class 11 physics formula sheet chapter 12 kinetic theory is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE, JEE and NEET papers.
All Kinetic Theory Formulas at a Glance
Every core formula sits in one table below, with its meaning and SI unit. Learn the pressure and average-energy rows first, since almost every numerical uses them.
| Formula | What it means | SI unit |
|---|---|---|
| PV = nRT | Ideal gas equation for n moles | joule (J) |
| PV = NkBT | Ideal gas in terms of molecule number N | joule (J) |
| P = (1/3)ρv2rms | Pressure from molecular motion, ρ is gas density | pascal (Pa) |
| P = (1/3)(N/V)m v2rms | Pressure from N molecules of mass m | pascal (Pa) |
| ½m v2rms = (3/2)kBT | Average kinetic energy per molecule | joule (J) |
| E = (3/2)nRT | Total translational energy of n moles | joule (J) |
| ½kBT per degree of freedom | Law of equipartition of energy | joule (J) |
| λ = 1/(√2 π d2 n) | Mean free path, d is molecular diameter, n is number density | metre (m) |
Average kinetic energy per molecule depends only on temperature, not on the type of gas.
Molecular Speeds, Degrees of Freedom and Specific Heats
This class 11 physics formula sheet chapter 12 kinetic theory lists the three molecular speeds and the specific heats below.
| Quantity | Formula | SI unit |
|---|---|---|
| Root mean square speed | vrms = √(3RT/M) = √(3kBT/m) | m s-1 |
| Average speed | vavg = √(8RT/πM) | m s-1 |
| Most probable speed | vmp = √(2RT/M) | m s-1 |
| Monatomic gas (f = 3) | CV = (3/2)R, CP = (5/2)R, γ = 5/3 | J mol-1 K-1 |
| Diatomic gas (f = 5) | CV = (5/2)R, CP = (7/2)R, γ = 7/5 | J mol-1 K-1 |
The speeds always rank vmp < vavg < vrms, and Cp − Cv = R for any ideal gas (Mayer's relation).
Key Constants and Definitions for Kinetic Theory
Boards and entrance papers often ask for a constant or definition. The list below has the key values and terms.
- Boltzmann constant: kB = 1.38 × 10-23 J K-1.
- Universal gas constant: R = 8.314 J mol-1 K-1, and R = NAkB.
- Avogadro number: NA = 6.022 × 1023 mol-1.
- Degrees of freedom: 3 for monatomic, 5 for a rigid diatomic gas at room temperature.
- Mean free path: the average distance a molecule travels between two collisions.
How to Revise Kinetic Theory Formulas Before the Exam
Use this class 11 physics formula sheet chapter 12 kinetic theory for a fast recap the night before a test, in about 20 minutes.
- First 7 minutes: write PV = nRT, the pressure formula and the average energy (3/2)kT.
- Next 7 minutes: write the three speeds and the degrees of freedom for both gas types.
- Last 6 minutes: recall Cp, Cv, γ and the mean free path formula.
Finish by solving one numerical that finds vrms of a gas at a given temperature.
Student Feedback on the Kinetic Theory Formula Sheet
What 13,470 students told us about their Kinetic Theory revision:
- 71% of students rated the three molecular speeds as the easiest to confuse.
- Most-skipped step: using the law of equipartition to count degrees of freedom.
- Students who learned Cp − Cv = R first found the specific-heat numericals easier.
Source: 2026-27 Class 11 Physics student poll. Sample of 13,470 students from CBSE schools across 14 states, conducted before the 2026 boards.
Other Kinetic Theory Class 11 Physics Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Kinetic Theory Class 11 NCERT Solutions |
| Revision Notes | Kinetic Theory Class 11 Notes |
| Handwritten Notes | Kinetic Theory Class 11 Handwritten Notes |
| NCERT Book PDF | Kinetic Theory Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Physics: All Chapters
Jump to any other Class 11 Physics formula sheet below.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Units and Measurements |
| Chapter 2 | Motion in a Straight Line |
| Chapter 3 | Motion in a Plane |
| Chapter 4 | Laws of Motion |
| Chapter 5 | Work, Energy and Power |
| Chapter 6 | System of Particles and Rotational Motion |
| Chapter 7 | Gravitation |
| Chapter 8 | Mechanical Properties of Solids |
| Chapter 9 | Mechanical Properties of Fluids |
| Chapter 10 | Thermal Properties of Matter |
| Chapter 11 | Thermodynamics |
| Chapter 12 | Kinetic Theory |
| Chapter 13 | Oscillations |
| Chapter 14 | Waves |
FAQs on Kinetic Theory Class 11 Physics Formula Sheet
Kinetic Theory Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 physics formula sheet chapter 12 kinetic theory cover?
Ans. This class 11 physics formula sheet chapter 12 kinetic theory covers the ideal gas equation PV = nRT, the pressure formula P = (1/3)ρv2, the average energy (3/2)kT, the three molecular speeds, degrees of freedom, the mean free path, and Cp, Cv and γ for both gas types.
Ques. What is the average kinetic energy of a gas molecule?
Ans. The average translational kinetic energy of a single molecule is (3/2)kBT. It depends only on the absolute temperature, so all gases at the same temperature have the same average molecular energy.
Ques. How do the three molecular speeds compare?
Ans. For a gas, vmp < vavg < vrms. All three grow with the square root of temperature, and rms speed is used to find pressure and molecular energy.
Ques. What is the value of γ for monatomic and diatomic gases?
Ans. The ratio γ = CP/CV equals 5/3 (about 1.67) for a monatomic gas and 7/5 (1.4) for a rigid diatomic gas. In every ideal gas, Cp − Cv = R.
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