NCERT Solutions Class 11 Physics Chapter 12 Kinetic Theory

The Class 11 Physics NCERT Solutions Chapter 12 Kinetic Theory will help students prepare for Boards, JEE Main, JEE Advanced, NEET, CUET and NDA in 2026-27. Every back-exercise question is solved with full working, so students can check each pressure derivation, rms-speed calculation, degrees-of-freedom count, and mean free path step by step.

This chapter links the behaviour of a gas to the motion of its molecules, and it sets up the thermodynamics work that follows.

• CBSE Weightage: 4 to 5 marks, usually one short answer plus one numerical on rms speed or the ideal gas equation.
• Questions solved: all Exercise 12.1 onward, covering the ideal gas equation, kinetic pressure, temperature, and mean free path.
• Key formulas: PV = nRT, P = ⅓ρv², v_rms = √(3RT/M), equipartition, mean free path.

Each solution in this Class 11 Physics NCERT Solutions Chapter 12 Kinetic Theory compilation is curated by subject experts, based on the 2026-27 NCERT textbook, and refined against the last five years of CBSE Board, JEE Main and NEET papers.

Kinetic Theory of Gases and the Molecular Model

The chapter builds the whole subject on one idea. A gas is a huge number of tiny molecules in constant, random motion. The kinetic theory of gases explains pressure, temperature, and heat from this motion alone. Getting the model right is the first step in solving any numerical in this chapter.

The NCERT questions here ask students to link a large-scale quantity, such as pressure, to the average behaviour of molecules. A real gas behaves like an ideal gas at low pressure and high temperature. The solved answers state which assumption each numerical uses, so no step is skipped. This habit prevents the most common conceptual slip in the chapter.

The Ideal Gas Equation and the Gas Laws

The ideal gas equation ties together pressure, volume, temperature, and the amount of gas. In the form PV = nRT, it holds the gas laws that came before it. The chapter uses it in most numericals, and the NCERT solutions apply it to every gas-property question.

• Boyle's law: at fixed temperature, PV is constant.
• Charles' law: at fixed pressure, V/T is constant.
• Avogadro's law: equal volumes of gases at the same pressure and temperature hold equal numbers of molecules.
• Molecular form: PV = Nk_BT, where k_B is the Boltzmann constant.

Numericals such as Exercise 12.1 and Exercise 12.3 use this equation to find a volume, a pressure, or the number of molecules. Always put the temperature in kelvin before you substitute. The Class 11 Physics NCERT Solutions Chapter 12 Kinetic Theory show the kelvin conversion on its own line so students never lose a mark on this step.

Kinetic Interpretation of Pressure of a Gas

The chapter derives pressure from molecular collisions with the container wall. Each molecule that bounces off a wall gives it a tiny push. Add up all these pushes over the whole wall, and you get the steady pressure of the gas. This derivation is a frequent short-answer question.

The result of the derivation is the central formula of the chapter, and the NCERT solutions show every stage of it.

This last form is the bridge to the next section. Pressure is directly linked to the average kinetic energy of the molecules. The solved answers rewrite the formula in whichever form the question needs, so students see how one relation feeds the next.

Kinetic Energy, Temperature and RMS Speed

Joining the pressure formula with the ideal gas equation gives the chapter's most important idea. Temperature is a measure of the average kinetic energy of the molecules. Nothing else in the gas sets the temperature. The NCERT solutions use this link in every speed and energy numerical.

• Average kinetic energy per molecule: ½m v²_rms = (3/2)k_BT, which depends only on temperature.
• RMS speed: v_rms = √(3k_BT/m) = √(3RT/M), where M is the molar mass.
• Speed and mass: at the same temperature, a lighter molecule moves faster than a heavier one.

Questions like Exercise 12.7 and Exercise 12.8 ask students to compare the rms speeds of two gases or to find a speed at a new temperature. The average kinetic energy of a molecule is the same for every gas at the same temperature. This single fact answers many objective questions in JEE Main and NEET, so the solved answers state it clearly.

Degrees of Freedom and the Law of Equipartition of Energy

A molecule can store energy in more than one way. The number of independent ways it can move is its number of degrees of freedom. A single atom can only move along three directions, but a molecule with two or more atoms can also rotate. The chapter counts these carefully because they fix the energy of the gas.

The law of equipartition of energy then shares the energy out equally. Each degree of freedom carries an average energy of ½k_BT per molecule. To find the total internal energy, multiply this share by the number of degrees of freedom and by the number of molecules. The solved answers show this multiplication step by step, so students can reuse it for any gas.

Specific Heat Capacity of Gases

Once the internal energy is known, the chapter finds the specific heat capacity of a gas. This is the heat needed to raise the temperature of one mole by one kelvin. A gas has two values, because it can be heated at constant volume or at constant pressure. The NCERT solutions derive both from the degrees of freedom.

The link between the two values is fixed by the Mayer relation, C_P − C_V = R. The ratio γ falls as the molecule gains more degrees of freedom. Numericals such as Exercise 12.10 test whether students can pick the right specific heat for the gas in the problem, so the solved answers name the gas type first.

Mean Free Path and Avogadro's Number

Between two collisions, a molecule travels a short straight path. The average length of this path is the mean free path. It sets how far a molecule goes before it changes direction, and it explains why smells spread slowly even though molecules move fast. This topic appears in both short-answer and objective questions.

• Mean free path: λ = 1/(√2 π d² n), where d is the molecular diameter and n is the number density.
• Pressure link: raising the pressure packs molecules closer, so the mean free path falls.
• Avogadro's number: N_A = 6.022 × 10²³ molecules in one mole of any substance.

Questions like Exercise 12.12 ask students to estimate the mean free path or the number of collisions per second. The mean free path is inversely proportional to both the number density and the square of the molecular size. The Class 11 Physics NCERT Solutions Chapter 12 Kinetic Theory keep every quantity in SI units before substituting, exactly as CBSE expects.

Exercise-wise Breakdown for Class 11 Physics Chapter 12 Kinetic Theory

The NCERT back-exercise splits into clear groups. Use this map to plan which answers to practise first for the 2026-27 boards. Every group links to the full solved set.

Solving the groups in this order builds the skills in the same sequence the chapter teaches them. Start with the ideal gas equation, then speeds, then degrees of freedom, because each group uses the one before it.

Common Mistakes Students Make in the Kinetic Theory Chapter

These slips happen while writing or calculating the answer, not because the concept is unclear. Each one costs 1 to 3 marks in the CBSE paper, so the solved answers point them out at the exact step.

Student Feedback on the Kinetic Theory Chapter

Practice Questions for Class 11 Physics Chapter 12 Kinetic Theory

Once the solved answers are clear, test yourself on the full question set. The practice page has every NCERT question with a step-by-step Solution and an Expert Solution behind a click.

Other Kinetic Theory Class 11 Physics Resources

NCERT Solutions for Class 11 Physics: All Chapters

Jump to the solutions for any other Class 11 Physics chapter below.

FAQs on Class 11 Physics Chapter 12 Kinetic Theory NCERT Solutions