NCERT Solutions for Class 11 Physics Chapter 13 – Kinetic Theory
Chapter 13 of Class 11 Physics, Kinetic Theory, provides a microscopic explanation of the macroscopic behaviour of gases, bridging the gap between atomic theory and classical thermodynamics. The chapter begins with the ideal gas equation (PV = nRT) and the molecular interpretation of pressure — arising from countless random collisions of gas molecules with container walls. Students derive the kinetic expression for pressure (P = ⅓ρ‹v²›) and connect it to temperature, showing that the average kinetic energy of a molecule is directly proportional to absolute temperature. This leads to expressions for RMS speed, mean speed, and most probable speed of gas molecules — all important for JEE and NEET. The chapter introduces degrees of freedom — the number of independent ways a molecule can absorb energy — and the profound Law of Equipartition of Energy, which states that each degree of freedom contributes ½kT to average energy. This explains why different gases have different molar specific heats. The mean free path concept quantifies how far a molecule travels between collisions, connecting microscopic kinetics to macroscopic transport phenomena like viscosity and conductivity. Kinetic Theory is one of the most conceptually rich and frequently tested chapters in Class 11 Physics.
NCERT Solutions PDF – Class 11 Physics Chapter 13 (All Exercises)
The PDF provides complete step-by-step solutions to all NCERT exercises on ideal gas laws, molecular speeds, equipartition, specific heats, and mean free path. Aligned with CBSE curriculum.
Important Formulas – Chapter 13: Kinetic Theory
| Formula | Expression | Description |
|---|---|---|
| Ideal Gas Equation | PV = nRT = NkT | n = moles; R = 8.314 J/mol·K; k = 1.38×10⁻²³ J/K; N = molecules |
| Kinetic Pressure | P = (1/3)ρ‹v²› = (1/3)(mN/V)‹v²› | Derived from molecular collisions with walls |
| RMS Speed | v_rms = √(3RT/M) = √(3kT/m) | M = molar mass; m = molecular mass |
| Mean Speed | v_mean = √(8RT/πM) | Average speed of molecules |
| Most Probable Speed | v_p = √(2RT/M) | Speed corresponding to peak of Maxwell distribution |
| Speed Ratio | v_p : v_mean : v_rms = 1 : 1.128 : 1.225 | √2 : √(8/π) : √3 |
| Average KE per molecule | KE = (3/2)kT | Directly proportional to absolute temperature |
| Equipartition of Energy | Energy per degree of freedom = (1/2)kT | Each quadratic term in energy contributes ½kT |
| Molar specific heat (Cv) | Cv = (f/2)R | f = degrees of freedom; monoatomic f=3, diatomic f=5 |
| Mean Free Path | λ = 1 / (√2 · n · πd²) | n = number density; d = molecular diameter |
| Avogadro's Number | N_A = 6.022 × 10²³ mol⁻¹ | Number of molecules per mole |
Subtopics Explained – Chapter 13: Kinetic Theory
Ideal Gas and Molecular Model
An ideal gas consists of point-mass molecules with no intermolecular forces, undergoing perfectly elastic random collisions. Real gases approach ideal behaviour at high temperatures and low pressures. The ideal gas law PV = nRT combines Boyle's, Charles's, and Avogadro's laws into one equation.
Pressure from Kinetic Theory
Gas pressure is the cumulative effect of billions of molecular collisions per second on container walls. The derivation shows P = (1/3)nmv², where n is number density and v is molecular speed. Connecting this to the ideal gas equation yields the fundamental result: average KE = (3/2)kT.
Molecular Speeds (Maxwell Distribution)
Molecules in a gas don't all move at the same speed. The Maxwell-Boltzmann distribution gives three characteristic speeds. v_rms is the root-mean-square speed (used in KE). v_mean is the arithmetic average. v_p (most probable) is the peak of the distribution. All three increase with temperature as √T.
Degrees of Freedom and Equipartition
Degrees of freedom (f) represent independent modes of energy absorption. Monoatomic gases (like He, Ar) have 3 translational DOF. Diatomic gases (H₂, O₂) have 5 (3 translational + 2 rotational). The Equipartition Theorem assigns ½kT per DOF, explaining why Cv = (3/2)R for monoatomic and (5/2)R for diatomic gases.
Mean Free Path
Mean free path (λ) is the average distance a molecule travels between successive collisions. It is inversely proportional to the number density and the square of molecular diameter. At standard conditions, λ for air ≈ 68 nm, much larger than molecular size (~0.3 nm). λ is important in transport phenomena — viscosity, conductivity, and diffusion all depend on it.
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Quick Reference Table – Degrees of Freedom and Specific Heats
| Gas Type | Examples | Degrees of Freedom (f) | Cv | Cp | γ = Cp/Cv |
|---|---|---|---|---|---|
| Monoatomic | He, Ne, Ar | 3 | (3/2)R | (5/2)R | 5/3 ≈ 1.67 |
| Diatomic (rigid) | H₂, O₂, N₂ | 5 | (5/2)R | (7/2)R | 7/5 = 1.4 |
| Diatomic (with vibration) | H₂ at high T | 7 | (7/2)R | (9/2)R | 9/7 ≈ 1.29 |
| Polyatomic (non-linear) | H₂O, NH₃ | 6 | 3R | 4R | 4/3 ≈ 1.33 |
NCERT Solutions for Class 11 Physics Chapter 13: Kinetic Theory – FAQs
The Kinetic Theory of Gases explains the behavior of gases by assuming that they consist of a large number of tiny particles moving randomly in all directions. These particles continuously collide with one another and with the walls of the container. The theory helps students understand concepts such as pressure, temperature, and volume at a microscopic level. In this chapter, NCERT focuses on connecting molecular motion with observable gas properties. Questions based on assumptions of the kinetic theory are frequently asked in examinations because they help students develop a deeper understanding of how gases behave under different physical conditions.
The kinetic theory is based on several assumptions regarding the behavior of gas molecules. It states that gas molecules are extremely small compared to the distance between them, move randomly, and experience perfectly elastic collisions. The molecules exert negligible intermolecular forces except during collisions. These assumptions simplify the study of gases and help derive important gas laws. Students are often asked to explain these assumptions in detail because they form the foundation of the entire chapter. Understanding them makes it easier to solve numerical problems related to pressure, temperature, and molecular speed.
One of the most important conclusions of the kinetic theory is that temperature is directly related to the average kinetic energy of gas molecules. As temperature increases, the molecules move faster and possess greater kinetic energy. This relationship explains why gases expand when heated and contract when cooled. NCERT numerical questions often involve this concept because it connects microscopic molecular motion with macroscopic physical observations. Students should clearly understand that temperature does not depend on the number of molecules but on their average kinetic energy. This concept is essential for advanced thermodynamics topics.
RMS speed, or Root Mean Square speed, represents the effective speed of gas molecules. Since molecules move in random directions with different speeds, RMS speed provides a useful average value for calculations. It depends on temperature and molecular mass. Lighter gas molecules generally have higher RMS speeds than heavier molecules at the same temperature. Questions involving RMS speed are among the most searched and frequently tested topics from this chapter. Understanding its significance helps students solve numerical problems and interpret molecular motion more accurately in kinetic theory.
An ideal gas strictly follows all assumptions of the kinetic theory and obeys gas laws under all conditions. Real gases, however, deviate from these assumptions due to intermolecular forces and finite molecular volume. In practical situations, gases behave ideally only at high temperatures and low pressures. NCERT explains this distinction to help students understand why theoretical models sometimes differ from real observations. Questions comparing ideal and real gases are common in examinations because they test conceptual understanding. A clear grasp of this difference also helps in studying thermodynamics and advanced gas behavior.