CBSE Class 11 Physics Revision Notes Chapter 12 Kinetic Theory

Kinetic Theory explains the measurable properties of gases through the continuous random motion of atoms and molecules.

For CBSE Class 11 Physics, the chapter connects pressure, temperature, gas laws, molecular energy, specific heat and collisions.

A gas contains a very large number of rapidly moving molecules. These molecules collide with each other and with the walls of their container. Their collective motion produces measurable properties such as pressure and temperature.

These CBSE Class 11 Physics Revision Notes Chapter 12 follow the 2026–27 chapter sequence. They cover gas laws, ideal gas behaviour, molecular pressure, rms speed, equipartition, specific heats and mean free path.

Key Takeaways

• Ideal gas equation: PV = μRT = NkBT connects macroscopic and molecular quantities.
• Gas pressure: Molecular collisions produce P = 1/3 nm<v²>.
• Temperature: The average translational kinetic energy per molecule is 3kBT/2.
• Mean free path: The average distance between collisions is λ = 1/(√2 πnd²).

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Access Class 11 Physics Chapter 12 Kinetic Theory Notes in 30 Minutes

These Kinetic Theory Class 11 Short Notes organise the chapter from molecular behaviour to measurable gas properties.

The same flow makes these Class 11 Physics Chapter 12 Kinetic Theory Notes suitable for concept and formula revision.

Molecular Nature of Matter

The molecular nature of matter states that matter consists of atoms or molecules. These particles remain in continuous motion and interact with one another.

Atomic Hypothesis

The atomic hypothesis may be summarised as follows:

• Matter consists of extremely small particles called atoms.
• Atoms combine to form molecules.
• Molecules of different substances differ in mass and structure.
• Particles attract one another at moderate separation.
• They repel strongly when brought very close.
• Molecular particles remain in continuous motion.

Dalton used atomic theory to explain the laws of definite and multiple proportions.

Molecular Spacing in Solids, Liquids and Gases

The arrangement and motion of molecules differ across the three states of matter.

Atoms in solids are usually separated by a few angstroms. Gas molecules are much farther apart compared with their own size.

Dynamic Equilibrium in a Gas

A gas appears static when viewed as a whole. At the molecular level, it remains highly active.

Molecules continuously:

• Move in random directions
• Collide with one another
• Strike the walls
• Change speed and direction

The average pressure, density and temperature remain constant in equilibrium. This is called dynamic equilibrium.

Behaviour of Gases and the Ideal Gas Equation

The behaviour of gases is described through pressure, volume, temperature and number of molecules.

Ideal Gas Equation

For μ moles of an ideal gas:

PV = μRT

Here:

• P = pressure
• V = volume
• μ = number of moles
• R = universal gas constant
• T = absolute temperature

The universal gas constant is:

R = 8.314 J mol⁻¹ K⁻¹

Since μ = N/NA:

PV = NkBT

Here:

• N = number of molecules
• NA = Avogadro constant
• kB = Boltzmann constant

The Boltzmann constant is:

kB = R/NA

kB = 1.38 × 10⁻²³ J K⁻¹

Another useful form of the ideal gas equation is:

P = nkBT

Here, n = N/V is the number density of molecules.

For a gas of density ρ and molar mass M0:

P = ρRT/M0

Boyle’s Law

For a fixed mass of gas at constant temperature:

PV = constant

Therefore:

P ∝ 1/V

This is Boyle’s law.

If volume decreases at constant temperature, pressure increases.

Charles’s Law

At constant pressure:

V/T = constant

Therefore:

V ∝ T

This is Charles’s law.

The temperature must be measured on the kelvin scale.

Avogadro’s Law

At the same temperature and pressure, equal volumes of all gases contain equal numbers of molecules.

This is Avogadro’s law.

At standard temperature and pressure, one mole of an ideal gas occupies about 22.4 litres.

One mole contains:

NA = 6.022 × 10²³ particles

Dalton’s Law of Partial Pressures

Consider a mixture of non-reacting ideal gases in the same container.

The total pressure is:

P = P1 + P2 + P3 + ...

This is Dalton’s law of partial pressures.

Each partial pressure is the pressure that one gas would exert if it alone occupied the container at the same temperature.

For each gas:

Pi = μiRT/V

Ideal Gas and Real Gas

An ideal gas is a theoretical gas that follows PV = μRT at every pressure and temperature.

Real gases approach ideal behaviour under certain conditions.

The difference between an ideal gas and real gas becomes significant at high pressure and low temperature.

Assumptions of the Kinetic Theory of Gases

The Kinetic Theory of Gases Class 11 model uses several simplifying assumptions.

• A gas contains a very large number of molecules.
• Molecules remain in continuous random motion.
• Each molecule obeys Newton’s laws of motion.
• Molecular dimensions are negligible compared with intermolecular separation.
• Intermolecular forces are negligible except during collisions.
• Molecules move in straight lines between collisions.
• Collisions among molecules are perfectly elastic.
• Collisions with the container walls are perfectly elastic.
• Collision duration is negligible compared with the time between collisions.
• Molecular motion has no preferred direction.
• Gas pressure results from collisions with the walls.

These assumptions form the basis of the kinetic theory of an ideal gas.

Pressure of an Ideal Gas

Gas pressure arises because moving molecules repeatedly transfer momentum to the container walls.

Molecular Origin of Gas Pressure

Consider a molecule of mass m moving with velocity components vx, vy and vz inside a cubic container.

When it strikes a wall perpendicular to the x-axis:

• Initial x-momentum = mvx
• Final x-momentum = −mvx
• Change in molecular momentum = −2mvx
• Momentum transferred to the wall = 2mvx

The repeated collisions of all molecules produce a force on the wall.

Pressure is force per unit area.

The final expression for the pressure of an ideal gas is:

P = 1/3 nm<v²>

Here:

• n = number of molecules per unit volume
• m = mass of one molecule
• <v²> = mean square speed

Since mass density ρ = nm:

P = 1/3 ρ<v²>

Pressure and Translational Kinetic Energy

Multiplying the pressure equation by volume:

PV = 1/3 Nm<v²>

The average translational kinetic energy of one molecule is:

= 1/2 m<v²>

Therefore:

PV = 2/3 N

If E is the total translational kinetic energy:

E = N

Then:

PV = 2E/3

Therefore:

E = 3PV/2

This relation connects macroscopic gas pressure with microscopic molecular motion.

Kinetic Interpretation of Temperature

The kinetic interpretation of temperature states that absolute temperature measures the average translational kinetic energy of gas molecules.

Average Kinetic Energy of a Molecule

From:

PV = 2E/3

And:

PV = NkBT

We get:

E = 3NkBT/2

Therefore, the average kinetic energy of a molecule is:

E/N = 3kBT/2

Or:

1/2 m<v²> = 3kBT/2

Important conclusions include:

• Average kinetic energy depends only on absolute temperature.
• It does not depend on pressure.
• It does not depend on volume.
• It does not depend on the type of ideal gas.
• Different ideal gases at the same temperature have equal average translational kinetic energy.

The internal energy associated with translation is:

Utrans = 3NkBT/2

For μ moles:

Utrans = 3μRT/2

Root Mean Square Speed

The root mean square speed is defined as:

vrms = √<v²>

Using the kinetic-energy relation:

vrms = √(3kBT/m)

For one mole:

vrms = √(3RT/M0)

Here:

• m = mass of one molecule
• M0 = molar mass

RMS speed represents a characteristic molecular speed.

Dependence of Molecular Speed on Mass and Temperature

From the rms-speed formula:

vrms ∝ √T

At a higher temperature, molecules move faster.

Also:

vrms ∝ 1/√m

At the same temperature, lighter molecules move faster than heavier molecules.

For two gases at the same temperature:

v1/v2 = √(m2/m1)

This relation also explains why lighter gases diffuse faster.

Law of Equipartition of Energy

Molecules can store energy through translation, rotation and vibration.

The law of equipartition of energy states:

For a system in thermal equilibrium, each independent quadratic energy mode contributes an average energy of 1/2 kBT per molecule.

For one mole, each mode contributes:

1/2 RT

Degrees of Freedom

The degrees of freedom of a molecule are the independent ways in which it can move or store energy.

The main types are:

• Translational degrees of freedom
• Rotational degrees of freedom
• Vibrational degrees of freedom

If a molecule has f active degrees of freedom:

Average energy per molecule = f/2 kBT

For μ moles:

U = f/2 μRT

Translational Degrees of Freedom

A molecule moving in three-dimensional space has three translational degrees of freedom.

They correspond to motion along:

• x-axis
• y-axis
• z-axis

Each contributes 1/2 kBT.

Therefore, translational energy per molecule is:

Etrans = 3/2 kBT

Rotational Degrees of Freedom

A diatomic molecule can rotate about two independent axes perpendicular to the line joining its atoms.

Therefore, at ordinary temperature, a rigid diatomic molecule has:

• 3 translational degrees of freedom
• 2 rotational degrees of freedom

Total active degrees of freedom:

f = 5

Its average energy per molecule is:

E = 5/2 kBT

A non-linear polyatomic molecule can have three rotational degrees of freedom.

Vibrational Degrees of Freedom

A vibrational mode contains both:

• Kinetic energy
• Potential energy

Each contributes 1/2 kBT.

Therefore, one vibrational mode contributes:

kBT per molecule

Vibrational modes become important at sufficiently high temperatures.

Specific Heat Capacity of Gases

The specific heat capacity of gases depends on the active degrees of freedom.

For one mole of an ideal gas:

U = fRT/2

Therefore:

Cv = fR/2

Using Mayer’s relation:

Cp = Cv + R

Hence:

Cp = (f + 2)R/2

The ratio of specific heats is:

γ = Cp/Cv

Therefore:

γ = (f + 2)/f

Monatomic Gas

A monatomic gas has only three translational degrees of freedom.

f = 3

Therefore:

Cv = 3R/2

Cp = 5R/2

γ = 5/3

Examples include helium, neon and argon.

Diatomic Gas

At ordinary temperatures, a diatomic gas has three translational and two rotational degrees of freedom.

f = 5

Therefore:

Cv = 5R/2

Cp = 7R/2

γ = 7/5

Examples include nitrogen and oxygen.

At higher temperatures, vibrational modes may become active and increase the specific heat.

Polyatomic Gas

For a rigid non-linear polyatomic molecule:

f = 6

Therefore:

Cv = 3R

Cp = 4R

γ = 4/3

The exact value may change when vibrational modes become active.

Mayer’s Relation and Ratio of Specific Heats

Mayer’s relation for an ideal gas is:

Cp − Cv = R

It is valid for monatomic, diatomic and polyatomic ideal gases.

The ratio of specific heats is:

γ = Cp/Cv

Specific Heat Capacity of Solids

Atoms in a solid vibrate about their mean positions.

Each atom has three vibrational directions. Every direction contains kinetic and potential energy.

Average energy per atom:

E = 3kBT

For one mole:

U = 3RT

Therefore, the molar heat capacity is approximately:

C = 3R

This is known as the Dulong-Petit result.

Mean Free Path of Gas Molecules

Gas molecules move rapidly but suffer repeated collisions. Their actual path is a sequence of short straight segments.

The mean free path is the average distance travelled by a molecule between two successive collisions.

Collision Time and Mean Free Path

Suppose gas molecules have diameter d and number density n.

The approximate collision rate is proportional to:

nπd²

The average time between collisions is:

τ = 1/(nπd²)

A more accurate treatment accounts for the relative motion of molecules.

The mean free path is:

λ = 1/(√2 πnd²)

Here:

• λ = mean free path
• n = number density
• d = molecular diameter

Factors Affecting Mean Free Path

From the formula:

λ ∝ 1/n

The mean free path increases when number density decreases.

Also:

λ ∝ 1/d²

Smaller molecules have a larger mean free path under similar conditions.

At constant temperature:

• Lower pressure means lower number density.
• Therefore, mean free path increases.

In a highly evacuated vessel, the mean free path may become comparable to the container size.

Mean free path helps explain:

• Diffusion
• Viscosity
• Thermal conduction
• Molecular transport in gases

Kinetic Theory Formula Sheet

These Kinetic Theory Class 11 Formulas bring together the main gas-law and molecular relations.

These Kinetic Theory Class 11 Notes connect each formula with molecular motion and measurable gas behaviour.

Important Differences for Quick Revision

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