How much of JEE Main comes from Kinetic Theory of Gases?

JEEGenie estimates about 3% of JEE Main marks come from Kinetic Theory of Gases, based on recent papers. The share varies from year to year.

Which formulas matter most in Kinetic Theory of Gases?

The Kinetic Theory of Gases sheet on this page has 20 formula entries, starting with Ideal Gas Equation, Avogadro's Law, Pressure of an Ideal Gas (Kinetic Theory), Root Mean Square Speed, Average Kinetic Energy per Molecule. Each one comes with when to use it and the trap to avoid.

What topics does Kinetic Theory of Gases cover for JEE?

Kinetic Theory of Gases covers Ideal Gas Equation, Kinetic Theory Postulates, RMS Speed, Degrees of Freedom, Mean Free Path, Specific Heats of Gases.

How should I revise Kinetic Theory of Gases before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Kinetic Theory of Gases questions on JEEGenie.

How many previous-year questions are there on Kinetic Theory of Gases?

JEEGenie has 30 previous-year questions on Kinetic Theory of Gases, and this page shows a few with worked explanations.

Is practice on Kinetic Theory of Gases free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Kinetic Theory of Gases for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 3% of JEE Main marks come from Kinetic Theory of Gases. This page covers 20 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Do not assume real gases always behave ideally; deviations occur at high pressure and low temperature.

Key points to know

Ideal Gas. An ideal gas is a theoretical gas composed of point particles with no intermolecular forces and perfectly elastic collisions.
Avogadro's Law. Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules.
Degrees of Freedom. Number of independent ways a molecule can store energy (translational, rotational, vibrational).
Mean Free Path. Average distance a molecule travels between successive collisions.
Dalton's Law of Partial Pressures. Total pressure exerted by a mixture of non-reacting gases equals sum of partial pressures of each gas.
Key Assumptions of Kinetic Theory. Gas molecules are point particles with no volume, no intermolecular forces, and perfectly elastic collisions.
Relation Between Pressure and Kinetic Energy. Pressure is directly related to the average translational kinetic energy per unit volume.
Temperature as a Measure of Kinetic Energy. Absolute temperature is proportional to the average translational kinetic energy of molecules.

Formula sheet

Name	Formula	When to use
Ideal Gas Equation	$P V = n R T$	Use for any problem involving state variables of an ideal gas, especially in thermodynamic processes.
Avogadro's Law	$V \propto n$ at constant $T$ and $P$	Use when comparing volumes or number of moles of different gases under same conditions.
Pressure of an Ideal Gas (Kinetic Theory)	$P = \frac{1}{3} \frac{N m {\overset{ˉ}{v}}^{2}}{V} = \frac{1}{3} ρ {\overset{ˉ}{v}}^{2}$	Use to relate macroscopic pressure to microscopic molecular properties (mass, speed, density).
Root Mean Square Speed	$v_{rms} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 k T}{m}}$	Use to calculate molecular speeds from temperature and molar mass, or to compare gases.
Average Kinetic Energy per Molecule	$\overset{ˉ}{K} = \frac{3}{2} k T$	Use to relate temperature to molecular energy, or to compare energies of different gases.
Total Internal Energy of an Ideal Gas	$U = \frac{f}{2} n R T$	Use to find internal energy change in thermodynamic processes (isothermal, adiabatic).
Molar Specific Heats of Ideal Gases	$C_{V} = \frac{f}{2} R$ , $C_{P} = (\frac{f}{2} + 1) R$ , $γ = \frac{C_{P}}{C_{V}} = 1 + \frac{2}{f}$	Use to compute heat capacity or adiabatic index for thermodynamic processes.
Maxwell-Boltzmann Speed Distribution	$f (v) = 4 π N {(\frac{m}{2 π k T})}^{3 / 2} v^{2} e^{- m v^{2} / (2 k T)}$	Use to understand molecular speed distributions or to derive average speeds.
Most Probable, Mean, and RMS Speeds	$v_{p} = \sqrt{\frac{2 k T}{m}} = \sqrt{\frac{2 R T}{M}}$ , $\overset{ˉ}{v} = \sqrt{\frac{8 k T}{π m}} = \sqrt{\frac{8 R T}{π M}}$ , $v_{rms} = \sqrt{\frac{3 k T}{m}} = \sqrt{\frac{3 R T}{M}}$	Use to compare molecular speeds or to compute average kinetic energy.
Using the Kinetic Theory to Derive Gas Laws	$P V = N k T = n R T$	Use when asked to derive ideal gas equation from microscopic theory.
Solving Problems with Gas Mixtures	$P_{total} = P_{1} + P_{2} + \dots$ , $P_{i} = \frac{n_{i} R T}{V}$	Use when dealing with multiple gases in the same container.
Calculating Number Density and Mean Free Path	$n = \frac{N}{V} = \frac{P}{k T}$ , $λ = \frac{1}{\sqrt{2} π d^{2} n}$	Use to find how far a molecule travels between collisions, or to relate pressure to density.
Mean Free Path	$λ = \frac{1}{\sqrt{2} π d^{2} n}$	Use to understand transport phenomena (diffusion, viscosity) or collision rates.
Law of Equipartition of Energy	$\overset{ˉ}{E} = \frac{f}{2} k T$ per molecule, $U = \frac{f}{2} n R T$	Use to compute internal energy or specific heats of polyatomic gases.
Adiabatic Process for Ideal Gas	$P V^{γ} = constant$ , $T V^{γ - 1} = constant$ , $T^{γ} P^{1 - γ} = constant$	Use for adiabatic compression/expansion problems (e.g., in engines).
Isothermal Process for Ideal Gas	$P_{1} V_{1} = P_{2} V_{2}$	Use for processes at constant temperature (e.g., slow expansion).
Dalton's Law of Partial Pressures	$P_{total} = \sum P_{i}$	Use for gas mixtures to find individual gas contributions.
Using the Kinetic Theory to Compare Gases	$\overset{ˉ}{K} = \frac{3}{2} k T$ , $v_{rms} \propto \frac{1}{\sqrt{M}}$	Use to compare molecular speeds or energies of different gases at same temperature.
Relation Between Pressure and Kinetic Energy	$P = \frac{2}{3} \frac{N}{V} \overset{ˉ}{K} = \frac{2}{3} n \overset{ˉ}{K}$ (where $n$ is number density)	Use to connect macroscopic pressure to microscopic energy.
Temperature as a Measure of Kinetic Energy	$\overset{ˉ}{K} = \frac{3}{2} k T$	Use to interpret temperature microscopically.

Open the Kinetic Theory of Gases formula page

What JEE asks

Ideal Gas. JEE often tests the assumptions of kinetic theory and when real gases deviate from ideal behavior.
Ideal Gas Equation. JEE frequently asks to combine this with other laws (Boyle's, Charles's) or to find missing variables.
Avogadro's Law. JEE may test this in stoichiometry or gas mixture problems.
Pressure of an Ideal Gas (Kinetic Theory). JEE often asks to derive this or use it to find molecular speeds or number density.
Root Mean Square Speed. JEE frequently asks to compute $v_{rms}$ or compare it for different gases at same temperature.
Average Kinetic Energy per Molecule. JEE often tests that at same temperature, all ideal gases have same average kinetic energy per molecule.
Total Internal Energy of an Ideal Gas. JEE often combines this with first law of thermodynamics to find heat or work.
Degrees of Freedom. JEE tests how $f$ changes with temperature and molecular structure.
Molar Specific Heats of Ideal Gases. JEE often asks to find $γ$ for different gases or use it in adiabatic relations.
Maxwell-Boltzmann Speed Distribution. JEE may ask qualitative questions about how distribution changes with temperature or mass.
Most Probable, Mean, and RMS Speeds. JEE often asks to compute one speed from another or compare for different gases.
Using the Kinetic Theory to Derive Gas Laws. JEE may ask to derive or explain the connection between pressure and temperature.
Solving Problems with Gas Mixtures. JEE often asks to find total pressure or mole fraction from given masses.
Calculating Number Density and Mean Free Path. JEE may ask to compute $λ$ or how it changes with pressure/temperature.
Mean Free Path. JEE tests how $λ$ varies with $P$ and $T$ (e.g., at constant $T$ , $λ \propto 1 / P$ ).
Law of Equipartition of Energy. JEE often asks to find $C_{V}$ or $C_{P}$ for gases with given $f$ .
Adiabatic Process for Ideal Gas. JEE often asks to find final $T$ or $P$ after adiabatic change.
Isothermal Process for Ideal Gas. JEE may ask to compute work done in isothermal expansion.
Dalton's Law of Partial Pressures. JEE often tests this in context of collecting gases over water or mixing gases.
Using the Kinetic Theory to Compare Gases. JEE often asks which gas has higher $v_{rms}$ or $\overset{ˉ}{K}$ .
Key Assumptions of Kinetic Theory. JEE may ask to state assumptions or identify when they break down.
Relation Between Pressure and Kinetic Energy. JEE often uses this to derive temperature dependence.
Temperature as a Measure of Kinetic Energy. JEE may ask to explain why temperature is a measure of average kinetic energy.

Common traps

Do not assume real gases always behave ideally; deviations occur at high pressure and low temperature. Ideal Gas
Do not forget to use temperature in Kelvin, not Celsius. Ideal Gas Equation
Do not apply this to real gases without corrections. Avogadro's Law
Do not confuse ${\overset{ˉ}{v}}^{2}$ (mean square speed) with $\overset{ˉ}{v}$ (mean speed); they are different. Pressure of an Ideal Gas (Kinetic Theory)
Do not confuse $M$ (molar mass in kg/mol) with $m$ (mass per molecule). Root Mean Square Speed
Do not forget this is per molecule; for per mole, multiply by $N_{A}$ : $\frac{3}{2} R T$ . Average Kinetic Energy per Molecule
Do not forget $f$ is degrees of freedom: 3 for monatomic, 5 for diatomic (at moderate T), etc. Total Internal Energy of an Ideal Gas
Do not forget that monatomic gases have only 3 translational degrees. Degrees of Freedom
Do not forget that $C_{P} - C_{V} = R$ for ideal gases. Molar Specific Heats of Ideal Gases
Do not confuse $f (v)$ with probability; it is the number of molecules with speed in $d v$ . Maxwell-Boltzmann Speed Distribution
Do not confuse the three speeds; they have different constants: $v_{p} < \overset{ˉ}{v} < v_{rms}$ . Most Probable, Mean, and RMS Speeds
Do not skip steps; show that $\frac{1}{2} m {\overset{ˉ}{v}}^{2} = \frac{3}{2} k T$ . Using the Kinetic Theory to Derive Gas Laws
Do not forget that each gas occupies the entire volume. Solving Problems with Gas Mixtures
Do not confuse $n$ (number density) with moles; use context. Calculating Number Density and Mean Free Path

Topics in Kinetic Theory of Gases

Ideal Gas Equation
Kinetic Theory Postulates
RMS Speed
Degrees of Freedom
Mean Free Path
Specific Heats of Gases

Previous-year questions on Kinetic Theory of Gases

JEEGenie has 30 previous-year questions on Kinetic Theory of Gases. A few worked examples follow.

Year	Questions
2023	2
2021	2
2020	1
2019	3
2017	1
2015	2
2014	1
2013	4
2012	1
1999	1
1998	2
1997	3
1996	1
1995	1
1993	1
1992	1
1988	1
1987	1
1984	1

Question 1 hard

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is

n

. The internal energy of one mole of the gas is

U_{n}

and the speed of sound in the gas is

v_{n}

. At a fixed temperature and pressure, which of the following is the correct option?

$v_{3} < v_{6}$ and $U_{3} > U_{6}$
$v_{5} > v_{3}$ and $U_{3} > U_{5}$
$v_{5} > v_{7}$ and $U_{5} < U_{7}$
$v_{6} < v_{7}$ and $U_{6} < U_{7}$

Answer: C

Explanation. For one mole of an ideal gas, internal energy:

U_{n} = \frac{n}{2} R T

U_{n} \propto n

Thus

U_{5} < U_{7}

(and also

U_{3} < U_{5} < U_{6} < U_{7}

). Speed of sound:

v_{n} = \sqrt{\frac{γ R T}{M}}, γ = 1 + \frac{2}{n}

v_{n} \propto \sqrt{1 + \frac{2}{n}}

n

increases,

γ

decreases, hence

v_{n}

decreases. Therefore

v_{5} > v_{7}

and also

v_{3} > v_{5} > v_{6} > v_{7}

. Checking options: -

v_{5} > v_{7}

✔ and

U_{5} < U_{7}

✔

\to

matches option C.

C

From NTA/IIT papers: JEE Advanced 2023

Question 2 medium

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T ?

$\frac{2}{3} k_{B} T$
$k_{B} T$
$\frac{3}{2} k_{B} T$
$\frac{1}{2} k_{B} T$

Answer: C

Explanation. By the equipartition theorem, each degree of freedom contributes

\frac{1}{2} k_{B} T

to the average thermal energy of a molecule. A monoatomic ideal gas has only 3 translational degrees of freedom (motion along x, y, and z axes). There are no rotational or vibrational degrees of freedom that contribute at normal temperatures. Therefore, the average energy per molecule is:

⟨ E ⟩ = 3 \times \frac{1}{2} k_{B} T = \frac{3}{2} k_{B} T

The correct answer is (C)

\frac{3}{2} k_{B} T

From NTA/IIT papers: JEE Main 2021 · 22 Jul Shift 2

Question 3 hard

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio

2 : 3

. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is

4 : 3

. The ratio of their densities is

$1 : 4$
$1 : 2$
$6 : 9$
$8 : 9$

Answer: D

Explanation. For an ideal gas,

P = \frac{ρ R T}{M}

, so

ρ = \frac{P M}{R T}

. At constant temperature, the ratio of densities is

\frac{ρ_{1}}{ρ_{2}} = \frac{P_{1} M_{1}}{P_{2} M_{2}}

. Given

\frac{P_{1}}{P_{2}} = \frac{4}{3}

and

\frac{M_{1}}{M_{2}} = \frac{2}{3}

, we get

\frac{ρ_{1}}{ρ_{2}} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9}

From NTA/IIT papers: JEE Advanced 2013

Frequently asked questions

How much of JEE Main comes from Kinetic Theory of Gases?: JEEGenie estimates about 3% of JEE Main marks come from Kinetic Theory of Gases, based on recent papers. The share varies from year to year.
Which formulas matter most in Kinetic Theory of Gases?: The Kinetic Theory of Gases sheet on this page has 20 formula entries, starting with Ideal Gas Equation, Avogadro's Law, Pressure of an Ideal Gas (Kinetic Theory), Root Mean Square Speed, Average Kinetic Energy per Molecule. Each one comes with when to use it and the trap to avoid.
What topics does Kinetic Theory of Gases cover for JEE?: Kinetic Theory of Gases covers Ideal Gas Equation, Kinetic Theory Postulates, RMS Speed, Degrees of Freedom, Mean Free Path, Specific Heats of Gases.
How should I revise Kinetic Theory of Gases before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Kinetic Theory of Gases questions on JEEGenie.
How many previous-year questions are there on Kinetic Theory of Gases?: JEEGenie has 30 previous-year questions on Kinetic Theory of Gases, and this page shows a few with worked explanations.
Is practice on Kinetic Theory of Gases free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.