NCERT · Class XI · Chapter 12

Kinetic Theory MCQs: Master the Invisible Motion of Gases

A focused bank of chapter‑wise and exam‑wise MCQs that turns Boltzmann’s constant, rms speeds, mean free path, and Maxwell–Boltzmann curves into fast, accurate decisions in the exam hall.

Ideal vs real gases Molecular speeds & distributions Degrees of freedom & γ Equipartition & internal energy
Start solving Kinetic Theory MCQs Smart filters · Exam tags · Attempt analytics as you solve.

Why these MCQs matter

Exams rarely ask you to reproduce full derivations; they test whether you can read a single line about a gas and instantly know which law, formula, or assumption to fire.

1. Mirrors real exam patterns

Items range from straight‑from‑NCERT checks to JEE/NEET style twists on rms speed, γ, and equipartition, so your practice stays aligned with what paper‑setters actually ask.

2. Builds formula instinct

Regular exposure trains you to recognise relations like \(v_{\text{rms}}\propto\sqrt{T/M}\), the \(PV=\tfrac{2}{3}E\) link, or how mean free path scales, without re‑deriving them every time.

3. Closes theory–application gap

Questions force you to connect verbal cues such as “rigid diatomic molecule” or “adiabatic expansion” with precise changes in internal energy, γ, and temperature.

4. Gives instant diagnostics

Exam labels and concept tags beside each MCQ let you see exactly which micro‑topics—Maxwell distribution, real‑gas deviations, or equipartition failures—are costing you marks.

Key concepts woven through this set

Molecular model & gas laws
Assumptions of kinetic theory, ideal‑gas equation, Boyle’s and Charles’ laws, and when real gases start to deviate.
Pressure & dimensional results
Pressure from molecular impacts, kinetic‑theory expression with the \(\tfrac{1}{3}\) factor, dimensional formulae, and the compressibility factor \(Z\).
Speeds & Maxwell–Boltzmann
Most probable, average, and rms speeds; how the Maxwell distribution shifts with temperature and mass; and why not all molecules share the same speed.
Mean free path & collisions
Dependence of mean free path on pressure and molecular diameter, when it becomes comparable to container size, and what controls collision frequency.
Degrees of freedom & γ
Translational and rotational modes, monoatomic vs diatomic gases, variation of γ with active degrees of freedom, and why equipartition can fail at low temperature.
Internal energy & processes
Internal energy as a function of temperature only for an ideal gas, behaviour in isothermal, adiabatic, and free expansions, and the relation \(U=\tfrac{f}{2}nRT\).

What you will learn by practising

  • How to decide, from a single line in a question, whether you need most probable, average, or rms speed.
  • How temperature, pressure, and molecular mass affect speed distributions, mean free path, and collision rate.
  • How to compute internal energy and γ using degrees of freedom, then apply them to isothermal and adiabatic changes.
  • How to translate qualitative statements on ideal and real gases into the exact mathematical laws they imply.
Built for analytics‑driven revision

On academia‑aeternum.com, every attempt contributes to your personal chapter profile: accuracy by concept cluster, difficulty level, and exam source. Use that data to decide whether to revise NCERT explanations, formula sheets, or full‑length mock tests next.

Treat this Kinetic Theory set as your microscopic lab: each MCQ is a controlled experiment that reveals how well you understand what gas molecules are doing behind the symbols on the page.

🎯 Knowledge Check

Physics — KINETIC THEORY

50 Questions Class 11 MCQs
1
The SI unit of Boltzmann constant \(k_B\) is
(Exam: CBSE – Class XI)
2
Which of the following quantities remains constant for an ideal gas during an isothermal process?
(Exam: CBSE – Class XI)
3
The kinetic theory of gases assumes that gas molecules are
(Exam: CBSE – Class XI)
4
For an ideal gas, the internal energy depends only on
(Exam: CBSE – Class XI)
5
The pressure of a gas is due to
(Exam: CBSE – Class XI)
6
According to kinetic theory, collisions between gas molecules are
(Exam: CBSE – Class XI)
7
The rms speed of gas molecules is proportional to
(Exam: CBSE – Class XI)
8
Which gas will have the highest rms speed at the same temperature?
(Exam: CBSE – Class XI)
9
The relation \(PV = \dfrac{2}{3}E\) connects pressure with
(Exam: CBSE – Class XI)
10
Mean free path of a gas molecule is
(Exam: CBSE – Class XI)
11
Which of the following increases the mean free path of a gas?
(Exam: CBSE – Class XI)
12
At absolute zero temperature, the rms speed of gas molecules is
(Exam: CBSE – Class XI)
13
The degrees of freedom of a monoatomic gas are
(Exam: CBSE – Class XI)
14
The value of \(\gamma = \dfrac{C_P}{C_V}\) for a monoatomic gas is
(Exam: CBSE – Class XI)
15
The law that relates average kinetic energy of molecules to temperature is
(Exam: CBSE – Class XI)
16
The average kinetic energy per molecule of an ideal gas is
(Exam: CBSE – Class XI)
17
Which of the following does not affect the rms speed of gas molecules?
(Exam: CBSE – Class XI)
18
Real gases deviate from ideal behaviour at
(Exam: CBSE – Class XI)
19
The compressibility factor \(Z\) for an ideal gas is
(Exam: JEE – Main)
20
Which velocity is always greater for a gas?
(Exam: JEE – Main)
21
The rms speed of oxygen molecules at temperature \(T\) is \(v\). The rms speed at temperature \(4T\) will be
(Exam: CBSE – Class XI)
22
If the pressure of an ideal gas is doubled while keeping temperature constant, the mean free path will
(Exam: CBSE – Class XI)
23
The mean free path of a gas is inversely proportional to
(Exam: CBSE – Class XI)
24
The average kinetic energy per molecule of an ideal gas depends on
(Exam: CBSE – Class XI)
25
For a diatomic gas at ordinary temperatures, the value of \(\gamma = \dfrac{C_P}{C_V}\) is
(Exam: CBSE – Class XI)
26
According to the law of equipartition of energy, the energy associated with one degree of freedom is
(Exam: CBSE – Class XI)
27
A monoatomic gas and a diatomic gas are at the same temperature. The ratio of their average kinetic energies per molecule is
(Exam: CBSE – Class XI)
28
The pressure exerted by an ideal gas is given by
(Exam: CBSE – Class XI)
29
When the temperature of an ideal gas is increased at constant volume, its pressure increases because
(Exam: CBSE – Class XI)
30
The number of degrees of freedom of a rigid diatomic molecule is
(Exam: JEE – Main)
31
Two gases A and B have molecular masses \(m\) and \(4m\) respectively. The ratio of their rms speeds at the same temperature is
(Exam: JEE – Main)
32
The compressibility factor \(Z\) of a real gas at high pressure is generally
(Exam: JEE – Main)
33
Which of the following quantities remains unchanged in an adiabatic expansion of an ideal gas?
(Exam: JEE – Main)
34
The equation \(PV^\gamma = \text{constant}\) applies to
(Exam: JEE – Main)
35
The average speed of gas molecules is related to rms speed by
(Exam: JEE – Main)
36
For a monoatomic ideal gas, the internal energy is
(Exam: JEE – Main)
37
The law of equipartition of energy fails at low temperatures because
(Exam: JEE – Advanced)
38
If the temperature of a gas is tripled, the ratio of its new rms speed to the old rms speed is
(Exam: JEE – Advanced)
39
The kinetic theory expression for pressure shows that pressure is independent of
(Exam: JEE – Advanced)
40
The mean free path of gas molecules becomes comparable to container dimensions under
(Exam: JEE – Advanced)
41
Which assumption of kinetic theory explains the validity of Boyle’s law?
(Exam: JEE – Advanced)
42
For a diatomic gas at high temperature, the value of \(\gamma\) approaches
(Exam: JEE – Advanced)
43
The total kinetic energy of one mole of an ideal gas at temperature \(T\) is
(Exam: JEE – Advanced)
44
The most probable speed of gas molecules depends on
(Exam: JEE – Advanced)
45
The kinetic theory successfully explains all except
(Exam: JEE – Advanced)
46
For an ideal gas undergoing free expansion, the temperature
(Exam: JEE – Advanced)
47
Which of the following graphs best represents ideal gas behaviour?
(Exam: JEE – Advanced)
48
The Maxwell–Boltzmann distribution shows that
(Exam: JEE – Advanced)
49
The ratio of rms speeds of helium and hydrogen gases at the same temperature is
(Exam: JEE – Advanced)
50
The kinetic theory of gases is most accurate when the gas is
(Exam: JEE – Advanced)
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Frequently Asked Questions

It is a theory that explains the macroscopic properties of gases (pressure, temperature, volume) in terms of the microscopic motion of gas molecules.

Gas consists of a large number of molecules in random motion; intermolecular forces are negligible except during collisions; collisions are elastic; molecular size is negligible compared to separation.

An ideal gas is a hypothetical gas that obeys the equation \(PV = nRT\) exactly at all pressures and temperatures.

Because real gases have finite molecular size and intermolecular forces, which cause deviations at high pressure and low temperature.

\(PV = nRT\), where \(P\) is pressure, \(V\) volume, \(n)\ number of moles, \(R)\ gas constant, and \(T\) absolute temperature.

\(R = 8.314, \text{J mol}^{-1}\text{K}^{-1}\).

It is the constant that relates temperature to energy at the molecular level: \(k_B = 1.38 \times 10^{-23},\text{J K}^{-1}\).

Pressure arises due to momentum transfer when gas molecules collide elastically with the walls of the container.

\(P = \frac{1}{3}\frac{Nm}{V}\overline{c^2}\).

Temperature is a measure of the average translational kinetic energy of gas molecules.

\(\overline{E_k} = \frac{3}{2}k_B T\).

No, it depends only on temperature.

It is defined as \(c_{\text{rms}} = \sqrt{\overline{c^2}} = \sqrt{\frac{3RT}{M}}\).

It is the speed possessed by the maximum number of molecules at a given temperature.

It is the average speed of all molecules in a gas.

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