NCERT · CLASS XI PHYSICS · CHAPTER 12

Kinetic Theory
of Gases

Molecules in motion — from microscopic chaos to macroscopic laws

IIT-JEE JEE Main NEET AIIMS BITSAT KVPY
Start the 50 MCQs →
AT A GLANCE

MCQ Snapshot

⚛ 50 Total Questions
🏆 6+ Exams Covered
📅 1995–2021 Years Spanned
🎯 Medium Avg Difficulty
✅ 100% Topic Coverage
📐 ~60% Formula-based Qs
EXAM RELEVANCE

Why These MCQs Matter

Kinetic Theory is a high-yield chapter — understand why mastering it pays dividends across every entrance exam.

JEE MAIN / JEE ADVANCED

MARKS WITH MINIMAL DERIVATION

Kinetic Theory contributes 1–2 questions per paper in JEE Main and often appears as a paragraph-based problem in Advanced. Questions test v_rms proportionality, equipartition, and γ — all solvable in under 60 seconds once concepts are internalised.

NEET / AIIMS

CONCEPTUAL OVER COMPUTATIONAL

NEET consistently tests the Maxwell–Boltzmann curve shape, degrees of freedom classification, and the physical meaning of pressure. These are one-liner concept questions — maximum marks, minimum time.

CLASS XI BOARDS

DIRECT FORMULA APPLICATION

Board examinations reward students who can state and apply the law of equipartition, express internal energy in terms of f, and relate Cᵥ to degrees of freedom. This chapter is 5–6 marks guaranteed in CBSE theory papers.

KVPY / OLYMPIAD

DEEPER REASONING TESTED

KVPY questions probe why equipartition fails at low T, why CO₂ deviates most from ideal behaviour, and how collision frequency relates to λ. These MCQs train exactly that level of analytical depth.

CONCEPTUAL MAP

Key Concepts Covered

Every question in this set maps to one or more of the following foundational ideas.

💨

Kinetic Pressure

P = ⅓ρ⟨v²⟩ — pressure from molecular momentum transfer

⚡

rms / avg / vₚ Speeds

v_rms > v_avg > v_p — the fundamental speed hierarchy

📈

Maxwell–Boltzmann

Right-skewed speed distribution; peak shifts with temperature

⚖️

Equipartition Law

Each degree of freedom carries ½kT of energy

🔬

Degrees of Freedom

Mono: 3 · Diatomic (room T): 5 · Diatomic (high T): 7

🛤️

Mean Free Path

λ = kT/(√2 πd²P) — inversely ∝ pressure and d²

🔋

Internal Energy

U = (f/2)nRT — depends only on temperature for ideal gas

🌡️

γ = Cₚ/Cᵥ

Mono: 5/3 · Diatomic: 7/5 · determines adiabatic behaviour

QUICK REFERENCE

Important Formulae

All formulae tested across these 50 questions, consolidated for rapid revision.

QUANTITY FORMULA KEY NOTE
rms Speed v_rms = √(3RT/M) ∝ √T, ∝ 1/√M
Average Speed v_avg = √(8RT/πM) ≈ 0.921 v_rms
Most Probable Speed v_p = √(2RT/M) Peak of M-B curve
Pressure (KTG) P = ⅓ρ⟨v²⟩ = nkT Microscopic origin of P
Avg KE/molecule KE = (3/2)kT Translation only
Internal Energy U = (f/2)nRT f = DoF
Molar Cv Cᵥ = (f/2)R Mono: 3R/2, Di: 5R/2
γ ratio γ = 1 + 2/f Mono:1.67, Di:1.4
Mean Free Path λ = 1/(√2 πd²n) n = number density
Speed Ratio v_rms : v_avg : v_p = √3 : √(8/π) : √2 ≈ 1.73 : 1.60 : 1.41
LEARNING OUTCOMES

What You Will Learn

By the end of this MCQ set, you will be able to:

PREPARATION GUIDE

Exam Strategy & Tips

Targeted strategies derived from analysing 25+ years of actual exam patterns in this chapter.

HIGH PRIORITY

Master the Speed Hierarchy First

v_rms > v_avg > v_p is asked in multiple forms every year. Memorise the exact ratios (√3 : √8/π : √2) — they resolve comparison questions in under 10 seconds.

CONCEPT PILLAR

Degrees of Freedom = Gateway to Everything

Every Cᵥ, Cₚ, γ, and internal energy question reduces to knowing f. Practice identifying f for mono (3), diatomic-room-T (5), diatomic-high-T (7) instantly.

JEE SPECIFIC

Formula Derivation > Rote Learning

Derive P = ⅓ρv² from scratch at least twice. IIT-JEE frequently tests the "factor 1/3" origin — understanding beats memorisation.

NEET / AIIMS

Maxwell–Boltzmann: Qualitative over Quantitative

NEET and AIIMS focus on curve shape, shift direction, and peak interpretation. You rarely need calculations — recognise the right-skew, and know what happens when T increases.

TIME SAVER

Proportionality Chains Save Time

Build a quick chain: v_rms ∝ √T ∝ 1/√M. When "temperature tripled" or "mass ratio 1:4" appears, apply the chain without writing full equations.

COMMON TRAP

Mean Free Path: Two-Variable Trap

λ = kT/(√2 πd²P). At constant T, λ ∝ 1/P. At constant P, λ ∝ T. JEE Main routinely tests both — identify which variable is held constant before solving.

Ready to Test Your Understanding?

50 questions · Instant feedback · Full explanations

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⏱ 00:00
Q1
The rms speed of oxygen molecules at temperature \(T\) is \(v_{\text{rms}}\). If the temperature is doubled, the new rms speed becomes
(Exam: IIT-JEE Year: 1998)
(A) \(v_{\text{rms}}\)
(B) \(\sqrt{2}\,v_{\text{rms}}\)
(C) \(2\,v_{\text{rms}}\)
(D) \(v_{\text{rms}}/2\)
Q2
At constant temperature, which quantity remains the same for all gases?
(Exam: NEET Year: 2016)
(A) Average speed
(B) rms speed
(C) Mean kinetic energy per molecule
(D) Most probable speed
Q3
The dimensional formula of pressure as obtained from kinetic theory is
(Exam: AIIMS Year: 2012)
(A) \(ML^{-1}T^{-2}\)
(B) \(MLT^{-2}\)
(C) \(M^{0}L^{-1}T^{-2}\)
(D) \(ML^{-2}T^{-1}\)
Q4
The average translational kinetic energy of a molecule of an ideal gas is
(Exam: BITSAT Year: 2010)
(A) \(\frac{1}{2}kT\)
(B) \(kT\)
(C) \(\frac{3}{2}kT\)
(D) \(3kT\)
Q5
The ratio of rms speed to average speed for an ideal gas is approximately
(Exam: IIT-JEE Year: 2001)
(A) 0.92
(B) 1.00
(C) 1.08
(D) 1.22
Q6
Two gases A and B have molecular masses in the ratio \(1:4\). At the same temperature, the ratio of their rms speeds is
(Exam: JEE Main Year: 2014)
(A) \(1:4\)
(B) \(1:2\)
(C) \(2:1\)
(D) \(4:1\)
Q7
Pressure of an ideal gas is due to
(Exam: NEET Year: 2018)
(A) Attractive forces between molecules
(B) Repulsive forces between molecules
(C) Collisions of molecules with container walls
(D) Weight of molecules
Q8
The most probable speed of gas molecules at temperature \(T\) is proportional to
(Exam: KVPY Year: 2011)
(A) \(T\)
(B) \(T^{2}\)
(C) \(\sqrt{T}\)
(D) \(1/T\)
Q9
The Maxwell–Boltzmann distribution shows that at a given temperature
(Exam: IIT-JEE Year: 2005)
(A) All molecules have same speed
(B) No molecule is at rest
(C) Speeds are distributed over a wide range
(D) Most molecules have rms speed
Q10
If the pressure of a gas is doubled while keeping rms speed constant, its density becomes
(Exam: JEE Main Year: 2019)
(A) Half
(B) Same
(C) Double
(D) Four times
Q11
The rms speed of hydrogen molecules at \(0^\circ\text{C}\) is maximum because
(Exam: NEET Year: 2015)
(A) Hydrogen is diatomic
(B) Hydrogen has smallest molecular mass
(C) Hydrogen is reactive
(D) Hydrogen is light gas
Q12
The correct order of speeds for a gas is
(Exam: AIIMS Year: 2014)
(A) \(v_{mp}>v_{avg}>v_{rms}\)
(B) \(v_{avg}>v_{mp}>v_{rms}\)
(C) \(v_{rms}>v_{avg}>v_{mp}\)
(D) All equal
Q13
Mean free path of gas molecules is independent of
(Exam: IIT-JEE Year: 1996)
(A) Pressure
(B) Temperature
(C) Molecular diameter
(D) Nature of gas
Q14
For an ideal gas, internal energy depends only on
(Exam: JEE Main Year: 2013)
(A) Pressure
(B) Volume
(C) Temperature
(D) Pressure and volume
Q15
Equipartition theorem fails at low temperature because
(Exam: KVPY Year: 2014)
(A) Collisions stop
(B) Quantum effects dominate
(C) Gas becomes non-ideal
(D) Molecules lose energy
Q16
Degrees of freedom of a monoatomic gas are
(Exam: NEET Year: 2017)
(A) 1
(B) 2
(C) 3
(D) 6
Q17
The value of \(\gamma=C_p/C_v\) for a monoatomic gas is
(Exam: IIT-JEE Year: 2003)
(A) \(5/3\)
(B) \(7/5\)
(C) \(4/3\)
(D) \(3/2\)
Q18
At absolute zero temperature, the kinetic energy of gas molecules ideally is
(Exam: NEET Year: 2020)
(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite
Q19
If temperature is measured in kelvin, average kinetic energy is proportional to
(Exam: BITSAT Year: 2012)
(A) \(T^2\)
(B) \(1/T\)
(C) \(T\)
(D) \(\sqrt{T}\)
Q20
The factor \(1/3\) in kinetic theory expression of pressure arises due to
(Exam: IIT-JEE Year: 1999)
(A) Elastic collisions
(B) Random motion in three dimensions
(C) Shape of container
(D) Molecular size
Q21
For a diatomic gas at room temperature, the value of degrees of freedom is
(Exam: IIT-JEE Year: 2004)
(A) 3
(B) 4
(C) 5
(D) 6
Q22
The internal energy of one mole of a diatomic ideal gas at temperature \(T\) is
(Exam: NEET Year: 2019)
(A) \(\frac{3}{2}RT\)
(B) \(\frac{5}{2}RT\)
(C) \(3RT\)
(D) \(\frac{7}{2}RT\)
Q23
The value of \(\gamma\) for a diatomic gas at room temperature is
(Exam: JEE Main Year: 2016)
(A) \(5/3\)
(B) \(7/5\)
(C) \(4/3\)
(D) \(3/2\)
Q24
Mean free path of gas molecules increases when
(Exam: AIIMS Year: 2010)
(A) Pressure increases
(B) Temperature decreases
(C) Molecular diameter increases
(D) Pressure decreases
Q25
Which graph best represents Maxwell–Boltzmann speed distribution?
(Exam: IIT-JEE Year: 2006)
(A) Straight line
(B) Rectangular curve
(C) Bell-shaped asymmetric curve
(D) Symmetric parabola
Q26
As temperature increases, the Maxwell distribution curve
(Exam: NEET Year: 2014)
(A) Becomes taller and narrower
(B) Shifts left and becomes narrower
(C) Shifts right and becomes broader
(D) Remains unchanged
Q27
The rms speed of gas molecules is independent of
(Exam: JEE Main Year: 2017)
(A) Temperature
(B) Molecular mass
(C) Nature of gas
(D) Pressure
Q28
At constant temperature, which gas has the highest rms speed?
(Exam: BITSAT Year: 2011)
(A) \(\mathrm{O_2}\)
(B) \(\mathrm{N_2}\)
(C) \(\mathrm{CO_2}\)
(D) \(\mathrm{H_2}\)
Q29
The pressure exerted by an ideal gas is proportional to
(Exam: IIT-JEE Year: 1997)
(A) Mean speed
(B) Square of mean speed
(C) Cube of mean speed
(D) Inverse of speed
Q30
The translational kinetic energy per mole of an ideal gas is
(Exam: NEET Year: 2013)
(A) \(\frac{1}{2}RT\)
(B) \(RT\)
(C) \(\frac{3}{2}RT\)
(D) \(3RT\)
Q31
Which of the following statements is correct?
(Exam: IIT-JEE Year: 2000)
(A) All molecules have equal speed at a given temperature
(B) Average speed equals rms speed
(C) rms speed is greater than average speed
(D) Most probable speed is maximum
Q32
The number of molecules striking unit area of the wall per second is proportional to
(Exam: AIIMS Year: 2013)
(A) Density
(B) Mean speed
(C) Density and mean speed
(D) Pressure only
Q33
When a gas is heated at constant volume, the pressure increases because
(Exam: NEET Year: 2021)
(A) Molecular mass increases
(B) Collision frequency increases
(C) Volume decreases
(D) Number of molecules increases
Q34
The equipartition theorem assigns energy \(\frac{1}{2}kT\) to
(Exam: JEE Main Year: 2015)
(A) Each molecule
(B) Each degree of freedom
(C) Each collision
(D) Each mole
Q35
Which gas shows maximum deviation from ideal behaviour at high pressure?
(Exam: IIT-JEE Year: 1995)
(A) \(\mathrm{H_2}\)
(B) \(\mathrm{He}\)
(C) \(\mathrm{NH_3}\)
(D) \(\mathrm{O_2}\)
Q36
The most probable speed of gas molecules corresponds to
(Exam: KVPY Year: 2012)
(A) Maximum area under curve
(B) Peak of Maxwell distribution
(C) Mean of speeds
(D) rms speed
Q37
The kinetic theory assumes that gas molecules
(Exam: NEET Year: 2012)
(A) Have finite volume
(B) Attract each other strongly
(C) Are point masses in random motion
(D) Are at rest
Q38
The ratio of specific heats depends on
(Exam: IIT-JEE Year: 2002)
(A) Pressure
(B) Temperature
(C) Degrees of freedom
(D) Volume
Q39
The mean free path becomes half if pressure is
(Exam: JEE Main Year: 2018)
(A) Doubled
(B) Halved
(C) Quadrupled
(D) Unchanged
Q40
For a monoatomic gas, molar heat capacity at constant volume is
(Exam: NEET Year: 2011)
(A) \(R\)
(B) \(\frac{3}{2}R\)
(C) \(\frac{5}{2}R\)
(D) \(3R\)
Q41
If the temperature of a gas is tripled, rms speed becomes
(Exam: IIT-JEE Year: 1998)
(A) Three times
(B) \(\sqrt{3}\) times
(C) \(1/3\) times
(D) Nine times
Q42
The pressure exerted by a gas on container walls is due to change in
(Exam: NEET Year: 2017)
(A) Energy
(B) Speed
(C) Momentum
(D) Direction only
Q43
The internal energy of an ideal gas during isothermal expansion
(Exam: JEE Main Year: 2020)
(A) Increases
(B) Decreases
(C) Remains constant
(D) Becomes zero
Q44
Maxwell distribution predicts that the number of molecules with zero speed is
(Exam: IIT-JEE Year: 2007)
(A) Maximum
(B) Minimum
(C) Finite
(D) Zero
Q45
The factor determining collision frequency in gases is
(Exam: AIIMS Year: 2011)
(A) Only molecular size
(B) Only speed
(C) Number density and speed
(D) Pressure only
Q46
For a given gas, which quantity changes with temperature?
(Exam: NEET Year: 2016)
(A) Molecular mass
(B) rms speed
(C) Gas constant
(D) Number of molecules per mole
Q47
At high temperatures, diatomic gases show additional degrees of freedom due to
(Exam: IIT-JEE Year: 2008)
(A) Translation
(B) Rotation
(C) Vibration
(D) Collision
Q48
The correct relation between mean free path \(\lambda\) and molecular diameter \(d\) is
(Exam: JEE Main Year: 2014)
(A) \(\lambda\propto d\)
(B) \(\lambda\propto d^2\)
(C) \(\lambda\propto 1/d\)
(D) \(\lambda\propto 1/d^2\)
Q49
Which quantity has the same value for all ideal gases at the same temperature?
(Exam: NEET Year: 2018)
(A) rms speed
(B) Average speed
(C) Mean kinetic energy per molecule
(D) Density
Q50
The kinetic theory of gases successfully explains
(Exam: Olympiad Year: Standard)
(A) Brownian motion
(B) Gas pressure
(C) Gas diffusion
(D) All of these

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