JEE (Advanced) · Physics, Class 11
Behaviour of Perfect Gas and Kinetic Theory: JEE Advanced PYQ, 2007–2026
Behaviour of Perfect Gas and Kinetic Theory (Physics, Class 11) has been asked 12 times in the 40 JEE (Advanced) papers from 2007–2026: about 0.3 questions a paper, 2% of all Physics questions. It is the 18th most-asked of 19 Physics chapters. The two 2026 papers had 0 from it. Last checked 28 October 2026.
Questions per year, both papers
Year by year.
| Year | Questions |
|---|---|
| 2007 | 1in 2 papers |
| 2008 | 1in 2 papers |
| 2009 | 1in 2 papers |
| 2010 | 1in 2 papers |
| 2011 | 0in 2 papers |
| 2012 | 1in 2 papers |
| 2013 | 1in 2 papers |
| 2014 | 0in 2 papers |
| 2015 | 1in 2 papers |
| 2016 | 0in 2 papers |
| 2017 | 1in 2 papers |
| 2018 | 0in 2 papers |
| 2019 | 0in 2 papers |
| 2020 | 2in 2 papers |
| 2021 | 0in 2 papers |
| 2022 | 0in 2 papers |
| 2023 | 1in 2 papers |
| 2024 | 0in 2 papers |
| 2025 | 1in 2 papers |
| 2026 | 0in 2 papers |
Each year has two papers, and the number of questions has fallen over time, so compare per paper and expect some drift.
Inside the chapter
Topics asked most.
- Ideal gas equation5
- Kinetic theory4
- Degrees of freedom3
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10 Behaviour of Perfect Gas and Kinetic Theory questions to practise.
Our own questions, written in the JEE Advanced pattern and checked, each with an explanation. Pick an option to see the answer.
Q1 · Physics · Behaviour of Perfect Gas and Kinetic Theory
A vessel holds a mixture of hydrogen (M = 2 g/mol) and oxygen (M = 32 g/mol) in thermal equilibrium. What is the ratio of the average translational kinetic energy of a hydrogen molecule to that of an oxygen molecule?
Answer: (D)
Each molecule has (3/2)kT of translational kinetic energy on average, whatever its mass. At the same temperature the ratio is 1 : 1; the lighter hydrogen molecules simply move faster, by a factor of 4 in rms speed.
Q2 · Physics · Behaviour of Perfect Gas and Kinetic Theory
An open flask, in contact with the atmosphere at constant pressure, is heated slowly from 300 K to 400 K. Treating the air as an ideal gas, what fraction of the air originally in the flask escapes?
Answer: (A)
The flask is open, so pressure P and volume V stay fixed while the number of moles changes. From PV = nRT, n = PV/(RT), so n ∝ 1/T. Then n₂/n₁ = T₁/T₂ = 300/400 = 3/4. The fraction that escapes is 1 − 3/4 = 1/4.
Q3 · Physics · Behaviour of Perfect Gas and Kinetic Theory
An air bubble is released at the bottom of a lake 30 m deep, where the water temperature is 280 K. As it rises slowly, it reaches the surface, where the temperature is 300 K. Treat the air as an ideal gas and the bubble as a sphere that stays in thermal equilibrium with the water. Take atmospheric pressure = 1.0 × 10⁵ Pa, density of water = 1000 kg m⁻³ and g = 10 m s⁻². What is the ratio of the bubble's radius at the surface to its radius at the bottom?
Answer: (A)
For a fixed amount of gas, PV/T is constant. The pressure at the bottom is P₁ = P₀ + ρgh = 1 × 10⁵ + 1000 × 10 × 30 = 4 × 10⁵ Pa. At the surface it is P₂ = 1 × 10⁵ Pa. Then V₂/V₁ = (P₁/P₂)(T₂/T₁) = 4 × (300/280) = 30/7 ≈ 4.29. Since V ∝ r³, r₂/r₁ = (30/7)^(1/3) ≈ 1.62. Pressure raises the volume by 4, the temperature adds only a small further increase, and the final step is the cube root.
Q4 · Physics · Behaviour of Perfect Gas and Kinetic Theory
Gas A and gas B have molecules of the same effective diameter. Each molecule of B is four times as massive as a molecule of A. Both gases are at the same temperature and pressure. The ratio of the mean free path of A to that of B is:
Answer: (A)
From p = nk_BT, equal p and T mean equal number density n for both gases. The mean free path λ = 1/(√2 π d² n) depends only on n and d. Both are equal here, so λ_A/λ_B = 1. Mass affects the average speed, and therefore the collision frequency (ν = v̄/λ), but not λ itself.
Q5 · Physics · Behaviour of Perfect Gas and Kinetic Theory
A gas mixture of helium (molar mass 4.00 g mol⁻¹) and oxygen (molar mass 32.0 g mol⁻¹) behaves ideally. At a total pressure of 1.00 atm and a temperature of 300 K, its density is 0.325 g L⁻¹. Taking R = 0.0821 L atm mol⁻¹ K⁻¹, what is the partial pressure of oxygen in the mixture?
Answer: (A)
Write PV = nRT as PM = ρRT, where M is the average molar mass. Then M = ρRT/P = 0.325 × 0.0821 × 300 / 1.00 ≈ 8.0 g mol⁻¹. For mole fraction x of oxygen, M = 32x + 4(1 − x) = 4 + 28x, so 28x = 4 and x = 1/7. By Dalton's law, the partial pressure of oxygen is x × P_total = (1/7)(1.00 atm) ≈ 0.14 atm.
Q6 · Physics · Behaviour of Perfect Gas and Kinetic Theory
An ideal gas of rigid diatomic molecules has a density of 1.2 kg/m³, and the rms speed of its molecules is 500 m/s. What is the internal energy of the gas per unit volume?
Answer: (C)
P = ρv²/3 = 1.2 × (500)²/3 = 1.0 × 10⁵ Pa. The energy of translation per unit volume is ½ρv² = (3/2)P, half of P for each of three degrees of freedom. A rigid diatomic molecule has five, so U/V = (5/2)P = 2.5 × 10⁵ J/m³.
Q7 · Physics · Behaviour of Perfect Gas and Kinetic Theory
A fixed mass of an ideal gas undergoes a quasi-static process in which its pressure is directly proportional to its volume (p ∝ V). During the process its volume increases to four times its initial value. Assuming the molecular diameter stays constant, what is the ratio (final/initial) of the number of collisions a molecule makes per second?
Answer: (C)
The collision frequency is z = v_avg/λ, with v_avg ∝ √T and λ = 1/(√2 π d² n) ∝ V for a fixed mass of gas. Since p ∝ V, the ideal gas law gives T ∝ pV ∝ V². When V becomes 4V, T becomes 16T, so v_avg ∝ √T becomes 4 times larger. Meanwhile n falls to one quarter, so λ becomes 4 times larger. Hence z_final/z_initial = 4/4 = 1. Equivalently, z ∝ n·v ∝ (1/V)(V) = constant.
Q8 · Physics · Behaviour of Perfect Gas and Kinetic Theory
Vessel A of volume 2 L contains an ideal gas at 3 atm. Vessel B of volume 3 L contains the same gas at 2 atm. Both are at the same temperature, which stays constant. They are connected by a tube of negligible volume and the gas is allowed to equalise. What is the final pressure?
Answer: (A)
At constant temperature, PV = nRT shows that n is proportional to PV. The total number of moles is unchanged, so P_final(V_A + V_B) = P_A V_A + P_B V_B. Substituting, P_final × 5 = 3×2 + 2×3 = 12, giving P_final = 2.4 atm.
Q9 · Physics · Behaviour of Perfect Gas and Kinetic Theory
A rigid, thermally insulated vessel contains an ideal gas mixture of 2 mol of helium (monatomic) and 1 mol of a diatomic gas whose molecules are rigid, so vibrational modes are not excited. Using the law of equipartition of energy, what is the ratio C_p/C_v of the mixture?
Answer: (A)
Heat capacities of non-reacting ideal gases in a mixture add. For a fixed volume, total C_v = n₁(3/2)R + n₂(5/2)R = 2×(3/2)R + 1×(5/2)R = 5.5R for 3 mol. Per mole, C_v = (11/6)R. Since C_p − C_v = R for an ideal gas, C_p = (17/6)R. Therefore γ = C_p/C_v = 17/11 ≈ 1.55. Do not average the γ values of the components, because γ is a ratio and does not add linearly.
Q10 · Physics · Behaviour of Perfect Gas and Kinetic Theory
By the law of equipartition, the atoms of a monatomic solid vibrate about their lattice sites like three-dimensional harmonic oscillators. Each atom has kinetic and potential energy for each of 3 directions. Take R = 8.3 J mol⁻¹ K⁻¹. How much heat is needed to raise the temperature of 0.5 mol of such a solid by 20 K?
Answer: (C)
Each atom in the solid oscillates in 3 directions. Each direction has one kinetic and one potential quadratic term, so there are 6 terms per atom. The energy per atom is 6 × ½k_BT = 3k_BT, and the energy per mole is U = 3RT. So the molar heat capacity is C = 3R. Then Q = nCΔT = 0.5 × 3 × 8.3 × 20 = 249 J.
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All 12 real JEE Advanced questions from Behaviour of Perfect Gas and Kinetic Theory.
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About Behaviour of Perfect Gas and Kinetic Theory in JEE Advanced.
How many questions come from Behaviour of Perfect Gas and Kinetic Theory in JEE Advanced?
Behaviour of Perfect Gas and Kinetic Theory (Physics, Class 11) has been asked 12 times in the 40 JEE (Advanced) papers from 2007–2026: about 0.3 questions a paper, 2% of all Physics questions. It is the 18th most-asked of 19 Physics chapters. The two 2026 papers had 0 from it.
Which topics of Behaviour of Perfect Gas and Kinetic Theory are asked most in JEE Advanced?
Ideal gas equation (5), Kinetic theory (4), Degrees of freedom (3), counted over the papers from 2007–2026.
Is Behaviour of Perfect Gas and Kinetic Theory important for JEE Advanced 2027?
It is in the syllabus in force, so it can be asked. By past papers it ranks 18 of 19 in Physics; use that to decide how much time it gets, not whether to study it.
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