Physics · Kinetic theory of gases · chapter 12 of 14

Class 11 Physics Chapter 12: Kinetic Theory MCQs with answers

10 multiple-choice questions on Kinetic Theory, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern, JEE Main and NEET, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
A sample of a real gas follows PV = μRT most closely when it is kept at
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Answer: (b) low pressure and high temperature

Real gases approach ideal behaviour at low pressures and high temperatures, where the molecules are far apart and their interactions negligible. High pressure or low temperature brings them close enough for intermolecular forces to matter.

Question 2
The average kinetic energy of a molecule of an ideal gas depends on
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Answer: (a) the absolute temperature of the gas only

½m v̄² = (3/2)kBT: it is proportional to the absolute temperature and independent of pressure, volume or the nature of the ideal gas.

Question 3
In a vessel at a fixed temperature, the rms speed of hydrogen molecules (molar mass 2 g mol⁻¹) is four times the rms speed of the molecules of a gas X in the same vessel. The molar mass of X is
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Answer: (c) 32 g mol⁻¹

vrms = √(3kBT/m), so at the same T, vrms ∝ 1/√M. vH/vX = √(MX/2) = 4 gives MX = 2 × 16 = 32 g mol⁻¹. Taking v ∝ 1/M gives 8, a slip.

Question 4
A diatomic molecule treated as a rigid rotator has a total number of degrees of freedom equal to
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Answer: (d) 5

Three translational degrees of freedom and two rotational ones (about the two axes normal to the line joining the atoms): 3 + 2 = 5. 7 would include a vibrational mode, which a rigid rotator does not have.

Question 5
For a monatomic ideal gas, the ratio γ = Cp/Cv is
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Answer: (a) 53

Cv = (3/2)R and Cp = Cv + R = (5/2)R, so γ = 5/3. 7/5 is the rigid diatomic value.

Question 6
By the law of equipartition of energy, the molar specific heat of a solid at ordinary temperatures is close to (R = 8.31 J mol⁻¹ K⁻¹)
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Answer: (c) 24.9 J mol⁻¹ K⁻¹

Each atom oscillates in three dimensions with average energy 3kBT, so U = 3RT per mole and, since ΔV is negligible for a solid, C = 3R = 24.9 J mol⁻¹ K⁻¹. 12.5 is (3/2)R, the monatomic gas value.

Question 7
The pressure of a gas is doubled while its temperature is kept constant. The mean free path of its molecules
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Answer: (d) becomes half

l = kBT/(√2 πd²P). At constant T, l ∝ 1/P, so doubling P halves l: the number density doubles and a molecule meets others twice as often.

Question 8
A vacuum chamber at 300 K holds 2.5 × 10¹⁶ gas molecules per cubic metre. The pressure in the chamber is about (kB = 1.38 × 10⁻²³ J K⁻¹)
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Answer: (b) 1.0 × 10⁻⁴ Pa

P = nkBT = 2.5 × 10¹⁶ × 1.38 × 10⁻²³ × 300 = 1.04 × 10⁻⁴ Pa. Leaving out T gives 3.5 × 10⁻⁷; using R for kB gives 6.2 × 10¹⁹; using 27 for T gives 9.3 × 10⁻⁶.

Question 9
The absolute temperature of an ideal gas is doubled. Its rms speed becomes
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Answer: (b) √2 times

vrms = √(3kBT/m) ∝ √T, so doubling T multiplies vrms by √2. 2 times would need vrms ∝ T; that is how the average kinetic energy changes.

Question 10
Four molecules in a model gas have speeds 1, 2, 3 and 4 m s⁻¹. Their rms speed is
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Answer: (b) 2.74 m s⁻¹

<v²> = (1 + 4 + 9 + 16)/4 = 7.5 m² s⁻², so vrms = √7.5 = 2.74 m s⁻¹. 2.50 is the mean speed: <v²> is not (<v>)². 7.50 is <v²> without the square root.

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