Kinetic Theory — Class 11 MCQs with Answers

Kinetic Theory — important questions & MCQs with answers (Class 11 Physics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   Ideal gas equation:

   APV = nRTBPV = TCP = nRTDPV² = nRT
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   Answer: PV = nRT

   Explanation: The ideal gas law PV = nRT links pressure, volume, moles and temperature via R = 8.314 J/(mol·K). Dropping n (P = RT) or T (PV = T), or squaring V, breaks the proportionality this law defines.

2. Q2 of 6Easy

   Ideal gas assumes molecules:

   AHave sizeBPoint particles with no interaction except elastic collisionsCHave viscosityDStick together
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   Answer: Point particles with no interaction except elastic collisions

   Explanation: The ideal gas model treats molecules as point particles with negligible size that interact only through instantaneous elastic collisions. Giving them finite size or viscosity describes real gases, which the ideal model ignores.

3. Q3 of 6Medium

   v_rms of nitrogen (M = 28 g/mol) at 300 K:

   A≈ 16 m/sB≈ 300 m/sC≈ 1000 m/sD≈ 517 m/s
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   Answer: ≈ 517 m/s

   Explanation: v_rms = √(3RT/M) = √(3 × 8.314 × 300 / 0.028 kg/mol) ≈ 517 m/s for nitrogen at 300 K. Forgetting to convert M from 28 g/mol to 0.028 kg/mol gives only about 16 m/s.

4. Q4 of 6Medium

   For diatomic gas at very high T, additional degree of freedom is:

   ACannot sayBTranslationalCRotationalDVibrational
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   Answer: Vibrational

   Explanation: At very high temperature, the bond of a diatomic molecule starts to vibrate, adding 2 extra degrees of freedom — one kinetic and one potential — on top of the usual 3 translational and 2 rotational modes. Calling this purely rotational misses the potential-energy term.

5. Q5 of 6Hard

   Internal energy of 1 mole of CO₂ (a linear molecule, treated as rigid) at temperature T:

   A(5/2)RTB(3/2)RTC(7/2)RTDVariable
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   Answer: (5/2)RT

   Explanation: CO₂ is a linear molecule, so it has 5 degrees of freedom (3 translational + 2 rotational, with no third rotation axis along the bond line), giving internal energy U = (5/2)RT per mole. Using (7/2)RT would add vibrational modes not counted at moderate temperature.

6. Q6 of 6Hard

   For mixture of gases, effective C_v:

   AAverageBSumCWeighted average by molesDCannot compute
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   Answer: Weighted average by moles

   Explanation: For a mixture, total internal energy is additive across components, so the effective C_v is the mole-weighted average of each gas's own C_v, not a simple unweighted average or sum. Treating it as a plain sum overcounts the mixture's total heat capacity.

Kinetic Theory notes: key concepts (Class 11 Physics)

Explaining gas behaviour from molecular motion: the assumptions of the kinetic model, the ideal gas equation and the gas laws it contains, pressure derived from molecular collisions, the three characteristic molecular speeds, temperature as kinetic energy, the equipartition theorem, molar specific heats, and the mean free path.

Assumptions of kinetic theory

Molecules are point masses in constant random motion, collisions are perfectly elastic, intermolecular forces are negligible, and molecular volume is tiny compared with the container.

Ideal gas equation

PV = nRT, the single relation combining all the gas laws. A real gas approaches this behaviour at low pressure and high temperature.

Boyle's law

At constant temperature the pressure of a fixed mass of gas varies inversely with its volume, so the product PV stays constant.

Charles's law

At constant pressure the volume of a fixed mass of gas is directly proportional to its ABSOLUTE temperature, which is why kelvin must be used.

Gay-Lussac's law

At constant volume the pressure of a fixed mass of gas is directly proportional to absolute temperature — the principle behind the constant-volume gas thermometer.

Avogadro's law

Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules, 6.02 × 10²³ per mole.

Kinetic interpretation of pressure

Pressure arises from the momentum transferred by molecules bouncing off the walls, giving P = ⅓ρv_rms² directly from mechanics.

Root mean square speed

The square root of the mean of the squared molecular speeds. It rises as the square root of temperature and falls as the square root of molar mass.

Mean and most probable speed

The average and the peak of the Maxwell speed distribution. The three speeds always stand in the fixed order v_mp < v̄ < v_rms.

Kinetic interpretation of temperature

The average translational kinetic energy per molecule is (3/2)kT, depending ONLY on temperature and not at all on the gas chosen.

Degrees of freedom

The number of independent ways a molecule can store energy: 3 for a monatomic gas, 5 for a rigid diatomic, and 6 for a non-linear triatomic.

Law of equipartition

In thermal equilibrium each degree of freedom carries an average energy of ½kT per molecule, which is what fixes the specific heats.

Internal energy of an ideal gas

Depends only on temperature and the number of degrees of freedom, with no contribution from intermolecular potential energy.

Molar specific heats

C_v is (f/2)R and C_p exceeds it by exactly R, because at constant pressure some heat is spent doing expansion work.

Mean free path

The average distance a molecule travels between successive collisions. It increases at lower pressure and decreases as molecules get larger.