Chapter 12: Kinetic Theory Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 1

Logic Check

Assertion (A): The average kinetic energy per molecule is the same for all ideal gases at the same temperature. Reason (R): Average kinetic energy per molecule equals (3/2)kBT, which depends only on absolute temperature T.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 2

Logic Check

Assertion (A): At the same temperature, lighter gas molecules have higher rms speed than heavier molecules. Reason (R): The rms speed vrms = √(3kBT/m) is inversely proportional to the square root of the molecular mass.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 3

Logic Check

Assertion (A): The internal energy of an ideal gas depends only on its temperature. Reason (R): In an ideal gas, intermolecular forces are negligible, so there is no potential energy contribution; all internal energy is translational kinetic energy.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 4

Logic Check

Assertion (A): Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules. Reason (R): From PV = NkBT, if P, V, and T are the same for two gases, N must be the same for both.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 5

Logic Check

Assertion (A): The pressure of a gas increases when the gas is compressed isothermally. Reason (R): At constant temperature, reducing volume increases the frequency of molecular collisions with the walls per unit area per unit time.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 6

Logic Check

Assertion (A): A diatomic gas has a higher molar specific heat at constant volume than a monatomic gas. Reason (R): A diatomic molecule has more degrees of freedom (5) than a monatomic molecule (3), so it stores more energy per degree of temperature rise.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 7

Logic Check

Assertion (A): Cp − Cv = R for all ideal gases, regardless of their atomicity. Reason (R): At constant pressure, extra heat R dT per mole must be supplied to do work against external pressure during expansion, in addition to raising the internal energy.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 8

Logic Check

Assertion (A): Gas molecules travel at speeds of the order of hundreds of metres per second, yet a gas takes minutes to diffuse across a room. Reason (R): The mean free path of gas molecules is very small (∼10⁻⁷ m at STP), causing frequent collisions that deflect molecules in random directions and make net displacement far slower than molecular speed.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 9

Logic Check

Assertion (A): The mean free path of gas molecules increases when the gas is heated at constant pressure. Reason (R): At constant pressure, increasing temperature decreases the number density n (from P = nkBT), and since l = 1/(√2 π n d²), l increases as n decreases.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 10

Logic Check

Assertion (A): Carbon (diamond) does not follow the Dulong-Petit law at room temperature. Reason (R): In diamond, the vibrational energy quanta ħω are much larger than kBT at room temperature, so vibrational modes are not thermally excited and do not contribute to specific heat.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 11

Logic Check

Assertion (A): In a mixture of helium and neon at the same temperature, helium molecules move faster on average than neon molecules. Reason (R): Helium has a smaller molar mass (4 u) than neon (20.2 u), and at the same temperature heavier molecules have greater kinetic energy.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 12

Logic Check

Assertion (A): The temperature of an ideal gas is a measure of its average translational kinetic energy per molecule. Reason (R): Absolute temperature T is defined by the relation ½mv̄² = (3/2)kBT, connecting the microscopic kinetic energy to the macroscopic temperature.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 13

Logic Check

Assertion (A): Real gases behave more like ideal gases at low pressures and high temperatures. Reason (R): At low pressures, molecules are far apart and intermolecular forces are negligible; at high temperatures, kinetic energies far exceed intermolecular potential energies.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 14

Logic Check

Assertion (A): Each vibrational degree of freedom contributes kBT (not ½kBT) to the average energy of a molecule. Reason (R): A vibrational mode has two independent quadratic energy terms—kinetic energy ½m(dy/dt)² and potential energy ½ky²—each contributing ½kBT by equipartition.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 15

Logic Check

Assertion (A): In kinetic theory, all collisions between gas molecules and the walls are assumed to be perfectly elastic. Reason (R): If collisions were inelastic, gas molecules would lose kinetic energy continuously, causing the gas temperature to fall spontaneously without heat removal.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 16

Logic Check

Assertion (A): The pressure of a gas is the same everywhere within the gas at equilibrium. Reason (R): Pressure in a gas at equilibrium acts only on the walls of the container and not within the gas itself.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 17

Logic Check

Assertion (A): A monatomic gas has a higher value of γ (= Cp/Cv) than a diatomic gas. Reason (R): A monatomic gas has fewer degrees of freedom, so a smaller fraction of the supplied heat goes into internal energy and a larger fraction into work, increasing γ.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 18

Logic Check

Assertion (A): The molar volume of any ideal gas at STP is 22.4 litres. Reason (R): From PV = µRT with µ = 1, P = 1 atm = 1.013 × 10⁵ Pa, and T = 273 K, the volume V = RT/P = 22.4 × 10⁻³ m³.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 19

Logic Check

Assertion (A): The rms speed of molecules is of the order of the speed of sound in the gas. Reason (R): The speed of sound in a gas is given by v_sound = √(γP/ρ) = √(γRT/M), which is close to vrms = √(3RT/M) since γ is of order 1.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 20

Logic Check

Assertion (A): Rotation of a diatomic molecule about its bond axis does not contribute to the specific heat at moderate temperatures. Reason (R): The moment of inertia about the bond axis is very large, requiring very high rotational energy to excite this mode.

Reasoning Options

ByteNotes

Chapter sections

Chapter 12: Kinetic Theory | Assertion-Reason

Assertion (A): The average kinetic energy per molecule is the same for all ideal gases at the same temperature. Reason (R): Average kinetic energy per molecule equals (3/2)kBT, which depends only on absolute temperature T.

Assertion (A): At the same temperature, lighter gas molecules have higher rms speed than heavier molecules. Reason (R): The rms speed vrms = √(3kBT/m) is inversely proportional to the square root of the molecular mass.

Assertion (A): The internal energy of an ideal gas depends only on its temperature. Reason (R): In an ideal gas, intermolecular forces are negligible, so there is no potential energy contribution; all internal energy is translational kinetic energy.

Assertion (A): Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules. Reason (R): From PV = NkBT, if P, V, and T are the same for two gases, N must be the same for both.

Assertion (A): The pressure of a gas increases when the gas is compressed isothermally. Reason (R): At constant temperature, reducing volume increases the frequency of molecular collisions with the walls per unit area per unit time.

Assertion (A): A diatomic gas has a higher molar specific heat at constant volume than a monatomic gas. Reason (R): A diatomic molecule has more degrees of freedom (5) than a monatomic molecule (3), so it stores more energy per degree of temperature rise.

Assertion (A): Cp − Cv = R for all ideal gases, regardless of their atomicity. Reason (R): At constant pressure, extra heat R dT per mole must be supplied to do work against external pressure during expansion, in addition to raising the internal energy.

Assertion (A): The mean free path of gas molecules increases when the gas is heated at constant pressure. Reason (R): At constant pressure, increasing temperature decreases the number density n (from P = nkBT), and since l = 1/(√2 π n d²), l increases as n decreases.

Assertion (A): Carbon (diamond) does not follow the Dulong-Petit law at room temperature. Reason (R): In diamond, the vibrational energy quanta ħω are much larger than kBT at room temperature, so vibrational modes are not thermally excited and do not contribute to specific heat.

Assertion (A): In a mixture of helium and neon at the same temperature, helium molecules move faster on average than neon molecules. Reason (R): Helium has a smaller molar mass (4 u) than neon (20.2 u), and at the same temperature heavier molecules have greater kinetic energy.

Assertion (A): The temperature of an ideal gas is a measure of its average translational kinetic energy per molecule. Reason (R): Absolute temperature T is defined by the relation ½mv̄² = (3/2)kBT, connecting the microscopic kinetic energy to the macroscopic temperature.

Assertion (A): Real gases behave more like ideal gases at low pressures and high temperatures. Reason (R): At low pressures, molecules are far apart and intermolecular forces are negligible; at high temperatures, kinetic energies far exceed intermolecular potential energies.

Assertion (A): Each vibrational degree of freedom contributes kBT (not ½kBT) to the average energy of a molecule. Reason (R): A vibrational mode has two independent quadratic energy terms—kinetic energy ½m(dy/dt)² and potential energy ½ky²—each contributing ½kBT by equipartition.

Assertion (A): In kinetic theory, all collisions between gas molecules and the walls are assumed to be perfectly elastic. Reason (R): If collisions were inelastic, gas molecules would lose kinetic energy continuously, causing the gas temperature to fall spontaneously without heat removal.

Assertion (A): The pressure of a gas is the same everywhere within the gas at equilibrium. Reason (R): Pressure in a gas at equilibrium acts only on the walls of the container and not within the gas itself.

Assertion (A): A monatomic gas has a higher value of γ (= Cp/Cv) than a diatomic gas. Reason (R): A monatomic gas has fewer degrees of freedom, so a smaller fraction of the supplied heat goes into internal energy and a larger fraction into work, increasing γ.

Assertion (A): The molar volume of any ideal gas at STP is 22.4 litres. Reason (R): From PV = µRT with µ = 1, P = 1 atm = 1.013 × 10⁵ Pa, and T = 273 K, the volume V = RT/P = 22.4 × 10⁻³ m³.

Assertion (A): The rms speed of molecules is of the order of the speed of sound in the gas. Reason (R): The speed of sound in a gas is given by v_sound = √(γP/ρ) = √(γRT/M), which is close to vrms = √(3RT/M) since γ is of order 1.

Assertion (A): Rotation of a diatomic molecule about its bond axis does not contribute to the specific heat at moderate temperatures. Reason (R): The moment of inertia about the bond axis is very large, requiring very high rotational energy to excite this mode.

Unlock all Assertion-Reason Questions

Practice in Quiz Mode