83 free MCQs on Kinetic Theory, each with its own worked answer and explanation. Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.
Take the timed Kinetic Theory chapterwise test →83 practice questions on Kinetic Theory, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Kinetic Theory notes.
Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed vp slightly less than the average vavg, which is slightly less than the root-mean-square speed vrms used in the pressure formula.
Q1.
The Boltzmann constant k equals the gas constant R divided by:
Q2.
At standard temperature and pressure (273 K, 1 atm), one mole of an ideal gas occupies about:
Q3.
In an ideal gas, molecules exert no force except during collisions, so the gas has no intermolecular:
Q4.
If the number of molecules in a fixed volume is doubled at constant temperature, the pressure:
Q5.
According to kinetic theory, gas molecules are assumed to undergo collisions that are:
Q6.
The pressure exerted by an ideal gas, according to kinetic theory, is given by P =
Q7.
The average kinetic energy of a gas molecule is directly proportional to:
Q8.
The number of degrees of freedom for a monatomic gas molecule is:
Q9.
For a diatomic gas at moderate temperatures (ignoring vibration), the number of degrees of freedom is:
Q10.
The law of equipartition of energy states that each degree of freedom contributes an average energy of:
Q11.
Mean free path of gas molecules is the:
Q12.
Which of the three characteristic molecular speeds (rms, average, most probable) has the highest value?
Q13.
The root mean square speed of gas molecules is given by:
Q14.
At absolute zero temperature, the kinetic energy of gas molecules (classically) is:
Q15.
For a monatomic ideal gas, the ratio of specific heats γ = Cp/Cv is:
Q16.
For a diatomic ideal gas (no vibration), the ratio of specific heats γ = Cp/Cv is:
Q17.
Kinetic theory assumes that the actual volume occupied by gas molecules is:
Q18.
The kinetic theory of gases assumes that gas molecules are in ___ motion:
Q19.
The pressure exerted by a gas arises from molecular collisions with the:
Q20.
In kinetic theory, the actual volume of the gas molecules themselves is taken to be ___ the container volume:
Q21.
The average kinetic energy of gas molecules depends only on the:
Q22.
At absolute zero, the kinetic energy of gas molecules is theoretically:
Q23.
In the kinetic theory, molecular collisions are assumed to be perfectly:
Q24.
The temperature scale used in the kinetic theory of gases is the:
Q25.
The number of molecules per unit volume of an ideal gas at 300 K and pressure 1.0 × 10<sup>5</sup> Pa is about (k = 1.38 × 10<sup>-23</sup> J/K):
Q26.
The rms speed of oxygen molecules (M = 32 g/mol) at 300 K (R = 8.31) is about:
Q27.
The molar heat capacity at constant volume of a diatomic ideal gas (R = 8.31) is:
Q28.
If the absolute temperature of an ideal gas is increased 4 times, the rms speed of its molecules becomes:
Q29.
Equal volumes of two different ideal gases at the same temperature and pressure have:
Q30.
Two gases, hydrogen (M=2 g/mol) and oxygen (M=32 g/mol), are at the same temperature. The ratio of their rms speeds (v<sub>H</sub><sub>2</sub> / v<sub>O</sub><sub>2</sub>) is:
Q31.
An ideal gas is heated at constant volume. The heat supplied increases:
Q32.
If the pressure of an ideal gas is doubled while keeping temperature constant, the rms speed of the molecules:
Q33.
For a gas mixture of monatomic and diatomic molecules with degrees of freedom f<sub>1</sub> and f<sub>2</sub> respectively in equal number of moles, the average degrees of freedom of the mixture is:
Q34.
The mean free path of gas molecules is inversely proportional to which factor (for fixed temperature)?
Q35.
A vessel contains a mixture of two ideal gases at the same temperature. Which statement is true regarding their molecules?
Q36.
If a gas obeys PV = (2/3)E where E is the total translational kinetic energy of the gas, this kinetic theory result combined with PV = nRT shows that E equals:
Q37.
Why does a balloon filled with helium gas leak (deflate) faster than one filled with air, through the same tiny porous wall?
Q38.
For a polyatomic gas with 3 translational, 3 rotational, and 2 vibrational degrees of freedom, the total degrees of freedom f is:
Q39.
For an ideal gas, internal energy depends only on:
Q40.
The rms speed of gas molecules, v<sub>rms</sub> = √(3RT/M), is proportional to:
Q41.
The average translational kinetic energy per molecule of a gas is:
Q42.
As the temperature of a gas increases, the rms speed of its molecules:
Q43.
In the relation PV = (1/3)Nm·v²_rms, the pressure is linked to the ___ of the molecules:
Q44.
At the same temperature, a lighter gas has a ___ rms speed than a heavier gas:
Q45.
The number of degrees of freedom of a monatomic gas molecule is:
Q46.
The number of degrees of freedom of a diatomic gas molecule at moderate temperature is:
Q47.
The mean free path is the average distance a molecule travels between successive:
Q48.
By what factor must the absolute temperature of an ideal gas be increased to double the rms speed of its molecules?
Q49.
A vessel holds 2 moles of helium and 3 moles of hydrogen at the same temperature T. The total internal energy of the mixture is:
Q50.
The mean free path of the molecules of a gas kept in a rigid closed container is λ. If the absolute temperature is doubled while the volume stays fixed, the mean free path:
Q51.
One mole of a monatomic gas (C<sub>v</sub> = 3R/2) is mixed with two moles of a diatomic gas (C<sub>v</sub> = 5R/2). The molar specific heat at constant volume of the mixture is:
Q52.
At the same temperature, the ratio of rms speeds of helium (M = 4) to methane (M = 16) is:
Q53.
One mole of a monatomic gas is mixed with one mole of a diatomic gas. The ratio γ = C<sub>p</sub>/C<sub>v</sub> of the mixture is:
Q54.
The internal energy of 2 moles of a polyatomic gas with 6 degrees of freedom at 300 K (R = 8.31) is about:
Q55.
Using P = (1/3)ρv<sub>rms</sub><sup>2</sup>, a gas at pressure 1 × 10<sup>5</sup> Pa and density 1.25 kg/m<sup>3</sup> has rms speed:
Q56.
A gas of N molecules is enclosed in a container. If the container volume is suddenly doubled at constant temperature (free expansion, no heat exchange), the rms speed of the molecules:
Q57.
Using kinetic theory, derive the relationship: if a gas has n moles and the total translational KE is (3/2)nRT, then for a diatomic gas with rotational energy also included, the total internal energy U at temperature T (f=5) is:
Q58.
A vessel contains N<sub>2</sub> gas at temperature T. If the temperature is raised such that the gas molecules begin to dissociate into individual N atoms at very high T, the degrees of freedom of the system effectively:
Q59.
Two ideal gas samples, A (monatomic) and B (diatomic), have equal moles and are at the same temperature. The ratio of their total internal energies U<sub>A</sub> : U<sub>B</sub> is:
Q60.
If the most probable speed of gas molecules is v<sub>p</sub> = √(2RT/M), and the rms speed is v<sub>rms</sub> = √(3RT/M), the ratio v<sub>rms</sub>/v<sub>p</sub> is:
Q61.
A closed rigid container has an ideal monatomic gas. Heat Q is supplied at constant volume, raising the temperature by ΔT. The fraction of heat that goes into increasing the rotational kinetic energy of the molecules is:
Q62.
The pressure of an ideal gas is given by P = (1/3)nm(v<sub>rms</sub>)², where n is number density and m is the mass of each molecule. If the gas is compressed isothermally to half its volume, the number density n doubles. The new pressure compared to the original is:
Q63.
Mean free path of a gas molecule is found to be λ at pressure P and temperature T. If the pressure is doubled at constant temperature, the new mean free path becomes:
Q64.
According to the Maxwell speed distribution, as temperature increases for a fixed gas, the distribution curve of molecular speeds:
Q65.
An ideal gas undergoes a process in which its pressure and volume are related by PV² = constant. Starting from an initial temperature T, if the volume of the gas doubles, the final temperature of the gas is:
Q66.
By the law of equipartition of energy, each degree of freedom contributes ___ per molecule:
Q67.
At the same temperature, the rms speed of oxygen (M = 32) compared with hydrogen (M = 2) is:
Q68.
If the absolute temperature of a gas is quadrupled, its rms speed becomes:
Q69.
The ratio of specific heats γ = Cp/Cv for a monatomic ideal gas is:
Q70.
The ratio γ = Cp/Cv for a diatomic ideal gas is:
Q72.
The mean free path of a gas is ___ proportional to the number density of molecules:
Q73.
The internal energy of an ideal gas depends only on its:
Q74.
At the same temperature, all ideal gases have the same average:
Q75.
The kinetic theory explains the gas laws by modelling a gas as a very large number of tiny:
Q76.
At the same temperature, the ratio of rms speeds of hydrogen (M = 2) to oxygen (M = 32) molecules is:
Q77.
At a fixed temperature, the average translational kinetic energy of a molecule depends on:
Q78.
The number of degrees of freedom of a rigid diatomic molecule at ordinary temperature is:
Q79.
At constant temperature, the pressure of a gas is doubled. Its mean free path becomes:
Q80.
The rms speed of gas molecules at 27°C is v. At 927°C, the rms speed becomes:
Q81.
The internal energy of 2 moles of a monatomic ideal gas at 300 K (R = 8.31 J/mol·K) is about:
Q82.
For a monatomic ideal gas, the ratio Cp/Cv equals:
Q83.
From kinetic theory, P = (1/3)ρ v²_rms. The rms speed in terms of pressure P and density ρ is:
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