Q.1 According to kinetic theory of gases, the pressure exerted by a gas is due to:
Attraction between molecules
Repulsion between molecules
Collisions of molecules with the walls
Weight of gas molecules
Explanation - Gas molecules move randomly and exert pressure by colliding with the container walls, transferring momentum.
Correct answer is: Collisions of molecules with the walls
Q.2 The average kinetic energy of an ideal gas molecule is proportional to:
Pressure
Volume
Temperature
Mass
Explanation - From kinetic theory, average kinetic energy per molecule is (3/2)kT, directly proportional to absolute temperature.
Correct answer is: Temperature
Q.3 The root mean square speed of gas molecules is given by:
√(3kT/m)
√(2kT/m)
√(kT/2m)
√(kT/m)
Explanation - The root mean square speed c = √(3kT/m), where k is Boltzmann constant and m is molecular mass.
Correct answer is: √(3kT/m)
Q.4 Which of the following assumptions is NOT made in kinetic theory of gases?
Molecules are point masses
Molecules exert forces on each other at all times
Collisions are perfectly elastic
Molecules are in random motion
Explanation - In kinetic theory, intermolecular forces are negligible except during collisions.
Correct answer is: Molecules exert forces on each other at all times
Q.5 If temperature of a gas is doubled, the average kinetic energy of its molecules becomes:
Halved
Unchanged
Doubled
Quadrupled
Explanation - Average kinetic energy is directly proportional to temperature (in Kelvin). Doubling T doubles KE.
Correct answer is: Doubled
Q.6 The ratio of average speed to root mean square speed of gas molecules is:
√(8/3π)
√(3π/8)
√(π/2)
√(2π/3)
Explanation - Average speed = √(8RT/πM), RMS speed = √(3RT/M). Their ratio = √(8/3π).
Correct answer is: √(8/3π)
Q.7 Boltzmann constant is defined as:
R/NA
NA/R
R×NA
1/RNA
Explanation - Boltzmann constant k = R/NA, where R = universal gas constant, NA = Avogadro number.
Correct answer is: R/NA
Q.8 The SI unit of Boltzmann constant is:
J/mol·K
J/K
J/kg·K
Pa·m³
Explanation - Boltzmann constant relates energy to temperature per particle, so unit = Joule per Kelvin.
Correct answer is: J/K
Q.9 Which of the following gases will have the highest RMS speed at the same temperature?
Oxygen
Nitrogen
Hydrogen
Carbon dioxide
Explanation - RMS speed is inversely proportional to √(molar mass). Hydrogen has the lowest molar mass.
Correct answer is: Hydrogen
Q.10 Mean free path of gas molecules increases when:
Pressure increases
Temperature increases at constant pressure
Volume decreases
Molecular size increases
Explanation - At higher temperature and constant pressure, molecules move faster and density reduces, increasing mean free path.
Correct answer is: Temperature increases at constant pressure
Q.11 The ratio of specific heats (Cp/Cv) for a monoatomic ideal gas is:
5/3
3/2
7/5
4/3
Explanation - For monoatomic gases: Cv = (3/2)R, Cp = (5/2)R, hence Cp/Cv = 5/3.
Correct answer is: 5/3
Q.12 Equipartition theorem states that each quadratic degree of freedom contributes:
½kT energy
kT energy
3/2 kT energy
2kT energy
Explanation - Equipartition theorem: each quadratic degree of freedom contributes ½kT to average energy per particle.
Correct answer is: ½kT energy
Q.13 Which of the following is not a degree of freedom for a linear diatomic molecule?
Rotation
Translation
Vibration
Cubical motion
Explanation - Degrees of freedom include translation, rotation, vibration, not cubical motion.
Correct answer is: Cubical motion
Q.14 At STP, one mole of an ideal gas occupies:
22.4 L
1 L
2.24 L
11.2 L
Explanation - According to ideal gas law, one mole of gas at STP occupies 22.4 liters.
Correct answer is: 22.4 L
Q.15 For an ideal gas, internal energy depends only on:
Pressure
Volume
Temperature
Number of molecules
Explanation - Internal energy of an ideal gas is due to kinetic energy of molecules, proportional only to temperature.
Correct answer is: Temperature
Q.16 The dimensional formula of Boltzmann constant is:
ML²T⁻²K⁻¹
MLT⁻²K⁻¹
ML²T⁻¹K⁻¹
M⁰L⁰T⁰
Explanation - Boltzmann constant k = energy/temperature, so dimensions are (ML²T⁻²)/K.
Correct answer is: ML²T⁻²K⁻¹
Q.17 Most probable speed of molecules in a gas is given by:
√(2kT/m)
√(3kT/m)
√(kT/m)
√(8kT/mπ)
Explanation - Most probable speed v_mp = √(2kT/m), derived from Maxwell distribution.
Correct answer is: √(2kT/m)
Q.18 Which of the following is true about ideal gases?
They obey PV = nRT at all conditions
They have intermolecular forces
Their molecules have finite volume
They liquefy at low temperature
Explanation - Ideal gases are defined by perfect adherence to the ideal gas equation under all conditions.
Correct answer is: They obey PV = nRT at all conditions
Q.19 The molecular speed distribution was first derived by:
Newton
Einstein
Maxwell
Boltzmann
Explanation - James Clerk Maxwell derived the distribution law for molecular speeds.
Correct answer is: Maxwell
Q.20 Which quantity remains constant for an isothermal process in an ideal gas?
Pressure
Volume
Temperature
Entropy
Explanation - In an isothermal process, the temperature of the system remains constant.
Correct answer is: Temperature
Q.21 At constant volume, the pressure of a gas is directly proportional to:
Temperature
Density
Volume
Mass
Explanation - From ideal gas law, P ∝ T at constant V and n.
Correct answer is: Temperature
Q.22 For one mole of a monatomic ideal gas, the molar heat capacity at constant volume is:
R
3/2 R
5/2 R
2R
Explanation - Cv = (f/2)R, with f = 3 for monatomic gases. Hence Cv = 3/2 R.
Correct answer is: 3/2 R
Q.23 For diatomic gases at room temperature, the value of γ = Cp/Cv is approximately:
5/3
7/5
3/2
4/3
Explanation - For diatomic gases with 5 degrees of freedom, Cp = 7/2R, Cv = 5/2R, γ = 7/5.
Correct answer is: 7/5
Q.24 The pressure exerted by 1 mole of an ideal gas at temperature T in volume V is given by:
RT/V
nRT/P
PV/T
V/RT
Explanation - From PV = nRT, for n = 1 mole, P = RT/V.
Correct answer is: RT/V
Q.25 At what temperature will the RMS speed of hydrogen molecules be equal to that of oxygen molecules at 300 K?
37.5 K
1200 K
2400 K
4800 K
Explanation - RMS speed ∝ √(T/M). Equating speeds: T_H2 / M_H2 = 300 / M_O2. Solving gives T_H2 ≈ 37.5 K.
Correct answer is: 37.5 K