Kinetic Theory of Gases — 50 High-Yield MCQs (English)

Covers assumptions, Maxwell speed distribution, rms/mean/most probable speeds, pressure derivation, mean free path, equipartition, transport properties. Correct answer shown after each question.

50 MCQs
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Maxwell Distribution Speeds & Energies Mean Free Path Transport Properties
1. Kinetic theory assumes gas molecules are:
A. Large and interacting continuously
B. Point-like and undergo elastic collisions
C. In fixed positions
D. Charged and bound
Answer: B
2. Pressure in kinetic theory arises from:
A. Gravitational attraction between molecules
B. Impact of molecules on container walls
C. Chemical reactions
D. Magnetic forces
Answer: B
3. Ideal gas law PV = nRT can be derived from kinetic theory using:
A. Molecular speed distribution and momentum transfer
B. Quantum mechanics
C. Electromagnetism
D. Solid-state models
Answer: A
4. Relation between pressure p, number density n and average kinetic energy per molecule (½ m v_rms^2) is:
A. p = n k_B T only
B. p = (2/3) n × (½ m v_rms^2)
C. p = n m g
D. p = (1/3) n m v_mean^2
Answer: B
5. RMS speed v_rms of molecules is related to temperature by v_rms =:
A. √(k_B T / m)
B. √(3 k_B T / m)
C. √(2 k_B T / m)
D. √(k_B T / 2m)
Answer: B
6. Most probable speed v_mp in Maxwell distribution is:
A. √(k_B T / m)
B. √(2 k_B T / m)
C. √(3 k_B T / m)
D. √(5 k_B T / m)
Answer: B
7. Average speed (⟨v⟩) for Maxwell distribution equals:
A. √(3kT/m)
B. √(kT/m)
C. √(8kT/π m)
D. √(2kT/m)
Answer: C
8. Equipartition theorem states that each quadratic degree of freedom contributes ______ to average energy per molecule.
A. (1/2) k_B T
B. k_B T
C. (3/2) k_B T
D. Zero
Answer: A
9. For a monoatomic ideal gas, molar specific heat at constant volume C_v,m =:
A. (3/2) R
B. (5/2) R
C. R
D. (7/2) R
Answer: A
10. Number density n (molecules per unit volume) relates to pressure and temperature as:
A. n = p / (k_B T)
B. n = k_B T / p
C. n = p V / k_B
D. n independent
Answer: A
11. Mean free path λ is the average distance travelled between:
A. Two successive collisions
B. Wall impacts
C. Thermal equilibration events
D. Quantum jumps
Answer: A
12. Mean free path λ in terms of number density n and molecular diameter d is approximately:
A. 1 / (n π d^2)
B. 1 / (√2 n π d^2)
C. n π d^2
D. √(n π d^2)
Answer: B
13. Collision cross-section σ for hard spheres of diameter d equals:
A. π d^2
B. 4 π d^2
C. π (2d)^2
D. d^2
Answer: A
14. Maxwell distribution function gives probability of molecules having a particular:
A. Position
B. Speed
C. Acceleration
D. Charge
Answer: B
15. For Maxwell distribution, shape broadens with:
A. Increasing temperature
B. Decreasing temperature
C. Increasing pressure only
D. Mass only
Answer: A
16. Root-mean-square speed is always ______ than average speed for Maxwell distribution.
A. Less
B. Greater
C. Equal
D. Unrelated
Answer: B
17. Equipartition theorem predicts internal energy per mole of monoatomic gas is (3/2)RT because monoatomic gas has:
A. Three translational degrees of freedom
B. Rotational degrees only
C. Vibrational degrees only
D. No degrees
Answer: A
18. For diatomic gases at room temperature, degrees of freedom counted for equipartition are typically:
A. 3 translational only
B. 5 (3 translational + 2 rotational)
C. 7 (including vibrations)
D. 1 only
Answer: B
19. Mean kinetic energy per molecule equals (3/2) k_B T for an ideal monoatomic gas. k_B is:
A. Gas constant
B. Boltzmann constant
C. Planck constant
D. Avogadro's number
Answer: B
20. If molecular mass increases at same temperature, rms speed of molecules:
A. Increases
B. Decreases
C. Remains same
D. Undefined
Answer: B
21. Molecular collisions in an ideal gas are assumed to be:
A. Inelastic with energy loss
B. Elastic conserving kinetic energy
C. Annihilating
D. Sticky
Answer: B
22. Transport properties like viscosity in gases increase with temperature because:
A. Mean free path decreases
B. Molecular speed increases and momentum transfer increases
C. Density increases
D. Collisions become sticky
Answer: B
23. Pressure exerted by gas on wall in kinetic theory is proportional to:
A. Number density × average momentum transfer per collision × collision rate
B. Temperature only
C. Volume only
D. Mass only
Answer: A
24. Boyle's law (PV = constant at fixed T) is consistent with kinetic theory because:
A. Number density changes with V keeping pV constant
B. Molecular speeds change with V at constant T
C. Average kinetic energy depends on pressure
D. Collisions become inelastic
Answer: A
25. The Sackur–Tetrode equation gives entropy of ideal monatomic gas and arises from:
A. Quantum statistical counting of microstates
B. Classical mechanics only
C. Electromagnetism
D. Thermochemistry
Answer: A
26. Diffusion coefficient in gases scales roughly as:
A. v_mean × λ (mean speed × mean free path)
B. λ / v_mean
C. v_mean^2
D. Independent of molecular properties
Answer: A
27. Under kinetic theory, speed distribution becomes narrower for a given gas when:
A. Temperature increases
B. Temperature decreases
C. Pressure decreases only
D. Molecular mass decreases
Answer: B
28. The assumption of negligible intermolecular forces is valid when gas is:
A. At high pressure and low temperature
B. At low density (high temperature, low pressure)
C. Condensed liquid
D. Solid
Answer: B
29. Thermal conductivity of a dilute gas is proportional to:
A. n k_B λ v_mean
B. Only viscosity
C. Volume only
D. Zero
Answer: A
30. In kinetic theory, pressure is independent of:
A. Molecular mass when temperature fixed
B. Temperature
C. Number density
D. Molecular collisions
Answer: A
31. The Boltzmann constant k_B relates macroscopic and microscopic temperatures via:
A. pV = N k_B T
B. E = k_B T per degree of freedom
C. Both A and B
D. None
Answer: C
32. Maxwell–Boltzmann statistics apply to gases when:
A. Quantum effects are negligible (classical limit)
B. Degenerate quantum gas
C. Bose–Einstein condensation
D. Electrons in metal
Answer: A
33. For molecular collisions, relative speed between two molecules matters because:
A. Collision frequency depends on relative speed
B. Individual speeds irrelevant
C. Pressure depends only on absolute speed
D. Volume depends on relative speed
Answer: A
34. Mean free time τ between collisions is related to mean free path λ and mean speed ⟨v⟩ by:
A. τ = λ / ⟨v⟩
B. τ = λ × ⟨v⟩
C. τ = ⟨v⟩ / λ
D. τ independent
Answer: A
35. For an ideal gas, increasing pressure at constant temperature reduces mean free path because:
A. Molecular diameter increases
B. Number density increases leading to more collisions
C. Temperature increases
D. Collisions vanish
Answer: B
36. Viscosity of an ideal gas is roughly independent of pressure at low densities because:
A. Mean free path decreases exactly compensating density increase
B. Collisions stop
C. Temperature drops
D. Molecular mass changes
Answer: A
37. In kinetic theory, pressure at height in gravitational field differs because:
A. Molecular speeds change with altitude
B. Number density varies with altitude due to hydrostatic balance
C. Mean free path is constant
D. Boltzmann constant varies
Answer: B
38. Root-mean-square, most probable and average speeds order for Maxwell distribution is:
A. v_mp < v_avg < v_rms
B. v_rms < v_avg < v_mp
C. v_avg < v_mp < v_rms
D. All equal
Answer: A
39. Kinetic theory prediction for pressure uses average of which velocity component?
A. ⟨v_x⟩ (average of one component) which is zero
B. ⟨v_x^2⟩ (mean square of component)
C. ⟨v⟩ directly
D. ⟨1/v⟩
Answer: B
40. For gas mixtures, each component contributes to total pressure independently according to:
A. Dalton's law of partial pressures
B. Raoult's law only
C. Henry's law only
D. Gibbs phase rule
Answer: A
41. Kinetic theory explains Brownian motion as resulting from:
A. Thermal collisions of fluid molecules with the particle
B. Gravitational pull only
C. Magnetic forces
D. Quantum tunnelling
Answer: A
42. Chapman–Enskog theory refines kinetic theory to predict:
A. Transport coefficients (viscosity, thermal conductivity, diffusion)
B. Quantum energy levels
C. Nuclear reactions
D. Solid elasticity
Answer: A
43. Under kinetic theory, the speed distribution depends explicitly on:
A. Temperature and molecular mass
B. Pressure only
C. Volume only
D. Shape of container
Answer: A
44. In kinetic theory derivation of p = (1/3) n m ⟨v^2⟩, factor 1/3 appears because:
A. Only one-third of molecules hit walls
B. Velocity components equally distributed in three directions
C. Collisions are inelastic
D. Mathematical approximation
Answer: B
45. When quantum effects become important for a gas, classical Maxwell–Boltzmann distribution fails at:
A. High temperature and low density
B. Low temperature and high density (degenerate regime)
C. Room conditions always
D. Never
Answer: B
46. Molecular speed distribution for heavier molecules at same temperature is:
A. Shifted to higher speeds
B. Shifted to lower speeds (narrower)
C. Unchanged
D. Bimodal
Answer: B
47. The concept of pressure in kinetic theory is microscopic average of momentum transfer per unit time per unit:
A. Volume
B. Area
C. Mass
D. Temperature
Answer: B
48. Mean translational kinetic energy per mole of ideal monoatomic gas equals:
A. (3/2) RT
B. (5/2) RT
C. RT
D. Zero
Answer: A
49. In kinetic theory, a dilute gas approximates ideal behavior because:
A. Intermolecular potential energy negligible compared to kinetic energy
B. Molecules attract strongly
C. Liquids form
D. Quantum effects dominate
Answer: A
50. Kinetic theory prediction that pressure ∝ temperature at constant volume is experimentally consistent because:
A. Molecular energies scale with temperature
B. Volume changes with T
C. Mass changes with T
D. None
Answer: A