STATISTICAL MECHANICS QUALIFYING
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
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1. The fundamental assumption of statistical mechanics states that
A. Energy is continuously distributed
B. Entropy always decreases
C. Systems are always isolated
D. All accessible microstates are equally probable
In equilibrium, each microstate consistent with macroscopic constraints
has equal probability.
2. The phase space of an N-particle classical system has dimension
A. 3N
B. 4N
C. 6N
D. 2N
Each particle contributes three position and three momentum coordinates.
3. The Boltzmann entropy is defined as
A. S = kT ln Z
B. S = −k ln p
C. S = k ln Ω
D. S = U/T
Entropy is proportional to the logarithm of the number of accessible
microstates.
,4. The canonical ensemble applies to systems with
A. Fixed energy and volume
B. Fixed particle number only
C. Fixed temperature, volume, and particle number
D. Fixed pressure and entropy
The canonical ensemble models systems in thermal contact with a heat
bath.
5. The partition function Z primarily determines
A. Microstates only
B. Dynamics
C. All thermodynamic properties
D. Only entropy
Thermodynamic quantities can be derived from Z.
6. The Helmholtz free energy is related to the partition function by
A. F = kT ln Z
B. F = −kT ln Z
C. F = U − TS
D. F = −TS
This relation connects microscopic statistics to macroscopic free energy.
7. The probability of a state with energy Ei in the canonical ensemble is
A. 1/Z
B. Ei/Z
C. exp(−βEi)/Z
D. βEi/Z
This is the Boltzmann distribution.
8. β in statistical mechanics is defined as
A. 1/k
B. T/k
C. 1/(kT)
D. kT
β simplifies expressions involving thermal energy.
, 9. The microcanonical ensemble assumes
A. Variable energy
B. Fixed temperature
C. Fixed energy, volume, and particle number
D. Fixed pressure
It describes isolated systems.
10.In the thermodynamic limit, N → ∞ while
A. Volume → 0
B. Temperature → 0
C. N/V remains constant
D. Pressure → ∞
This ensures well-defined intensive properties.
11.The most probable distribution of particles among energy levels is found by
A. Minimizing energy
B. Maximizing entropy
C. Maximizing temperature
D. Minimizing free energy
Equilibrium corresponds to maximum entropy.
12.Maxwell–Boltzmann statistics apply to
A. Indistinguishable fermions
B. Bosons
C. Classical distinguishable particles
D. Quantum gases only
It is valid when quantum effects are negligible.
13.Fermi–Dirac statistics describe
A. Photons
B. Classical gases
C. Particles obeying the Pauli exclusion principle
D. Phonons
Fermions cannot occupy the same quantum state.
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
DOWNLOAD PDF
1. The fundamental assumption of statistical mechanics states that
A. Energy is continuously distributed
B. Entropy always decreases
C. Systems are always isolated
D. All accessible microstates are equally probable
In equilibrium, each microstate consistent with macroscopic constraints
has equal probability.
2. The phase space of an N-particle classical system has dimension
A. 3N
B. 4N
C. 6N
D. 2N
Each particle contributes three position and three momentum coordinates.
3. The Boltzmann entropy is defined as
A. S = kT ln Z
B. S = −k ln p
C. S = k ln Ω
D. S = U/T
Entropy is proportional to the logarithm of the number of accessible
microstates.
,4. The canonical ensemble applies to systems with
A. Fixed energy and volume
B. Fixed particle number only
C. Fixed temperature, volume, and particle number
D. Fixed pressure and entropy
The canonical ensemble models systems in thermal contact with a heat
bath.
5. The partition function Z primarily determines
A. Microstates only
B. Dynamics
C. All thermodynamic properties
D. Only entropy
Thermodynamic quantities can be derived from Z.
6. The Helmholtz free energy is related to the partition function by
A. F = kT ln Z
B. F = −kT ln Z
C. F = U − TS
D. F = −TS
This relation connects microscopic statistics to macroscopic free energy.
7. The probability of a state with energy Ei in the canonical ensemble is
A. 1/Z
B. Ei/Z
C. exp(−βEi)/Z
D. βEi/Z
This is the Boltzmann distribution.
8. β in statistical mechanics is defined as
A. 1/k
B. T/k
C. 1/(kT)
D. kT
β simplifies expressions involving thermal energy.
, 9. The microcanonical ensemble assumes
A. Variable energy
B. Fixed temperature
C. Fixed energy, volume, and particle number
D. Fixed pressure
It describes isolated systems.
10.In the thermodynamic limit, N → ∞ while
A. Volume → 0
B. Temperature → 0
C. N/V remains constant
D. Pressure → ∞
This ensures well-defined intensive properties.
11.The most probable distribution of particles among energy levels is found by
A. Minimizing energy
B. Maximizing entropy
C. Maximizing temperature
D. Minimizing free energy
Equilibrium corresponds to maximum entropy.
12.Maxwell–Boltzmann statistics apply to
A. Indistinguishable fermions
B. Bosons
C. Classical distinguishable particles
D. Quantum gases only
It is valid when quantum effects are negligible.
13.Fermi–Dirac statistics describe
A. Photons
B. Classical gases
C. Particles obeying the Pauli exclusion principle
D. Phonons
Fermions cannot occupy the same quantum state.
