At positive temperature, how is a canonical microstate's probability assigned?

• Divide its energy by the total of all energies
• Divide its Boltzmann factor by the partition function
• Give every state the same probability regardless of energy

Which quantities are fixed in the microcanonical ensemble?

• Energy, volume and particle number
• Temperature, volume and particle number
• Temperature, pressure and particle number

Dividing each canonical Boltzmann factor by the partition function makes the state probabilities sum to 1.

A sealed, rigid box is perfectly insulated and has no work input or other energy exchange. Which ensemble describes its equilibrium gas?

• Canonical, because insulation fixes the temperature
• Microcanonical, because E,V,N remain fixed
• Fixed-pressure ensemble, because sealing fixes pressure

A sealed, rigid flask exchanges heat with a large room and has equilibrated at its steady temperature. Which ensemble models the gas?

• Microcanonical: sealing prevents every energy exchange
• Fixed-pressure ensemble: the room fixes the gas pressure
• Canonical: T,V,N are fixed while energy can fluctuate

For an ordinary short-range system away from singular regimes, why can matched canonical and microcanonical ensembles approach the same local thermodynamic averages at large N?

• Canonical energy becomes sharply concentrated relative to its mean
• Canonical energy becomes exactly fixed for every finite particle count
• Canonical temperature must approach absolute zero as particle count grows

A five-particle system is in a heat bath. A friend claims ensemble equivalence guarantees every average matches a microcanonical calculation. Which reply is justified?

• Heat-bath contact makes the system perfectly isolated
• Five particles do not justify a large-system equivalence claim
• Every observable must differ whenever a system has five particles

A canonical system at positive finite T has two states of different energies. Rafi assigns them equal probabilities without an approximation. What is the problem?

• Equal probabilities follow whenever particle number is fixed
• Different energies require different volume constraints instead
• Canonical probabilities depend on energy through Boltzmann factors