The Microcanonical and Canonical Ensembles · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Two rulebooks for odds in physics

Science · Thermal & Statistical Physics · ages 21-22
Name ______________________   Date ____________

  1. How are odds assigned in the canonical ensemble?

    • Equal odds for every microstate
    • Odds from the Boltzmann factor
    • Odds picked at random

  2. What is held fixed in the microcanonical ensemble?

    • Energy, volume, and particle count
    • Temperature and pressure
    • Only the entropy

  3. The partition function normalizes the canonical odds.

    Circle one:   True   False

  4. A perfectly insulated box holds a gas with no heat flow. Which book suits it?

    • Canonical, because all boxes use it
    • Microcanonical, because its energy is fixed
    • Neither, because gases need thermostats

  5. A gas sits in a sealed flask on a bench at steady room temperature. Which book suits it?

    • Microcanonical, because the flask is sealed
    • A rulebook for fixed pressure only
    • Canonical, because the room sets its temperature

  6. Why do the two books agree for a vast crowd of particles?

    • The energy wobbles shrink to nothing beside the total
    • The temperature drops to zero
    • The particles stop moving

  7. Five particles sit in a heat bath. A friend claims both books give the same averages. Why is that premature?

    • Baths only work for isolated systems
    • Agreement needs a vast crowd, not five particles
    • Five particles cannot have a temperature

  8. A student applies equal odds to a thermostat held gas and gets wrong averages. What is the error?

    • Equal odds need a colder thermostat
    • The gas should be treated as isolated instead
    • A thermostat fixes temperature, so Boltzmann odds apply
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Two rulebooks for odds in physics W1-mt_NSCYLK-brt-s1

  1. Odds from the Boltzmann factor · At fixed temperature, odds follow the Boltzmann factor.
  2. Energy, volume, and particle count · An isolated system fixes energy, volume, and particle count.
  3. True · It scales the Boltzmann factors so the odds sum to one.
  4. Microcanonical, because its energy is fixed · No heat flow fixes the energy, which is the microcanonical case.
  5. Canonical, because the room sets its temperature · Heat flows through the bench setup, so temperature is the fixed quantity.
  6. The energy wobbles shrink to nothing beside the total · Relative wobbles vanish for huge crowds, so averages match.
  7. Agreement needs a vast crowd, not five particles · With few particles the wobbles stay large and the books disagree.
  8. A thermostat fixes temperature, so Boltzmann odds apply · The thermostat sets temperature, which selects the canonical book.
Worksheet · LightMySky