Entropy from Counting: The Molecular Meaning of the Third Law · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Entropy is a count of arrangements

Science · Chemistry · ages 20-21
Name ______________________   Date ____________

  1. Four labelled particles are shared between two boxes. How many microstates are there?

    • 16
    • 8
    • 6

  2. What is a microstate?

    • A single molecule moving at top speed
    • One distinct arrangement of positions and energies
    • A perfect crystal at absolute zero

  3. A perfect crystal at absolute zero has exactly zero entropy.

    Circle one:   True   False

  4. Two labelled particles are shared between two boxes. How many microstates are there? Type the number.

    Answer: ______________

  5. For four labelled particles in two boxes, which distribution is most probable?

    • Four on the left, none on the right
    • Three on one side and one on the other
    • Two particles in each box

  6. Why does solid carbon monoxide keep residual entropy near absolute zero?

    • Its molecules were never cooled far enough
    • Each molecule freezes pointing either way
    • Its partition function shrinks on cooling

  7. A student claims solid nitrogen keeps as much residual entropy as solid carbon monoxide. What is wrong?

    • Nitrogen cannot form a solid at all
    • Nitrogen looks the same flipped end to end
    • Nitrogen has the larger partition function

  8. Samples A and B are at the same T with the same mean energy <E>. Sample A has the larger Z. What follows?

    • A has the larger entropy
    • B has the larger entropy
    • Their entropies must be equal
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Answer key

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

Entropy is a count of arrangements W1-mt_ihl5fEjoLL-s1

  1. 16 · Two boxes to the power four particles gives 16 placements.
  2. One distinct arrangement of positions and energies · A microstate is one specific arrangement the sample can adopt.
  3. True · One arrangement means W is 1, and the log of 1 is zero.
  4. 4 · Two boxes to the power two particles gives 4 arrangements.
  5. Two particles in each box · Six of the 16 microstates share the particles evenly, more than any other split.
  6. Each molecule freezes pointing either way · The frozen head to tail muddle leaves many arrangements, so W stays above 1.
  7. Nitrogen looks the same flipped end to end · Flipping nitrogen changes nothing, so almost no extra arrangements survive.
  8. A has the larger entropy · At the same T with the same <E>, S differs only by k ln Z, so larger Z means larger S.
Worksheet · LightMySky