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Physics · Advanced university

Entropy difference from multiplicity ratio

Use the microcanonical equal-a-priori-probability model and a ratio of multiplicities.

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Method and conditions

Use the microcanonical equal-a-priori-probability model and a ratio of multiplicities.

ΔS/kB = ln(Ω₂/Ω₁)

Worked examples

In a microcanonical model, the multiplicity increases by a factor 236. Find ΔS/kB. Round the final result to 4 decimal places if needed.

S=kB ln Ω, so the difference divided by kB is ln(236).

5.4638

In a microcanonical model, the multiplicity increases by a factor 311. Find ΔS/kB. Round the final result to 4 decimal places if needed.

S=kB ln Ω, so the difference divided by kB is ln(311).

5.7398

Try it

  1. In a microcanonical model, the multiplicity increases by a factor 286. Find ΔS/kB. Round the final result to 4 decimal places if needed.

  2. In a microcanonical model, the multiplicity increases by a factor 59. Find ΔS/kB. Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 5.656

    S=kB ln Ω, so the difference divided by kB is ln(286).

  2. 4.0775

    S=kB ln Ω, so the difference divided by kB is ln(59).

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