Entropy of a Microcanonical Ensemble

Highlights of the activity

1. Students are placed into small groups and asked what the entropy of a system with an arbitrary number of eigenstates (each with the same energy) is.
2. Students will derive the result written on Boltzmann's tombstone.

Reasons to spend class time on the activity

The students at this point have typically been given several statistical mechanical expressions that are common in the thermodynamics branch of quantum mechanics. This activity allows students to derive a broad expression for the energy in terms of the number of energy eigenstates a system has. Students also enjoy knowing this result is the expression found on Boltzmann's tombstone. This activity is best done following the Solve for the Fairness Function activity.

Reflections

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Instructor's Guide

• Wiki version