Entropy of a Microcanonical Ensemble

Highlights of the activity

1. This small group activity is designed to give students a chance to derive an expression for the entropy of a system with an arbitrary number of eigenstates.
2. Students use what they know to derive an expression for the entropy of a system with an arbitrary number of eigenstates.
3. The whole class discussion focuses on ensuring that students understand the steps required to derive the expression for the entropy of a system with an arbitrary number of eigenstates.

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