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Introducing Legendre Transforms

Keywords: Internal Energy, Helmholtz, Gibbs, Enthalpy, Interlude, Small Group Activity, Total Differential, Differentials, Legendre Transformations


Highlights of the activity

  1. This small group activity is designed to give students a chance to derive expressions for Helmholtz and Gibbs free energies and Enthalpy
  2. Students use $F=U-TS$ to derive the Helmholtz free energy equation, and then the Gibbs free energy and the Enthalpy.
  3. The whole class discussion focuses on the derivation processes, as to ensure that every student is capable of independently reproducing the derivations.

Reasons to spend class time on the activity

This activity is a good introduction to using Legendre transforms. The concept of the Legendre transform is first introduced by giving $F=U-TS$, but the small groups then have to apply this concept to find the Gibbs free energy and the Enthalpy. Because Legendre transforms are important for finding all of the Maxwell relations, this is a useful exercise to refer to in future class activities related to Maxwell relations.


Instructor's Guide

Authors: Corinne Manogue
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