Introducing Legendre Transforms

Highlights of the activity

1. Given $F=U-TS$, small groups of students will find the Helmholtz free energy equation.
2. By adding or subtracting terms of $TS$ or $pV$, the groups must find functions which are only a function of entropy, pressure, and number or temperature, pressure, and number.
3. Students will derive the Gibbs free energy and the Enthalpy.

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.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

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