PDM Variables

Highlights of the activity

1. This small group activity is designed to help students become familiar with the Partial Derivative Machine (PDM), a mechanical system which allows students to measure partial derivatives and determine various physical quantities, including potential energy.
2. Students use the PDM to determine which properties of the physical system they can control and which ones they can measure.
3. The whole class wrap up discussion focuses on the fact that not all of the properties of the physical system are independently controllable, and leads students to think about what is being held fixed when they measure a derivative.

Reasons to spend class time on the activity

This activity occurs during the “Interlude”, a brief course on the basic mathematics used in the “Energy and Entropy” Paradigm. This course primarily focuses on an introduction to partial derivatives and total differentials. We would like our students to have an understanding of how to measure partial derivatives, as well as understand that the “thing held constant” both has physical and mathematical consequences. This activity uses the Partial Derivative Machine (PDM) to gain a mechanical intuition of how to measure partial derivatives, avoiding the nuances of a thermodynamical system. Using the PDM, the students learn which properties are controllable, which properties are measurable, and ultimately how to measure the derivative using small differences.

For a description of the Partial Derivative Machine visit this page.

Reflections

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Instructor's Guide

• Wiki version