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# Isowidth and Isoforce Stretchability

**Keywords:**Thermo & Stat Mech, Partial Derivative, PDM, Interlude, Small Group Activity

### Highlights of the activity

- This small group activity is designed to show students how to calculate derivatives using small differences while paying attention to what is held constant.
- Students use the Partial Derivative Machine to measure partial derivatives while keeping different variables of the system constant.
- The whole class discussion focuses on how to represent derivatives in multiple ways, experimentally measure derivatives, and show that the “thing held constant” both has physical and mathematical consequences.

### 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 how to measure the derivative using small differences, and observe that the property being held constant really matters.

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