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## Activity Name: Instructor's Guide

### Main Ideas

### Students' Task

*Estimated Time: 30 min*

### Prerequisite Knowledge

Students should already be familiar with the Partial Derivative Machine and the vocabulary allowing them to translate between the PDM and thermodynamic systems. Students should be able to identify work as area under a curve with the proper variables graphed!

### Props/Equipment

- Tabletop Whiteboard with markers

### Activity: Introduction

Students are told to consider the Partial Derivative Machine as an example of an elevator, where one side (the left) is the elevator itself, which can be loaded with “people” represented by 100 g weights. (The right side can be conceptualized as the counterweights, though we typically allow students to discover this on their own.) Students are then told to:

- Load the elevator with 4 people
- Raise the elevator 3 floors (3 cm)
- Unload the elevator
- Lower the elevator to the original floor

Students should be warned not to take data during this activity, but to view it as an engineering strategy problem.

### Activity: Student Conversations

When students load the elevator, they tend to leave the force on the other side constant, which causes the height of the elevator to change abruptly. Ask students why this is undesirable in an elevator! What should be held constant instead and why?

When students raise the elevator, do they add one big weight or a lot of small weights? Which is more desirable?

The purpose of the elevator is to do work on something (lifting the people). This is also the goal of a heat engine. Where did the energy to do this work come from?

Why is it necessary to unload the elevator and return it to the original floor? What would be true physically about the elevator's usefulness if this step were not carried out? What is true mathematically about the state of the system at the end of the cycle?

### Activity: Wrap-up

Students should be asked to think about what a cycle like the elevator would look like for a system like a gas in a piston. Which quantities are analogous? What kinds of cycles are possible? What would these cycles look like physically?

### Extensions

There is a homework problem for this activity in which students are given data and asked to do calculations analogous to those that would be done for a thermodynamic cycle.