• Work
• Processes
• Cycles

Estimated Time: 30 min

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!

• Tabletop Whiteboard with markers
• Partial Derivative Machine

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 cats represented by 50 g weights. The students imagine themselves holding onto the right side of the elevator and controlling it by pulling on the string. Students are then told to:

• Load the elevator with the first 2 cats
• Raise the elevator 2 floors (2 cm) from the Food to the Sleeping Area
• Unload the elevator
• Lower the elevator to the original floor
• Repeat the process for the final 2 cats

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

Students should be asked to qualitatively sketch graphs of $x_L$ vs $F_L$, $x_R$ vs $F_R$, and $x_L$ vs $x_R$.

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 cats). 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?

Students should understand that they did positive work on the right side of the elevator, which in turn did positive work on the cats (meaning that the cats did negative work on the elevator).

• 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.

• 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?