# Thermodynamic Analogies

## Prerequisites

Student should be able to:

• Read basic graphs to determine the values of different variables.
• Recall fundamental thermodynamic variables like pressure, volume, and temperature.

## In-class Content

### Lecture: PDM Dictionary (25 minutes)

Consider a canonical thermodynamic system that consists of a gas in a cylinder with a moveable piston. Help me draw a picture on the board.

SWBQ: On your small whiteboard, tell me a quantity you can measure for this system.

Students should generate the following. For each, follow up with: How would you measure _ for this system? Then label them the picture, along with a way to measure that quantity:

• Volume ($V$) - It can change if the piston moves and you can measure height with a ruler.
• Temperature ($T$) - Put a thermometer in it!
• Pressure ($p$) - If in equilibrium, $F_{net} = 0$, so if we account for the mass of the piston and the external pressure we can determine the pressure. (What happens if there's disequilibrium?)

Follow-up: How would you hold each of these variables constant?

There is an analogy between the gas in a piston and the PDM. With your group, discuss what is analogous between the two systems.

Good questions for helping students:
• How do you change quantities in the gas?
• How do you change quantities in the PDM?
• How do you hold quantities constant?
• Are there similarities in the dimensions of quantities between the two systems?

Final dictionary:

• $p \rightarrow F_L$
• $V \rightarrow x_L$
• $T \rightarrow$ ? (students may not have enough information, but it should go to $F_R$.)

We are probably going to need a fourth variable here. It turns out this fourth variable is Entropy ($S$), which you will learn about more during the rest of the course. This is a good place to note that holding entropy constant is equivalent to insulating the system and remarking on how this is different from holding temperature constant.

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