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## Naming and Classifying Thermodynamic Variables: Instructor's Guide

### Main Ideas

- Recognizing thermodynamic variables
- Analyzing dimensions of variables
- Defining intensivity & extensivity
- Comparing and categorizing thermodynamic variables
- Finding conjugate pairs

### Students' Task

##### Part 1

*Estimated Time: 20 minutes without wrap-up *

- Students must write down a variable they think would be important in thermodynamics.
- As a class, students will discuss any variables that are redundant or not likely to appear in thermodynamics.
- Class will discuss the units of each thermodynamic variable.

##### Part 2

*Estimated Time: 5 minutes*

- Students must determine which thermodynamic variables are intensive or extensive.

##### Part 3

*Estimated Time: 5 minutes *

- Students are asked to find the conjugate pairs among the thermodynamic variables.

### Prerequisite Knowledge

##### Part 1

- Familiarity with introductory thermodynamics
- Familiarity with analysis of variable dimensions
- Familiarity with important thermodynamics variables

##### Part 2

- Basic understanding of extensivity vs intensivity

##### Part 3

- Basic understanding of conjugate pairs

### Props/Equipment

- Tabletop Whiteboard with markers
- Notecards

### Activity: Introduction

##### Part 1

To begin the activity, students are asked to write down on their small whiteboards a thermodynamic variable they believe is important for thermodynamics. The instructor then asks students to hold up their whiteboards and writes the variables given by each student on the board.

##### Part 2

Students will be most successful if they have been introduced to the definition of intensive and extensive, as well as what intensivity and extensivity imply for a variable. Using their notecards containing important thermodynamic variables and their dimensions, students are asked to sort the thermodynamic variables into an intensive group and an extensive group. The instructor may also have students write their groupings onto small white boards if they wish to present and compare the answers of students.

##### Part 3

Using their notecards, students are asked to pair up the thermodynamic variables that make conjugate pairs. Students can be asked to write their conjugate pairs on a small white board if the instructor wishes to present any answers.

### Activity: Student Conversations

##### Part 1

Doing this as a whole class seemed like a good choice. Each group had a different list, so comprising a huge list was quite interesting. It eliminated questions that many of us may have had later about whether variables were thermodynamic variables or not. The few minutes spent on it seemed to be an excellent way to introduce the course, prior to other lectures about the variables. -Amanda Abbott

##### Part 2

After viewing several years worth of videos, it appears that students make the most connections if a basic definition is given first, rather than just allowing students to group them by themselves. While there are still variations among groups, the variations are much smaller and produce better discussions than if there is too much freedom given to groups. -Amanda Abbott

##### Part 3

### Activity: Wrap-up

##### Part 1

Before concluding **Part 1**, any important thermodynamic variables that were not discovered in the student conversations should be written on the board along with their dimensions. The instructor should also have students write down the important thermodynamic variables (and their dimensions) selected in the student conversations each on a single note card. It should be emphasized that the majority of the variables given by students *could* be thermodynamic variables, but only several of them will be relevant to most thermodynamic problems, especially in the Energy and Entropy course.

##### Part 2

Important intensive and extensive variables:

Intensive | Extensive |
---|---|

$p$ | $V$ |

$\sigma$ | $A$ |

$\tau$ | $L$ |

$T$ | $S$ |

$\mu$ | $N$ |

##### Part 3

Before concluding **Part 3**, students should notice that the conjugate pairs have one intensive and extensive variable in them. It can also be made apparent that, among the conjugate pairs, the thermodynamic force term is always the intensive variable while the displacement term is always the extensive variable. Students should also notice and be informed that the product of any conjugate pair has dimensions of energy. This closing discussion would lead well into a lecture concerning how the internal energy of systems is expressed in terms of conjugate pairs; this is clearly visible in the thermodynamic identity.

Important Conjugate pairs that should be mentioned:

$pV$ *(Pressure & Volume)*

$\sigma A$ *(Surface Tension & Area)*

$L \tau$ *(Length & Tension)*

$ST$ *(Entropy & Temperature)*

$N \mu$ *(Number & Chemical Potential Energy)*

### Extensions

##### Part 1

##### Part 2

If students are still confused about some of the properties, attempt to associate the property with the class. For example, while the number of students in the whole class is twice as large as half the class, the average body temperature is still the same. Though the number of students doubles, with the weight and volume doubling as well, the density remains the same.