## Activity: Generalized Leibniz Notation

Static Fields 2022 (4 years)
This short small group activity introduces students to the Leibniz notation used for partial derivatives in thermodynamics; unlike standard Leibniz notation, this notation explicitly specifies constant variables. Students are guided in linking the variables from a contextless Leibniz-notation partial derivative to their proper variable categories.
What students learn
• Leibniz notation is learned or refreshed
• Explicit denotation of constant variables (the modified Leibniz notation used in thermodynamics is unique in this way)
• Media
1. In the middle column below, list each variable in the box connected to the description of the role of the variable.

2. If $a=c^3+7bc-5b^2$, find $\left(\frac{\partial a}{\partial b}\right)_c$
3. For the same function, find $\left(\frac{\partial b}{\partial c}\right)_a$
• assignment Zapping With d 1

assignment Homework

##### Zapping With d 1
Energy and Entropy 2021 (2 years)

Find the differential of each of the following expressions; zap each of the following with $d$:

1. $f=3x-5z^2+2xy$

2. $g=\frac{c^{1/2}b}{a^2}$

3. $h=\sin^2(\omega t)$

4. $j=a^x$

5. $k=5 \tan\left(\ln{\left(\frac{V_1}{V_2}\right)}\right)$

• face Energy and Entropy review

face Lecture

5 min.

##### Energy and Entropy review
Thermal and Statistical Physics 2020 (3 years)

This very quick lecture reviews the content taught in Energy and Entropy, and is the first content in Thermal and Statistical Physics.
• group Paramagnet (multiple solutions)

group Small Group Activity

30 min.

##### Paramagnet (multiple solutions)
• Students evaluate two given partial derivatives from a system of equations.
• Students learn/review generalized Leibniz notation.
• Students may find it helpful to use a chain rule diagram.

Author Information
Corinne Manogue and Ian Founds
Keywords
Learning Outcomes