Activity: Generalized Leibniz Notation
Static Fields 2023 (6 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.
- group Small Group Activity 10 min. Student handout (PDF)
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)
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Media
In the middle column below, list each variable in the box connected to the description of the role of the variable.
- If \(a=c^3+7bc-5b^2\), find \[\left(\frac{\partial a}{\partial b}\right)_c\]
- For the same equation, 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 \(d\):
\[f=3x-5z^2+2xy\]
\[g=\frac{c^{1/2}b}{a^2}\]
\[h=\sin^2(\omega t)\]
\[j=a^x\]
- \[k=5 \tan\left(\ln{\left(\frac{V_1}{V_2}\right)}\right)\]
- face Energy and Entropy review
face Lecture
5 min.
Energy and Entropy review
Thermal and Statistical Physics 2020 (3 years)thermodynamics statistical mechanics
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
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