Activities
Students consider the change in internal energy during three different processes involving a container of water vapor on a stove. Using the 1st Law of Thermodynamics, students reason about how the internal energy would change and then compare this prediction with data from NIST presented as a contour plot.
Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.
Student groups design an experiment that measures an assigned partial derivative. In a compare-and-contrast wrap-up, groups report on how they would measure their derivatives.
Students generate a list of properties a glass of water might have. The class then discusses and categorizes those properties.
This very quick lecture reviews the content taught in https://paradigms.oregonstate.edu/courses/ph423, and is the first content in https://paradigms.oregonstate.edu/courses/ph441.
In this remote-friendly activity, students use a microwave oven (and optionally a thermometer) to measure the latent heat of melting for water (and optionally the heat capacity). From these they compute changes in entropy. See also Ice Calorimetry Lab.
This lecture introduces the idea of entropy, including the relationship between entropy and multiplicity as well as the relationship between changes in entropy and heat.
These lecture notes covering week 8 of https://paradigms.oregonstate.edu/courses/ph441 include a small group activity in which students derive the Carnot efficiency.
These lecture notes from the ninth week of https://paradigms.oregonstate.edu/courses/ph441 cover phase transformations, the Clausius-Clapeyron relation, mean field theory and more. They include a number of small group activities.
These are notes, essentially the equation sheet, from the final review session for https://paradigms.oregonstate.edu/courses/ph441.
Problem
You are given the following Gibbs free energy: \begin{equation*} G=-k T N \ln \left(\frac{a T^{5 / 2}}{p}\right) \end{equation*} where \(a\) is a constant (whose dimensions make the argument of the logarithm dimensionless).
Compute the entropy.
Work out the heat capacity at constant pressure \(C_p\).
Find the connection among \(V\), \(p\), \(N\), and \(T\), which is called the equation of state (Hint: find the volume as a partial derivative of the Gibbs free energy).
- Compute the internal energy \(U\).
Problem
The Gibbs free energy, \(G\), is given by \begin{align*} G = U + pV - TS. \end{align*}
- Find the total differential of \(G\). As always, show your work.
- Interpret the coefficients of the total differential \(dG\) in order to find a derivative expression for the entropy \(S\).
- From the total differential \(dG\), obtain a different thermodynamic derivative that is equal to \[ \left(\frac{\partial {S}}{\partial {p}}\right)_{T} \]
This short small group activity introduces students to the Leibniz notation used for partial derivatives in thermodynamics, in which the variables being held constant are given explicitly. Students are guided to associate variables to their proper categories.