Partial Derivatives from a Contour Map--Thermo Version

Small Group Activity: Partial Derivatives from a Contour Map--Thermo Version

None 2023

Students calculate two different (thermodynamic) partial derivatives of the form \(\left(\frac{\partial A}{\partial B}\right)_C\) from information given on the same contour map.

Small Group Activity schedule 30 min. description Student handout (PDF)

What students learn They must recognize that

they have to calculate the derivative as a ratio of small changes
they must identify the numerator and denominator variables on the graph.
they must pick two points that lie along a curve with \(C=\)constant.

Media

Find the following derivatives \begin{equation} \left(\frac{\partial p}{\partial T}\right)_S\qquad\qquad\qquad \left(\frac{\partial p}{\partial V}\right)_T \end{equation} from the contour map below

Keywords

Learning Outcomes