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

Surfaces/Bridge Workshop 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.
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
    • 2564/ContourSquishability.gif
    • 2564/thermo_states_blacksquare_tpu_sv_horizlabels_axis_lg.png

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

Learning Outcomes