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# Constant Lines in the U-V Plane

**Keywords:**Partial Derivative, Interlude, Small Group Activity

### Highlights of the activity

- This small group activity is designed to show students that lines which were perpendicular in one coordinate system are not necessarily perpendicular in others.
- Students use erasable markers to draw constant value lines for two functions of the same independent variables.
- The whole class discussion focuses on ensuring that students understand that lines which were perpendicular in one coordinate system are not necessarily perpendicular in others.

### Reasons to spend class time on the activity

We have found that many students have worked mostly with variables that are independent of one another. However, in thermodynamics, many of the variables are dependent on each other where changing one must change the other. This exercise helps students to visualize graphically that whenever dealing with thermodynamic variables, there is no sense in which those variables are perpendicular to (i.e. independent of) each other.