Students consider how changing the volume of a system changes the internal energy of the system. Students use plastic graph models to explore these functions.

Student discuss how many paths can be found on a map of the vector fields \(\vec{F}\) for which the integral
\(\int \vec{F}\cdot d\vec{r}\) is positive, negative, or zero. \(\vec{F}\) is conservative.
They do a similar activity for the vector field \(\vec{G}\) which is not conservative.

Students examine a plastic "surface" graph of the gravitational potential energy of a Earth-satellite system to make connections between gravitational force and gravitational potential energy.

Students examine a plastic "surface" graph of the electric potential due to two changes plates (near the center of the plates) and explore the properties of the electric potential.

Students will estimate the work done by a given electric field. They will connect the work done to the height of a plastic surface graph of the electric potential.

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 prompted to consider the scalar superposition of the electric potential due to multiple point charges. First a single point charge is discussed, then four positive charges, then an electric quadrupole. Students draw the equipotential curves in the plane of the charges, while also considering the 3D nature of equipotentials.

Little is needed. Some students might be bothered by thinking about entropy if it hasn't been mentioned at all in class. Try doing this activity as a follow-up to the “Changes in Internal Energy" about the first law of thermodynamics.

Students determine the “squishibility” (an extensive compressibility) by taking \(-\partial V/\partial P\) holding either temperature or entropy fixed.

Students need to understand that the surface represents the electric potential in the center of a parallel plate capacitor. Try doing the activity “Electric Potential of a Parallel Plate Capacitor” before this activity.

Students should know that

objects with like charge repel and opposite charge attract,

object tend to move toward lower energy configurations

The potential energy of a charged particle is related to its charge: \(U=qV\)

The force on a charged particle is related to its charge: \(\vec{F}=q\vec{E}\)

Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.

In this activity, students will explore how to calculate a derivative from measured data. Students should have prior exposure to differential calculus. At the start of the activity, orient the students to the contour plot - it's busy.