The tutor defines the term state function.

A state function is one that is independent of path. Another way of explaining it: for a state function, if you end up where you started, nothing has changed.

An example of a state function is heat content of a cup of water. Let’s imagine it starts at 25°C. If you heat it from 25°C to 99°C, then let it cool back to 85°C, its ending heat content will be the same as if you just heat it from 25°C to 85°C. The heat content of an object of fixed mass depends only on its temperature, not how it arrived at that temperature.

Gravitational potential energy is also a state function. It depends on mass and height according to

E_gp=mgh

Therefore, a given object’s gravitational potential energy depends on its current height, but not how it arrived there.

Position is a state function, but distance is not. A runner who travels exactly one lap of a track has not changed position, but has travelled 400m (typically). Running another lap, the runner’s position will be restored, but their distance will increase to 800m.

Source:

White, J. Edmund. Physical Chemistry: College Outline Series. New York: Harcourt Brace Jovanovich, 1987.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.