Path functions are properties or quantities whose values depend on the transition of a system from the initial state to the final state. The two most common path functions are heat and work.
For path functions, the path from an initial state to the final state is crucial. Each part, or segment of the path to the final state is necessary to take into account. For example, a person may decide to hike up a 500 ft mountain. Regardless of what path the person takes, the starting place and the final place on top of the mountain will remain constant. The person may decide to go straight up to the mountain or decide to spiral around to the top of the mountain. There are many different ways to get to the final state, but the final state will remain the same.
Two important examples of a path function are heat and work. These two functions are dependent on how the thermodynamic system changes from the initial state to final state. These two functions are introduced by the equation ΔUΔU which represents the change in the internal energy of a system.
ΔU=q+w