Question

Why is the work done is a path function?

Answer 1

Path Functions: Path functions are qualities or quantities whose values rely on a system's transition from its starting to the final state. Heat and work are the two most prevalent path functions.

Explanation:

Let us consider the following P-V Diagram:

:

1. The work done by a system is given by the area under the curve of the P-V Graph.
2. The initial and final state of the process is the same. Consider path A, the area under this curve is greater than the area under curve path B. Hence, the work done by the system if it took path A is greater.
3. If work done was not a path function, the work done by this system should have been equal in both paths. But by analyzing, we can conclude that the work done is path-dependent.

Hence, it is proven that the work done by a system is path-dependent, and therefore it is a path function.