Neither q nor w is a state function but q+w is a state function. Why?

In thermodynamics, a state function is a property whose value depends only on the current state of the system, not on how that state was reached. Both heat (q) and work (w) are not state functions because they depend on the path taken to reach a particular state.

However, their sum, q + w, is a state function. This is because the total energy change of a system, which is represented by q + w, depends only on the initial and final states of the system, not on the specific path taken to transition between those states.

In other words, while heat and work individually may vary depending on the process, their sum is independent of the process and only depends on the initial and final states of the system, making it a state function.