In short
A state function is a property whose value depends only on the present state of a system, not on the path by which it arrived there. Internal energy, enthalpy, entropy and pressure are state functions.
The change in a state function between two states is the same by any route. Heat and work are path functions: their values depend on how the change was carried out. This is why Hess's law works for enthalpy: the total enthalpy change from reactants to products is fixed, even though the route may differ. Path length is also a path-dependent quantity.
Water is heated from to either on a hot plate or by stirring. The internal energy change is the same by both routes, but the heat and the work are not.
Also searched as: path function vs state function, state function, path vs state functions, path and state functions.
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