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A good example of state vs path functions is thinking of two points on a map, A and B, that are 100 km apart if you were to draw a straight line from one to the other. That 100km is representative of a state function. There are two roads to get from A to B, one road is 120km, the other is 180km. This is representative of a path function, as the distance from A to B by this would depend on which road (path) is taken.
State functions don't depend on the "path" they take. Usually they'll usually just involve the intial and final states. Some examples are enthalpy, temperature, density, volume, and pressure. Nonexamples have many parameters/variables in their equations because we have to consider them when calculating their values, meaning they don't depend on the path they take. Some nonexamples are work and heat.
state functions only depend on the final value, not the way you got there. for example in a state function it wouldn't matter if you walked down bruinwalk or through the tennis courts to get to Lavelle's lecture, it only matters that you showed up at the lecture and that the lecture is your current location/state.
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