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A state property is a value that is determined by the current state, and not dependent upon the path taken to obtain that state. For example, E, P, V, T, and Density are all things that could be considered state properties. These properties can also be added or subtracted. Examples of properties that are not state properties are Work and Heat, because they depend upon the path taken to get there.
The example of altitude in the lecture from last week is a good example, as for a state function we just see the initial and final and compare it regardless of the path take (the two teams traveled a total different amount of distance but ended up in the same point of altitude). However in terms of work it would be different values.
For example volume, if you have 10 L of water then add 7 L and removed 3 L, you will end up with 14 L left while the overall change in of water would be 3L even thought there were changes in the intermediate steps. With this example, it shows that state functions does not depend on the steps in-between but instead the initial and final states.
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