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To illustrate with an example, work can't be a state function because it is proportional to the distance travelled or volume generated against an opposing force. So if you move an object from point A to B in a straight line, you do some work. But if you take a different, longer path that winds its way to B, it will take more work to do that even though the final and initial states are the same as if you just moved the object from A to B in a straight line.
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