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State properties are quantities that are independent of how a substance was prepared. Work is dependent on path, so it is not a state function. Since work is not a state property/function, heat cannot be either, since the first law of thermodynamics states that the change in the initial energy of a system is equal to the sum of heat and work transferred between the system and surrounding areas.
State properties do not depend on the path taken; they depend on the state of the substance. Work and heat are not considered because they take into account the path taken. Ex. In work, the formula is force times distance. If you have two molecules at the same starting point, molecule A that reaches point x in a straight line and molecule B that reaches point x in a exaggerated zigzag pattern, then although they both reach the same end point, their distances are different and therefore will have different values for work.
State properties do not depend on the path taken. For example, for work, it depends on the distance traveled. A system that takes a shorter path will have performed less work than a system that a system that took a longer path. The final value is dependent on how the system was carried out.
I think Lavelle explained this concept well with the analogy of a mountain and hikers. If one group of hikers took a steep path to reach the top of the mountain and another group took a leisure path to the top of the mountain both groups have ended up at the same spot regardless of which path was taken.
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