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state functions can be considered both extensive and intensive; a good example are heat capacity values. regular heat capacity, for example, is an extensive property because it depends on the mass amount in that particular moment. specific heat capacity(and molar heat capacity), on the other hand, is an intensive property, because it is a property that is universal to that particular material; it's innate. Heat capacity is the only state property that I've seen distinctly has this quality; I think properties like P & V are dependent on amounts, so they're extensive.
There's no direct relationship between these two concepts. State functions are simply properties that don't consider the path taken to achieve a given state, only considering the final state itself. Extensive properties are properties that change based on the amount of matter present. For example, heat capacity is an extensive property because the energy required to heat a given mass increases as the amount of mass increases. Specific heat capacity, on the other hand, is an intensive property because the term itself specifies that it is the heat required to increase the temperature of 1 gram of substance by 1 degree Celsius. Because it already specifies that it is a per gram term, the number of grams itself is irrelevant.
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