Physical Chemistry/State Functions

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The following demonstrates what's a state function and what's not a state function.

is not exact differential for a gas obeying van der Waals' equation, but is as demonstrated below:

We assume quasistatic situation, so .

Now, you take the cross partial derivatives.

They are not equal; hence, is not exact differential (not a state function).

However, if we take it will be exact differential (a state function).

Take the cross partial derivatives.

Both are equal making exact differential (a state function).