So I am having real trouble understand what equation of state are and how we form them. My issue stem from reading multiple sources. So I understand that an equation of state is used to building a relationship between variables to describe at state of a system.
For example P=P(V,T) where P=NKT/V is a function of state but then I read then I started reading about gibbs and Helmholtz and enthalpy ect and suddenly I am very confused.
So looking at gibbs for example.
We have two equations
but both kinda describe that state of the system. But I did not think an equation of state could be a differntial equation but according to one book I have read that relate dE to equation of state which has cause me great confusion.