(adsbygoogle = window.adsbygoogle || []).push({}); What exactly constitutes an Equation of State?

As the title says I'm not quite sure what I need to get to have an equation of state in thermodynamics.

I think I understand that an equation of state is an equation that relates different state variables of the system such as volume, temperature, pressure, chemical potential, etc...

However, I am not sure how to know exactlywhichvariables to find a relation between.

For example isn't this the equation of state for an ideal gas? [tex]U=\frac{3}{2}Nk_{b}T[/tex]

So that is a relation between the number of particles, internal energy, and temperature.

We've also done problems where we find from a given Gibbs Free Energy the equation of state of some gas and the final relation is between volume, pressure, and temperature.

So how do I know which variables to get a relation between?

For example we have another problem where given entropy (as a function of energy; with volume constant) find the equation of state.

I didn't ask this in the homework section because it's not a question about my homework.. sure it might help on my homework but I am not asking about a specific problem, my issue is conceptual. It's something I'm confused about in general.

Thanks.

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# What exactly constitutes and Equation of State?

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