# What exactly constitutes and Equation of State?

1. Sep 29, 2011

### spacelike

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 exactly which variables to find a relation between.

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

Last edited: Sep 29, 2011