An equation of state is a constitutive relation among thermodynamic state properties.

For a simple compressible substance it often relates pressure, specific volume and temperature:

$$f(p,v,T)=0.$$

The equation is not a conservation law. It describes the material itself and must come from a model, experiment or microscopic theory.

Suppose a model has the form

$$p=\frac{RT}{v-b}-\frac{a}{v^2},$$

where $a$ and $b$ are material-model parameters and $R$ is a constant for the chosen substance model. Given $T$ and $v$, the equation predicts $p$. Given $p$ and $T$, solving it for $v$ may produce more than one mathematical root in regions where phase behavior is important.

Different equations of state are useful in different regimes. A very simple model may be accurate for dilute gases but fail near condensation or at high density. Engineering thermodynamics therefore treats an equation of state as an approximation whose range of validity must be checked.