Equation of state

The equation of state of a physical system in thermal equilibrium is a function that takes a system's thermodynamic, macroscopic variables as arguments and constrains them. This is usually pressure, volume and temperature:

The actual form of $f$ depends on the substance. $f$ is regarded as continuous and differentiable, expect at most at special points.

The equation of state leaves only two of the three variables independent and it can be represented as a surface in three dimensional phase space. The system is then constrained to this surface. Reversible transformations can be represented as curves that lie on this surface, whereas irreversible transformations lie anywhere in space, except fully on the surface, or may not be representable at all¹. Moreover, intermediate points in irreversible transformations do not have uniform values for variables and cannot therefore be represented as points in space.