Real substances are often described by measured or computed property tables rather than one simple equation of state. Tables may list saturated-liquid and saturated-vapor values, superheated-vapor states or compressed-liquid states.

The first step is to identify the thermodynamic region from the known properties. Then choose the appropriate table and locate the state.

When the desired state lies between tabulated entries and the interval is sufficiently small, linear interpolation estimates a property $y$:

$$y\approx y_1+\frac{x-x_1}{x_2-x_1}(y_2-y_1).$$

Suppose a superheated-vapor table at fixed pressure gives specific volume $v_1=0.55\ \mathrm{m^3/kg}$ at $T_1=300^\circ\mathrm C$ and $v_2=0.59\ \mathrm{m^3/kg}$ at $T_2=340^\circ\mathrm C$. At $315^\circ\mathrm C$,

$$v\approx0.55+\frac{15}{40}(0.04)=0.565\ \mathrm{m^3/kg}.$$

Interpolation is a numerical approximation, not a new thermodynamic law. Near critical points or strongly curved property behavior, closer data or a more accurate property model may be needed.