71A equation of state is a relation among the state variables of a system. There are many possible ways to express them and one of such is the virial equation of state.
It was given by Kammelingh Onnes and also known as Kamerlingh Onnes Equation state. It is basically derived from statistical mechanics where mechanical considerations among system components (herein gas molecules) are considered.
Express Compressibility of a gas Z=f(p) at some constant T and n.
If using Taylor's theorem, You expand it, You'll get what is called the Virial equation of state and B,C,D... are virial coefficients dependent on gas temperature T and gas molecules. If appropriate assumptions are made about the mathematical form of intermolecular forces, theoretical expressions can also be developed for each of the coefficients. In this case B corresponds to interactions between pairs of molecules, C to triplets, and so on.
Validity
It can also be used to work out the Boyle Temperature (the temperature at which B = 0 and ideal gas laws apply) from a and b from the Van der Waals equation of state, if you use the value for B shown below:
