Virial expression

The relation between pv and p in a term of power series may be expressed as

(2.144)

For any gas

(2.145)

(2.146)

An alternative expression is

(2.147)

Both expressions in Eqs.(2.146) and (2.147) are known as virial expansions or virial equations of state, first introduced by the Dutch physicist, Kammerlingh onnes B´, C´, B, C,…….. etc. are called virial coefficients. B´ and B are called second virial coefficients, C´ and C are called third virial coefficients, and so on. For a given gas, these coefficients are functions of temperature only.

The ratio is called the compressibility factor, Z. for an ideal gas Z=1. The magnitude of Z for a certain gas at a particular pressure and temperature gives an indication of the extent of deviation of the gas from the ideal gas behavior.

The virial expansions become

(2.148)

and

(2.149)

The relations between B', C' and B, C… can be derived as follows

(2.150)     (2.151)