Example 1:

What is the virial equation of state? Prove that B´ = B/[RT]
Ans: The virial equation of state is expressed as a power series in terms of reciprocal volumes:

This is the pressure explicit virial equation in which the coefficients B, C, D, etc., are the second, third, fourth virial coefficients. Alternatively, we can have the volume explicit virial equation

The pressure explicit virial expression Eqn can be presented as

(A)

Putting the value of P on the RHS of Eqn(3),we get

(B)

Both Eqns (A) and (B) are identical. They represent the virial equation of state as a power series in reciprocal volumes. So equating the coefficients of I/v²
BRT = B´(RT)²

Therefore

B´ = B/[RT]