The truncated virial equation (density form) is Z = B + 1 According to Eqn. 7.52, the

The truncated virial equation (density form) is Z = Bρ + 1 According to Eqn. 7.52, the virial coefficient is given by

where the low pressure limit of g(r) given by Eqn. 7.57 is to be used. Another commonly cited equation for the virial coefficient is Eqn. 7.59. Show that the two equations are equivalent by the following steps:

(a) Beginning with

insert the low-pressure limit for g(r), and simplify as much as possible.

(b) Integrate by parts to obtain

(c) Show that the left-hand side of the answer to part (b) may be written as

for a physically realistic pair potential. Then combine integrals to complete the derivation of Eqn. 7.59.

Transcribed Image Text:

-1 = 120 00 PNA NA (du) RT dr 0 g(r) 47²dr 7.52