Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

112 Perturbation Theories for Fluids and Solids

of Equation 5.15 into the virial equation for the HS fluid (2.43), taking into account

also the relationships (5.13), one obtains (Thiele 1963, Wertheim 1963)

Z

v

PY

=

1 +2η +3η

2

(

1 −η

)

2

, (5.16)

which is the PY virial equation.

Alternatively, using expression (5.15) and taking into account the compressibility

equation in the form of (4.7), one obtains (Thiele 1963) the PY compressibility

equation

Z

c

PY

=

1 +η +η

2

(

1 −η

)

3

, (5.17)

which is the same as the SPT equation (5.10).

The same result of Equation 5.15, and hence the PY compressibility equation

(5.17), can be obtained from Equations 4.8 and 4.9, taking into