March 2013
Intermediate to advanced
406 pages
14h 48m
English
Content preview from Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
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Free Energy Perturbation Theories for Simple Fluids and Solids 143
where we have made use of the energy equation (2.46). Denoting
F =
1
β
β
0
U
E
dβ
= 2πNk
B
Tρ
β
0
dβ
∞
0
u
1
(
r
)
g
r, β
r
2
dr, (6.54)
we have
F
Nk
B
T
=
F
0
Nk
B
T
+
F
Nk
B
T
, (6.55)
which is the expression of the free energy in the generalized van der Waals (GvdW)
theory for simple fluids (Vera and Prausnitz 1972, Sandler 1985).
For the particular case of the SW fluid
U
E
= 2πNρ
∞
0
u
1
(
r
)
g
(
r, β
)
r
2
dr =−2πNερ
λσ
σ
g
(
r, β
)
r
2
dr =−
1
2
NεN
c
(
ρ, T
)
,
(6.56)
where N
c
(ρ, T) is the coordination number, that is, the average number of particles
that interact with every particle in the fluid. In the low-density limit g(r, β) →
e
−βu(
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