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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Hard-Sphere Fluid and Solid 127
(1996b,c) determine the parameters by imposing appropriate conditions. The first one
consists in approximating the average position of the nearest neighbors calculated
from g
(1)
(r) with that calculated from g
(1)
0
(r). From Equation 2.33 this condition is
equivalent to
∞
σ
g
(
1
)
(
r
)
r
3
dr
∞
σ
g
(
1
)
(
r
)
r
2
dr
=
∞
σ
g
(
1
)
0
(
r
)
r
3
dr
∞
σ
g
(
1
)
0
(
r
)
r
2
dr
. (5.104)
The second condition, which is exact, guarantees that the number of particles within
the first peak is the coordination number of the lattice
4πρ
∞
σ
g
(
1
)
(
r
)
r
2
dr = n
1
. (5.105)
The third condition, also exact, is the fulfillment of the virial equation (2.43) for a
given EOS, as, for example, ...
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