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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Some Basics on Statistical Mechanics 23
The compressibility factor can be expanded in power series of the density, the
virial expansion,
Z = 1 +
∞
n=2
B
n
(
T
)
ρ
n−1
, (2.37)
where the virial coefficients B
n
(T) depend only on temperature and are related to
the pair potential. In particular, the second virial coefficient of a fluid with spheri-
cally symmetric pair potential can be easily obtained from the virial equation (2.36)
introducing the low density expression (2.35) of the RDF, yielding
B
2
=−
2π
3
β
∞
0
du
(
r
)
dr
e
−βu
(
r
)
r
3
dr =−2π
∞
0
f
(
r
)
r
2
dr, (2.38)
or
B
2
=−
1
2
V
f
(
r
12
)
dr
12
, (2.39)
where f (r) = e
−βu(r)
−1 is the Mayer function. The derivation of the expressions for ...
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