Chemistry Reference
In-Depth Information
The hard-sphere terms are
+
()
−
(
)
3
HS
ξ
3
ξ
p
RT
=
6
ξ
3
1
ξξ
ξ
2
3
0
12
+
(9.14)
(
)
(
)
2
3
π
1
−
ξ
−
1
−
ξ
3
3
3
The hard-sphere quantities are
n
n
c
c
π
π
ρ
∑∑
ξ
=
ρσ
q
=
x
σ
q
;
q
=
0123
, ,,
q
j
j
j
j
6
6
j
=
1
j
=
1
(9.15)
n
n
c
c
π
π
ρ
∑∑
0
0
q
0
0
q
ξ
=
ρσ
=
x
σ
;
q
=
012
, ,,3
q
j
j
j
j
6
6
j
=
1
j
=
1
where
3
2
HS
σ
=
b
(9.16)
3
i
ii
π
For a pure component, 9.14 becomes
+
()
2
(
)
HS
=
ξ
ξ
ξ
ξ
3
−
ξ
p
RT
3
ρ
+
(9.17)
(
)
(
)
2
3
1
−
ξ
1
−
1
−
ξ
and Equation 9.15 plus Equation 9.16 give
ξ=
1
2
b
ii
HS
(9.18)
The elements of the
n
c
×
n
c
matrix
b
HS
in Equation 9.7 are calculated with the
following equations,
HS
HS
bb
+
2
HS
ii
jj
b
=
(9. 19)
ij
α
α
T
T
1
2
T
=>
073
.
i
*
T
HS
HS
∗
i
i
HS
bVb
=
,
b
=
(9. 20)
ii
ii
ii
i
T
T
=<
β
T
β
e
T
073
.
2
i
1
i
*
i
