Environmental Engineering Reference
In-Depth Information
We rewrite Eq. (2.2) as
RT
a
ab
3
2
vb
v v
p
0
.
(2.7)
pp
T
=
, where
p
and
T
-critical pressure and tempera-
ture, all three roots of Eq. (2.7) are equal to the critical volume
When
p
=
p
and
T
k
v
k
RT
a
ab
.
(2.8)
3
2
v
b
k
v
v
0
p
p
p
k
k
k
v
=
v
=
v
=
v
Because the
, then Eq. (2.8) must be identical to the equa-
1
2
3
k
tion
3
3
2
2
3
vv vv vv
.
vv
v
3
vv
3
vv v
0
(2.9)
1
2
3
k
k
k
k
Comparing the coefficients at the equal powers of
v
in both equations leads to
the equalities
RT
a
ab
2
3
b
k
3;
v
3;
v
.
v
(2.10)
k
k
k
p
p
p
k
k
k
Hence
v
2
3;
a
vp b
k
kk
3
(2.11)
p
,
v
,
T
, we
Considering (the Eq. (2.10)) as equations for the unknowns
obtain
a
8
a
p
;
v
3;
bT
.
(2.12)
k
2
k
k
27
b
27
bR
From Eqs. (2.10) and (2.11) or (2.12) we can find the relation
RT
pv
8
3
k
(2.13)
kk
Instead of the variables
p
,
v
,
T
let's introduce the relationship of these vari-
ables to their critical values (leaden dimensionless parameters).
v
T
p
τ
=
w
=
π
=
;
;
.
(2.14)
T
V
p
k
k
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