PETE 310 Lectures # 32 to 34. Cubic Equations of State. …Last Lectures. Instructional Objectives. Know the data needed in the EOS to evaluate fluid properties Know how to use the EOS for single and multicomponent systems
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Equations of State (EOS) are mathematical relations between pressure (P) temperature (T), and molar volume (V).
For multicomponent mixtures in addition to (P, T & V) , the overall molar composition and a set of mixing rules are needed.
T
c
c
CP
e
e
sur
sur
T
Pres
Pres
2
v
P
1
T
1
L
2

P
has
es
V
L
V
Mo
Mo
la
la
r
r
V
V
o
o
lu
lu
m
m
e
e
PV Phase BehaviorPressurevolume behavior indicating isotherms for a pure component system
CP
CP
e
e
e
sur
sur
sur
T
T
Pres
Pres
Pres
2
2
4
4
T
T
1
1
v
v
3
3
5
5
A
A
A
2
2
2
1
1
P
P
1
1


L
L
1
1
1
A
A
A
1
1
1
¶
¶
æ
æ
ö
ö
P
P
1
1
1
0
0
2
2
2
>
>
ç
ç
÷
÷
0
0
V
V
~
~
0
¶
¶
è
è
ø
ø
V
V
T
T
2
2


P
P
has
has
es
2
2
L
L
V
V
7
7
6
6
Mo
Mo
la
la
r
r
V
V
o
o
lu
lu
m
m
e
e
with
Note: “x” could be either the molar volume, or the density, or the zfactor
where
where x1, x2 and x3 are the three roots.
From the shape of the polynomial we are only interested in the first quadrant.
CP
CP
e
e
e
sur
sur
sur
T
T
Pres
Pres
Pres
2
2
4
4
T
T
1
1
v
v
3
3
5
5
A
A
A
2
2
2
1
1
P
P
1
1


L
L
1
1
1
A
A
A
1
1
1
¶
¶
æ
æ
ö
ö
P
P
1
1
1
0
0
2
2
2
>
>
ç
ç
÷
÷
0
0
V
V
~
~
0
¶
¶
è
è
ø
ø
V
V
T
T
2
2


P
P
has
has
es
2
2
L
L
V
V
7
7
6
6
Mo
Mo
la
la
r
r
V
V
o
o
lu
lu
m
m
e
e
http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/tartalia.html
http://www.1728.com/cubic.htm
(i = 1, 2, 3 ,…Nc)