Environmental Engineering Reference
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V , y i , T 3 , P 3
F 1 ,w i ,T 1 ,P 1
F 2 , x i , T 2 , P 2
L , x i , T 4 , P 4
Figure 3.6 A non-adiabatic two-phase equilibrium-based process.
The above examples involve only intensive (not a function of process volume, such as
density) variables. The analysis can be expanded to include extensive (total flowrate, total
heat load, for example) variables.
Figure 3.6 shows a non-adiabatic (heat is either lost to or gained from the environment
surrounding the control volume) two-phase equilibrium-based process. There are two feed
streams and two exit streams. The exit streams are in thermodynamic equilibrium.
The number of independent variables is:
4 C
(component mole fractions)
4
(stream flowrates)
4 T
4 P
Q
(net heat exchange (non-adiabatic process))
13
The number of independent equations is:
4
4 C
+
(sum of mole fractions equals unity)
C
(component mass balances)
1
(energy balance)
C
(phase equilibrium relationships)
1
(temperature equality (exit T are equal))
1
(pressure equality (exit P are equal))
2 C
+
7
DF
=
V
E
=
4 C
+
13
(2 C
+
7)
=
2 C
+
6
.
To solve this problem uniquely, one would have to specify 2 C
6 variables. One example
would be to specify the composition, flowrate, T and P of the two feed steams. If the exit
streams are not in thermodynamic equilibrium, then the phase equilibrium relationships
cannot be used and the exit streams may not be at the same T and P .
+
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