[Luyben] Process Mod.. - Student subdomain for University of Bath

FUNDAMENTALS 25
For liquids the PP term is negligible compared to the U term, and we use the
time rate of change of the enthalpy of the system instead of the internal energy of
the system.
d@ W
-=F,p,ho-Fph+Q--VkC,
dt
The enthalpies are functions of composition, temperature, and pressure, but
primarily temperature. From thermodynamics, the heat capacities at constant pressure,
C, , and at constant volume, C,, are
cp=(gp c”=(g)” (2.25)
To illustrate that the energy is primarily influenced by temperature, let us
simplify the problem by assuming that the liquid enthalpy can be expressed as a
product of absolute temperature and an average heat capacity C, (Btu/lb,“R or
Cal/g K) that is constant.
h=C,T
We will also assume that the densities of all the liquid streams are constant. With
these simplifications Eq. (2.24) becomes
WT)
- = pC&F, To - FT) + Q - IVkC, (2.26)
PC, d t
Example 2.7. To show what form the energy equation takes for a two-phase system,
consider the CSTR process shown in Fig. 2.6. Both a liquid product stream F and a
vapor product stream F, (volumetric flow) are withdrawn from the vessel. The pressure
in the reactor is P. Vapor and liquid volumes are V, and V. The density and
temperature of the vapor phase are p, and T, . The mole fraction of A in the vapor is
y. If the phases are in thermal equilibrium, the vapor and liquid temperatures are
equal (T = T,). If the phases are in phase equilibrium, the liquid and vapor compositions
are related by Raoult’s law, a relative volatility relationship or some other
vapor-liquid equilibrium relationship (see Sec. 2.2.6). The enthalpy of the vapor
phase H (Btu/lb, or Cal/g) is a function of composition y, temperature T,, and
pressure P. Neglecting kinetic-energy and potential-energy terms and the work term,
Fo VL CA P T
CA0
I
PO
To
P
FIGURE 2.6
Two-phase CSTR with heat removal.