Page 458 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.2 The Energy Balance 429
8.2.2 Evaluating the Work Term

It is customary to separate the work term, W, into’jlow work and other
work, Ws. Flow work is work that is necessary to get the mass into and out of
the system. For example, when shear stresses are absent, we write

[rate of flow work]
1=1 /In
Flow work and n h
/yyI
shaft work W = -c F,PV, + F,PV, + Ws (8-4)
,:1
where P is the pressure (Pa) and VI is the specific volume (m3/mol of i)
The term Firs, often referred to as the shu$ work, could be produced from
such things as a stirrer in a CSTR or a turbine in a PFR. In most instances, the
flow ,work term is combined with those terms in the energy balance that repre-
sent the energy exchange by mass flow across the system boundaries. Substi-
tuting Equation (8-4) into (8-3) and grouping terms, we have

The energy E, is the sum of the internal energy (U, ), the kinetic energy (uf/2),
the potential energy (gzi), and any other energies, such as electric or magnetic
energy or light:

UL
E, = U, + 2 + gz, + other (8-6)
2
In almost all chemical reactor situations, the kinetic, potential, and “other”
energy terms are negligible in comparison with the enthalpy, heat tra~~deir, and
work terms, and hence will be omitted; that is,

E, = U, (8-7)
We recall that the enthalpy, H, (J/mol), is defined in terms of the internal
energ:y U, (J/mol), and the product PV, (1 Pa.m3/mol = 1 J/mol.):

Enthalpy HI = U, + PV, (8-8)
Typic(a1 units of HI are
(HI 1 = moli or Mi xi
cal
Btu
J
or
Enthalpy carried into (or out of) the system can be expressed as the sum
of the net internal energy carried into (or out of3 the system by mass flow plus
the flow work:
F,H, = Fi(Ui+ PV,)