An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 121

U j , other than in an electro-hydro facility, or for simple flow loop calcu-
lations. Thus, Eqn (3.123) can be simplified to

In most cases, E j z

X

N S

X

N S

d ð nU Þ

¼ Q W s þ

F j0 H j0 F j H j (3.127)

d t

j ¼1 j ¼1

The energy balance equation for open system is reduced to that for closed system if there is
no flow in or out of the system, i.e. F 0. When chemical reaction occurs, internal energy

changes and so are the enthalpies according to the species change.
Since

¼

X

N S

nU ¼ nH pV ¼ H j n j pV (3.128)

j ¼1

and enthalpy is only a function of temperature for ideal gases and nearly so for condensed
matters (i.e. liquids or solids),

d H j
d t ¼

d T
d t

C P j (3.129)

where C Pj is the molar heat capacity of species j. Differentiating both sides of Eqn (3.108) and
substituting Eqn (3.129) as needed, we obtain

X

N S

X

N S

d n j
d t

d ð nU Þ d T

d t þ

d ð pV Þ

¼ C P j n j H j (3.130)

d t d t

j ¼1 j ¼1

which expresses how the left hand side of Eqn (3.126) can be evaluated. Next, we apply the
general mole balance equation,

X

N R

d n j
d t

F j0 F j þ n ji r i V ¼ (3.131)

i ¼1

Equation (3.127) can be rearranged to give

V X

N R

d n j
d t H j

F j H j ¼ F j0 H j þ n ji r i H j (3.132)

i ¼1

Thus,

P

N S

H j0 P

N S

F j H j ¼ P

N S

H j0 P

N S

V P

N R

r i P

N S

n ji H j þ P

N S

d n j
d t H j

F j0 F j0 F j0 H j

j ¼1 j ¼1 j ¼1 j ¼1 i ¼1 j ¼1 j ¼1

(3.133)

H j0

H j ¼ P

N S

V P

N R

r i DH Ri þ P

N S

d n j
d t H j

F j0

j ¼1 i ¼1 j ¼1