Page 189 - Modelling in Transport Phenomena A Conceptual Approach

6.3. CONSERVATION OF ENERGY 169

4. As a result of perfect mixing, temperature and concentration of the system
are uniform, i.e., tout = csys and Tout = Tsys.
5. Changes in kinetic and potential energies are negligible.

Since chemical reaction is involved in this case, it is more appropriate to work
on molar basis. Therefore, Eq. (6.3-17) simplifies to
(RjL)in - (I;TjL),,t + Qid = 0 (6.3-30)

Any molar quantity of a mixture, 4, can be expressed in terms of partial molar
quantities2, iji, as
?j c.iqi (6.3-31)
=
i
Multiplication of &. (6.3-31) by molar flow rate, n, gives

(6.3-32)

Therefore, Eq. (6.3-30) is expressed as

On the other hand, macroscopic mole balance for species i, Eq. (6.1-6), is

(hilin - (hilout + ~ y E aij Tj = 0 (6.3-34)
s
j
Multiplication of Eq. (6.3-34) by gi(T) and summation over all species gives

[,nifJi(T)Iin - [ChiRi(T)] -Vsys Erj (-AHrxn,j) = 0 (6.3-35)
out j
where the heat of reaction is defined by

AHrxn,j = CaijHi(T) (6.3-36)
i
Subtraction of Eq. (6.3-35) from Eq. (6.3-33) yields

2Partial molar quantities, unlike molar quantities of pure substances, depend also on the
composition of the mixture.