Page 229 - Modelling in Transport Phenomena A Conceptual Approach

7.5. CONSERVATION OF ENERGY 209

Subtraction of Eq. (7.512) from Eq. (7.5-10) yields

Dividing Eq. (7.513) by the volumetric flow rate, &, gives

where T is the residence time. Expressing the partial molar enthalpy of species i
in terms of the partial molar heat capacity by Eq. (6.841) gives

where

Note that Eq. (7.5-15) reduces to Eq. (6.3-42) under steady conditions. On the
other hand, for a batch reactor, i.e., no inlet and outlet streams, Eq. (7.515) takes
the form

It is important to note that Eqs. (7.5-15) and (7.518) are valid for systems in
which pressure remains constant.

Example 7.9 The reaction described in Example 6.6 is to be carried out in a
batch reactor which operates adiabatically. The reactor is initially charged with
2000 moles of species A and 2400 moles of specaes B at a temperature of 25°C.
Determine the time required for 80% conversion of A if the reactor volume is 1 m3.