11.4.1 Adiabatic Energy Balance

In the previous section, we derived Equation (11-28), which relates conversion to temperature and the heat added to the reactor, . Let’s stop a minute and consider a system with the special set of conditions of no work, , adiabatic operation , let T_i0 = T₀ and then rearrange (11-28) into the form

11-29

In many instances, the ΔC_P(T – T_R)term in the denominator of Equation (11-29) is negligible with respect to the term, so that a plot of X vs. T will usually be linear, as shown in Figure 11-2. To remind us that the conversion in this plot was obtained from the energy balance rather than the mole balance, it is given the subscript EB (i.e., X_EB) in Figure 11-2.

Figure 11-2. Adiabatic temperature–conversion relationship.

Equation (11-29) applies to a CSTR, PFR, or PBR, and also to a batch (as will be shown in Chapter 13). For and , Equation (11-29) gives us the explicit relationship between X and T needed to be used in conjunction with the mole balance to solve reaction engineering problems as discussed in Section 11.1.