Steady-state conversion energy balance equation

Determining the conversion of monomer can only be as accurate as the method of quantifying the heat liberated from the reaction. The usual method is to take the difference between the inlet and outlet jacket water temperatures multiplied by the specific heat and flow rate of the water. This steady-state energy balance equation is ... 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

Solve the energy balance equation for temperature and find the steady-state operating temperatures of the reactor and the conversions corresponding to these temperatures. Additional data are ... 

Equation 10.4.a-7 is a necessary but not sufficient condition for stability. In Other words, if the criterion is satisfied, the reactor may be stable if it is violated, the reactor will be unstable. (Aris [1] prefers to use the reverse inequality as a sufficient condition for instability.) The reason is that in deriving Eq. 10.4.a-7, it was implicitly assumed that only the special perturbations in conversion and temperature related by the steady-state heat generation curve were allowed. To be a general criterion giving both necessary and sufficient conditions, arbitrary perturbations in both conversion and temperature must be considered. Van Heerden s reasoning actually implied a sense of time ( tends to move... ), and so the proper criteria can only be clarified and deduced by considering the complete transient mass and energy balances. 

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