Exercise $3.$ In an adiabatic chemical reactor the following reaction takes place

$A+BC$

where the reaction kinetics is of order cero and is given by the following expression,

$r_A=-k_0$exp$(\frac{-E_a}{RT(t)})$

$-$Make a list with all the assumptions you need including the necessary parameter for the energy balance.

$-$Write the differential equation as a function of time that describes the system dynamics.

$-$Express the dynamic model of the previous instruction in terms of deviation variables and determine

the expression for the constant time, $,$ and the increase of steady state, $K.$

$-$Determine the reactor transfer function. Under which conditions is the time constant negative? What

consequences might this have? Discuss your answer.