The chemical reaction of transforming theAreactant into the B product has first order kinetics and is performed in a CSTR. Build the mathematical model of the system, the Bode plots and the transfer...

The chemical reaction of transforming theAreactant into the B product has first order kinetics and is performed in a CSTR. Build the mathematical model of the system, the Bode plots and the transfer function for the transfer path T^o
_ag
to T^o
(i.e. heating agent temperature to reactor temperature). Determine also the type of the dynamic behavior and parameters (gain, time constant, pure time delay) characterizing the dynamic behavior of the heat transfer process. The mass of the reactor wall may be considered negligible.

The following data are known: volume of reactor V = 1m³, heat transfer area A_T
= 4m², heat transfer coefficient KT = 1000 kcal/m²h
^∘C, flow rates of the equal inlet and outlet streams F = 5 m³/h, specific heat of the reactant and products c_p
= 1 kcal/kg
^∘C, density of the reactant and products ρ = 1000 kg/m³, temperature of the inlet stream T^o
_i
= 40
^∘C, cooling agent temperature T^∘
_ag
= 20
^∘C, heat of reaction ΔH_r
= −20 kcal/mol, nominal concentration of A component C_A
= 0.5 kmol/m³
, reaction rate constant at steady-state temperature T∗∘, k(T∗∘) = 0.002 s −1, activation energy E = 15 kcal/mol, gas constant R = 1.989 kcal/kmol K. Note: the reaction rate constant can be expressed as k = a exp(−E/(RT^∘
)). This expression can be linearized around the steady state temperature T^∗
o
by the first two terms of the Taylor series expansion: