Exercise $1.$ In a CSTR reactor the following irreversible elemental reaction takes place

$A+B$ Products

where the consumption rate of $A$ is given by$,$

$r_A(\frac{\text{l}\text{b}\text{m}\text{o}\text{l}}{\text{g}\text{a}\text{l}*min})=-k{c}_A(t)c_B(t)$

The reactor is perfectly mixed, and the temperature, volume and density of the reaction mixture can be

assumed as constant. If the concentration of the reactants coming into the system, $c_{A0}$ y $c_{B0}[lbmo\frac{l}{g}al],$

are constant.

$-$Find the transfer function that relate the exit concentrations, $c_A(s)$ and $c_B(s),$ with the inlet flow

variations, $F_A(t)$ y $F_B(t)[ga\frac{l}{m}in].$

$-$Draw the block diagram for the reactor showing all the transfer functions.

$-$Find the global transfer function for $c_A(s)$ in therms of the inlet variables only.

$-$Find the effective time constants $($negative reciprocals of the roots$)$ and the gain in the steady state.