Adapted from the textbook by Smith and Corripio. Consider an adiabatic,

exothermic, perfectly mixed chemical reactor where the reaction $A+$BlongrightarrowC

takes place. Let

$=$ density of reactants and products $($constant$),$ kmole $\frac{?}{m^3}$

$f=$ flow of inlet and outlet streams $($constant$),\frac{m^3}{s}$

$T_i(t)=$ inlet temperature, $K$

$T(t)=$ Temperature in reactor and outlet, $K$

$H_r=$ heat of reaction $($constant$),\frac{J}{k}$mole

$c_p,c_v=$ heat capacities $($constant$),\frac{J}{k}$mole$*K$

$V=$ volume of liquid in tank $($constant$),m^3$

The kinetics of the reaction are zeroth order. Determine the transfer function

between the outlet temperature and the inlet temperature. Express the time

constant and the steady state gain in terms of the physical parameters. Can

the time constant be negative in this case? What would be the consequence of

a negative time constant? Hint: if the time constant is negative, what happens

to the root of the characteristic equation?