Consider a single-tank CSTR with a reaction 2A to B that follows a second-order rate law = ^2. This reactor is held at a constant temperature and volume , with a single stream flowing in with a volumetric flow rate qi and concentration i, and an outgoing product stream with a flow rate and concentration . This system is originally at steady state input of i and output !. (a) Write the mass and concentration balances for this system. (b) Write the design equation in the form: / = (i,) (c) Use linearization to express the design equation in deviation variables. (d) Write the linearized transfer function, () = '/i(). (e) Write an expression for () with a step change in i() = (). How does the steady-state gain and time constant of this process depend on ?