The following reactions are carried out in an isothermal continuous stirred tank reactor. ABBCrA=k1CArB=k2CB2k1=1.1min1k2=0.1m3/kmolmin B is desired product and concentration of B is controlled using PI controller. The feed stream of 1m3/min containing 0.8kmol/m3 at steady state operation passes through the reactor having a volume of 2m3. If the volume of reaction mixture does not change with time. a. Derive the transfer function between inlet concentration of A and outlet concentration of B, and find the ultimate value of outlet concentration of B when inlet concentration is increased to 0.9kmol/m3. b. The transfer functions of measuring device and control valve are given below. Using Routh Hurwitz criterion, determine the ultimate gain of controller if integral time is 0.1 . Gm(s)=Gf(s)=1