In the following process, a solution with cA0 concentration and F=1m3/s flow rate is connected to a CSTR with volume equal to 10m3, while the outlet flow rate is equal to F. Both the inlet and outlet flow rates are constant. In the CSTR, a first order isothermal reaction takes place with a rate constant k=0.1s1. At the exit of the tank, a pipe of L=10m is connected, through which brine solution flows at a velocity equal to 10m/s. At the end of the pipe, concentration is measured (ignore the measuring device and valve dynamics) and fed to a P-only control, which, in turn, adjusts the inlet concentration. a. Show the block diagram representation with the appropriate transfer functions that connect cAO to cA1 - b. For a given unit step change in cAO ', what is the time domain open-loop response of cAI '? Sketch the approximate response. c. Use a first order Pade approximation for the time delay and find the acceptable values of Kc for reasonable control action