You are the owner of a company that makes a chemical product in a large CFSTR with a theoretical detention time t. Production has not been as good as you had hoped. An engineer hired to help solve problems in the plant suggests installing baffles in the reactor, effectively dividing it into a series of CFSTRs.

Write out the mass balance and the resulting equation describing the effluent concentration as a function of time for a pulse input tracer test before any baffles are installed.

(b) Repeat part (a) for the concentration of the effluent from the tank once one baffle has been installed, dividing the tank into two identical CFSTRs. (Hints: The response of the first compartment to the pulse input is similar to that obtained in part (a), but you must revise your answer to account for the smaller volume. The revised result for the output from the first compartment constitutes the input to the second compartment. The solution for the concentration in the second compartment is most easily obtained using the convolution process described in the chapter and represents the response of the full, two-compartment reactor to the pulse input.)

(c) Repeat part (a) for the concentration of the effluent from the tank once two baffles have been installed, dividing the tank into three identical CFSTRs

(a) Write out the mass balance and the resulting equation describing the effluent concentration as a function of time for a pulse input tracer test before any baffles are installed. (b) Repeat part (a) for the concentration of the effluent from the tank once one baffle has been installed, dividing the tank into two identical CFSTRs. (Hints: The response of the first com- partment to the pulse input is similar to that obtained in part (a), but you must revise your answer to account for the smaller volume. The revised result for the output from the first com- partment constitutes the input to the second compartment. The solution for the concentration in the second compartment is most easily obtained using the convolution process described in the chapter and represents the response of the full, two-compartment reactor to the pulse input.) (c) Repeat part (a)for the concentration of the effluent from the tank once two baffles have been installed, dividing the tank into three identical CFSTRs