The CSTR reactor is used to treat industrial wastewater applying chemical reaction which destroys the waste with the rate constant of k=0.216day1. The reactor volume is 500m3 and the volumetric flow rate at the single inlet and outlet is 50m3/day. During the steady-state CSTR operation waste inlet concentration is 100mg/L and waste outlet concentration is 32mg/L. Now, consider the case when for an unknown reason waste treatment rector needs to be shut down. Therefore, starting at a certain time zero the waste concentration entering the CSTR is zero. Notice, the waste concentration out from the CSTR reactor will start to decrease from its previous steady-state value 32mg/L, since the water flow is kept at the same 50m3/ day (reactor flushing or cleaning is taking place). a) Show how one obtains the transient waste outlet concentration equation (as shown below) for the waste removal as a function of time after the inlet concentration was set to zero. C0 is here the outlet concentration prior to CSTR shut down. Note in the equation, at t=0,C=C0=32mg/L, which makes sense. C=C0e[(k+tR1)t] b) By applying the equation above in part a) calculate how many days it will take for the CSTR tank outlet concentration to reach 10% of its initial steady-state operation value? Make sure you show CSTR reactor residence time for the given flow rate and volume in your solution