Question

6. Textbook 4-32 (for CMFR show all work, for PFR can use formulas derived in class or book)

for CMFR, I think you are supposed to derive from dM/dt = CinQin - CoutQout + rV

Also, not sure which equation to use for PFR from book but possibly it is ln( Cout/Cin) = -k (V/Q)

Answer 1

Here, For a Reactor, we have, Efficiency = 25 % & Q = 14 m^3/d, k = 0.05 d^- 1 implies C_in - C_out/ C_in = 0.95 implies C_out/ C_in = 0.05 rightarrow CMFR: Now, Here it is given that Reactor is in steady state with First order Reaction. Therefore dM/dt = 0 implies C_in middot C_out Q_out = kv c_out implies C_out/ C_in = 1/1 + kt {Q_in = Q_out} t = Detection period = V/Q implies 0.05 = 1/1 + 0.05t implies 1 + 0.05t = 20 implies t = 19/0.05 = 360 days therefore v = Q. t = 14 times 380 = 5320 m^3 rightarrow PFR: For PFR in steady state, we know, C_out/C_in = e^- kt implies 0.05 = e^- kt implies k middot t = 2.99573227 implies t = 59.9146455 day therefore V = Q middot t = 14 times 59.9146455 = 838.805 m^3