Question

A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are F = 75 L/h and V = 200 L, respectively. The glucose concentration in the feed $C_{S0} = 15$ g/L. Assume Monod kinetics with specific cell growth rate $μ_{g} = (1/C_{C})\cdot (dC_{C}/dt)=(μ_{m}\cdot C_{S})/(K_{S}+C_{S}),$ where $μ_{m} = 0.25 h⁻¹$ and $K_{S} = 1$ g/L. The recycle ratio is $α = 0.5$ and the cell concentration factor is $β = 2.0.$ Assume maintenance and death rates to be zero, input feed to be sterile $(C_{C0}=0),$ and steady-state operation. The glucose concentration in the recycle stream, $C_{S1},$ in g/L, rounded off to 1 decimal place, is _________

Official answer: 2.9 to 3.1