Question

For a continuous reactor with \(D=0.2~h^{-1}\), residence time (\(\tau\)) is

• A. 2 h
• B. 3 h
• C. 5 h
• D. 10 h

Hint:

Always remember: \[ \boxed{ D=\frac{1}{\tau} } \] A higher dilution rate means a shorter residence time, while a lower dilution rate means cells remain longer inside the reactor.

Answer 1

The Correct Option is C

Concept: In a continuous stirred tank reactor (CSTR), the dilution rate (\(D\)) is related to the residence time (\(\tau\)) by \[ \boxed{ D=\frac{1}{\tau} } \] or equivalently, \[ \boxed{ \tau=\frac{1}{D} } \] Residence time represents the average time the culture remains inside the bioreactor before being removed.

Step 1: Write the relationship.
\[ \tau=\frac{1}{D} \] Given, \[ D=0.2~h^{-1} \]

Step 2: Substitute the value.
\[ \tau=\frac{1}{0.2} \] \[ =5~h \]

Step 3: Choose the correct option.
Therefore, \[ \boxed{\tau=5~h} \] Hence, \[ \boxed{Option (C) is correct \]