70. The working volume (in liter) of a chemostat with 0.1 h−1 dilution rate and 100ml/h feed flow
rate is ____
The working volume of a chemostat is calculated using the dilution rate formula. Based on the given parameters, the
correct working volume is 1 liter.
Correct Answer
The working volume of the chemostat is 1 liter.
Formula and Calculation
The dilution rate (D) is defined as the feed flow rate (F) divided by the working volume (V):
D = F / V
Rearranging the formula to calculate volume:
V = F / D
Given values:
- Feed flow rate, F = 100 ml/h = 0.1 L/h
- Dilution rate, D = 0.1 h−1
Substituting into the formula:
V = 0.1 / 0.1 = 1 L
Formula Breakdown
- The standard chemostat equation is D = F / V
- Rearranged to solve for volume: V = F / D
- Unit consistency is critical: 100 ml/h must be converted to 0.1 L/h
At steady state, this working volume ensures constant cell density without washout,
which is a key principle in chemostat operation.
Option Analysis (Common Exam Traps)
Although no explicit options are given, common incorrect answers in competitive exams
like GATE Biotechnology include:
- 0.1 L – Error due to not converting ml to liters
- 10 L – Mistakenly using the formula as V = D × F
- 1000 L – Ignoring unit consistency altogether
The correct answer of 1 liter aligns with standard bioreactor design
and microbial kinetics principles.
