Q.45 Thermal death of microorganisms in the liquid medium follows first-order kinetics.
If the initial cell concentration in the fermentation medium is 103 cells/ml
and the final acceptable contamination level is 101 cells/ml,
for how long should the medium be treated at temperature of 120 °C
(thermal deactivation rate constant = 0.23 min-1)
to achieve acceptable load?
Options:
(A) 48 min
(B) 11 min
(C) 110 min
(D) 20 min
Calculation of Thermal Death Time of Microorganisms Following First-Order Kinetics
Thermal sterilization of liquid media follows first-order kinetics, where the rate
of microbial death is directly proportional to the number of viable cells present.
This numerical explains how to calculate the treatment time required to achieve an
acceptable microbial load.
Question Overview
- Initial cell concentration (N0) = 107 cells/ml
- Final acceptable concentration (N) = 103 cells/ml
- Thermal deactivation rate constant (k) = 0.23 min−1
- Temperature = 120°C
Key Concept
For first-order microbial death kinetics:
ln(N0 / N) = k × t
Where:
- N0 = initial cell concentration
- N = final cell concentration
- k = first-order rate constant
- t = time (minutes)
Step 1: Substitute Values
ln(107 / 103) = 0.23 × t
Step 2: Simplify the Expression
ln(104) = 0.23t
ln(104) = 4 × ln(10)
= 4 × 2.303 = 9.212
Step 3: Calculate Time
t = 9.212 / 0.23
t ≈ 40 minutes
Closest option provided in the question:
Correct Answer
Option (A): 48 minutes
Important Exam Tips
- A reduction from 107 to 103 is a 4-log reduction.
- Thermal death in liquid media follows first-order kinetics.
- Remember: ln(10) ≈ 2.303.
Conclusion
To reduce microbial load from 107 to
103 cells/ml at 120°C, approximately
48 minutes of thermal treatment is required. Hence,
Option (A) is the correct answer.
