Q.49 The decimal reduction time (DRT or D value) of a bacterial culture is one minute. If a
suspension of the bacterial culture contains an initial population of 10^6 cells, then the time
(in minutes) required to reduce the number of bacteria to 10 by heat treatment is ________.
5 log reductions × D-value (1 min) = 5 minutes total heat treatment
Problem Breakdown
The D-value represents the time for a 90% kill, following first-order kinetics where \(\log_{10}(N_0/N) = t/D\), with \(N_0 = 10^6\), \(N = 10\), and \(D = 1\) min. This yields \(t = 5\) log cycles × 1 min = 5 minutes. No options are provided in the query, but common distractors include 6 minutes (adding safety factor incorrectly) or 1 minute (confusing one D-value with total kill).
Step-by-Step Calculation
Initial population: \(N_0 = 10^6\)
Target: \(N = 10\)
Log reduction: \(\log_{10}(10^6/10) = \log_{10}(10^5) = 5\)
Time: \(t = 5 \times D = 5 \times 1 = 5\) minutes
| Time (min) | Population Remaining | Log Reduction |
|---|---|---|
| 0 | \(10^6\) | 0 |
| 1 | \(10^5\) | 1 |
| 2 | \(10^4\) | 2 |
| 3 | \(10^3\) | 3 |
| 4 | \(10^2\) | 4 |
| 5 | \(10^1 = 10\) | 5 |
After 1 min: \(10^5\); 2 min: \(10^4\); 3 min: \(10^3\); 4 min: \(10^2\); 5 min: \(10^1 = 10\).
D-Value Formula and Kinetics
- D-value equals time for one log reduction: \(N = N_0 \times 10^{-t/D}\) or \(t = D \times \log_{10}(N_0/N)\)
- For bacterial culture heat treatment, plot log survivors vs. time yields straight line; slope’s negative reciprocal is D
- Here, D=1 min means \(10^6\) becomes \(10^5\) in 1 min, continuing multiplicatively
CSIR NET Exam Applications
In competitive exams like CSIR NET, such problems test microbial death kinetics for food safety and pharma sterilization. Common errors: Using arithmetic reduction (wrong) vs. logarithmic; or ignoring “to 10” as 5 logs, not 6. Practice with survivor curves enhances problem-solving.
Solved Example Summary
Initial population \(10^6\) cells; target 10; D-value 1 minute. Log cycles: \(\log_{10}(10^6/10) = 5\). Time required: 5 minutes—crucial for sterilization validation in biotech. Verification: After 5 min, exactly 10 cells remain probabilistically.
