Q. 79 The decimal reduction time ( ππππ ) for Clostridium botulinum spores is 0.2 min . The time required
to reduce the spore count from ππππ to one spore at πππβπ is ____ minutes.
D-Value Concept
D-value quantifies microbial heat resistance as time for a 10-fold population drop at fixed temperature. For C. botulinum at 121Β°C, D121 = 0.2 min ensures commercial sterility targets 12D processes. This follows first-order kinetics: N = N0 Γ 10-(t/D), where t is time.
Step-by-Step Calculation
Initial spores: N0 = 1012; final: N = 1 = 100. Log reduction needed: log(N0/N) = 12. Time t = 12 Γ D121 = 12 Γ 0.2 = 2.4 minutes. Formula confirms probability of survival drops to 10-12.
Common Options Explained
- 2.4 minutes (Correct): Matches 12D exactly for 1012 to 100.
- 0.2 minutes (Wrong): One log only, leaves ~1011 spores.
- 1.2 minutes (Wrong): 6D reduction to ~106 spores, inadequate for sterility.
- 12 minutes (Wrong): Ignores D-value; assumes 1 min per log.
- 24 minutes (Wrong): Doubles logs unnecessarily (e.g., 1012 to 10-12).
Sterilization Applications
12D concept prevents botulism in low-acid foods via 121Β°C processing. Actual D121 approximates 0.21 min; problem uses 0.2. z-value (~10Β°C) adjusts for temperature shifts.
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