Subtopic: Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods
Question Statement:
A batch of $100000$ ($10^5$) cans of low-acid food, each initially containing $10^2$ spores of Clostridium botulinum, undergoes a commercial $12\text{-D}$ thermal sterilization process. The probability of finding a non-sterile container in the entire batch (expected number of surviving spores in the whole batch) is ________ (answer in decimal).
Answer Key:
0.00001
Step-by-Step Solution & Explanation
1. Initial total spore population across the batch of $10^5$ cans:
$N_0 = 10^5 \times 10^2 = 10^7\text{ spores}$
2. A $12\text{-D}$ reduction reduces the population by $12$ log cycles ($10^{12}$ times):
$N = N_0 \times 10^{-12} = 10^7 \times 10^{-12} = 10^{-5} = 0.00001$
This represents an expected failure rate of 1 non-sterile can in $100,000$ cans.