A pilot sterilization was carried out in a vessel containing 100 m3 medium withan initial spore concentration of 108 spores/ml. The accepted level ofcontamination after sterilization is 1 spore in the entire vessel. The specific deathrate constant for the spore is 2 min-1 at 121 ˚C. Assuming no death takes placeduring the heating and cooling cycles, the holding time at 121 ˚C (rounded off tonearest integer) is _____________min
Question
A pilot sterilization was carried out in a vessel containing 100 m3 medium withan initial spore concentration of 108 spores/ml. The accepted level ofcontamination after sterilization is 1 spore in the entire vessel. The specific deathrate constant for the spore is 2 min-1 at 121 ˚C. Assuming no death takes placeduring the heating and cooling cycles, the holding time at 121 ˚C (rounded off tonearest integer) is _____________min
Solution
The problem can be solved using the first order reaction kinetics formula:
N = N0 * e^(-kt)
where: N is the final number of spores (1 spore in this case), N0 is the initial number of spores (108 spores/ml * 100 m3 * 10^6 ml/m3 = 10^16 spores), k is the specific death rate constant (2 min^-1), t is the time we want to find.
Rearranging the formula to solve for t gives:
t = -ln(N/N0) / k
Substituting the given values into the formula gives:
t = -ln(1/10^16) / 2 = 18.42 minutes
Rounding off to the nearest integer gives a holding time of 18 minutes.
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