Decimal reduction time of a bacterial strain is $20$ min. Specific death rate constant in $min^{-1}$ (rounded off to two decimal places) is____.
Calculating Specific Death Rate Constant from DRT
The Decimal Reduction Time (DRT) is the time required to reduce the number of viable microorganisms by 90% (or one logarithm cycle) at a specific temperature.
The relationship between the specific death rate constant ($k_d$) in $min^{-1}$ and the DRT is given by the formula:
$ k_d = \frac{\ln(10)}{DRT} $
DRT Calculation Steps
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Identify the given Decimal Reduction Time (DRT):
$ DRT = 20 \text{ min} $
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Substitute the DRT value into the formula. Note that $\ln(10) \approx 2.302585$.
$ k_d = \frac{2.302585}{20 \text{ min}} $
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Calculate the value:
$ k_d \approx 0.115129 \text{ min}^{-1} $
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Round the result to two decimal places as required:
$ k_d \approx 0.12 \text{ min}^{-1} $
The specific death rate constant is approximately $0.12 \text{ min}^{-1}$. This value falls within the expected range of 0.1 to 0.13.
Important Questions from Sterilization of Air and Media
The decimal reduction time of a microbe during sterilization at $120 \text{ °C}$ with a first order thermal death rate constant of $1 \text{ min}^{-1}$ will be _______________ min (rounded off to 1 decimal place).
- A pilot sterilization was carried out in a vessel containing $100 \text{ m}^3$ medium with an initial spore concentration of $10^8 \text{ spores/ml}$. The accepted level of contamination after sterilization is 1 spore in the entire vessel. The specific death rate constant for the spore is $2 \text{ min}^{-1}$ at $121 \text{ }^\circ C$. Assuming no death takes place during the heating and cooling cycles, the holding time at $121 \text{ }^\circ C$ (rounded off to nearest integer) is ________________ min.
Moist heat sterilization of spores at $121 \text{ } ^\circ C$ follows first order kinetics as per the expression:
$ \frac{dN}{dt} = -k_d N $
where, N is the number of viable spores, t is the time, $k_d$ is the rate constant and $ \frac{dN}{dt} $ is the rate of change of viable spores.
If $k_d$ value is $1.0 \text{ min}^{-1}$, the time (in minutes) required to reduce the number of viable spores from an initial value of $10^{10}$ to a final value of 1 is (up to two decimal places)______.
- Decimal reduction time of bacterial spores is 23 min at $121 \ °C$ and the death kinetics follow first order. One liter medium containing $10^9$ spores per mL was sterilized for 10 min at $121 \ °C$ in a batch sterilizer. The number of spores in the medium after sterilization (assuming destruction of spores in heating and cooling period is negligible) will be ____________________ $ \times 10^7$.
- An industrial fermentor containing $10,000 \text{ L}$ of medium needs to be sterilized. The initial spore concentration in the medium is $10^6 \text{ spores mL}^{-1}$. The desired probability of contamination after sterilization is $10^{-3}$. The death rate of spores at $121 \text{ °C}$ is $4 \text{ min}^{-1}$. Assume that there is no cell death during heating and cooling phases. The holding time of the sterilization process is __________ min (rounded off to the nearest integer).
