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).
Decimal Reduction Time Calculation
The Decimal Reduction Time (D-value) represents the time needed to decrease the microbial population by 90% (one log reduction) under specific conditions, such as a given temperature.
Understanding the Thermal Death Rate
The question states a first-order thermal death rate. This means the rate at which microbes are killed is proportional to the number of microbes present. The rate constant ($k$) quantifies this rate.
Formula for D-value
For a first-order death rate, the D-value can be calculated using the thermal death rate constant ($k$) with the following formula:
$ D = \frac{\ln(10)}{k} $
Here:
- $D$ = Decimal Reduction Time (in minutes)
- $k$ = First-order thermal death rate constant (in $\text{min}^{-1}$)
- $\ln(10)$ ≈ 2.3026
Calculation Steps
- Given Rate Constant: The problem provides $k = 1 \text{ min}^{-1}$.
- Substitute into Formula: Plug the value of $k$ into the D-value equation.
$ D = \frac{\ln(10)}{1 \text{ min}^{-1}} $
- Compute D-value: Using the approximate value for $\ln(10)$:
$ D \approx \frac{2.3026}{1 \text{ min}^{-1}} \approx 2.3026 \text{ min} $
- Round to One Decimal Place: The question asks for the answer rounded to one decimal place.
$ D \approx 2.3 \text{ min} $
The decimal reduction time is 2.3 minutes.
Important Questions from Sterilization of Air and Media
- 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.
Decimal reduction time of a bacterial strain is $20$ min. Specific death rate constant in $min^{-1}$ (rounded off to two decimal places) is____.
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).
