The initial number of microbes present in 1 liter medium before sterilization is 1011organisms/ml. Calculate ▼overall and holding time if k=2.54 min-1 and ▼holding = 37.23.
Question
The initial number of microbes present in 1 liter medium before sterilization is 1011organisms/ml. Calculate ▼overall and holding time if k=2.54 min-1 and ▼holding = 37.23.
Solution
To calculate the overall and holding time, we need to use the given values of the initial number of microbes (1011 organisms/ml), the growth rate constant (k = 2.54 min-1), and the holding time (▼holding = 37.23).
Step 1: Calculate the overall time (▼overall): ▼overall = ln(Nf/Ni) / k
Where Nf is the final number of microbes and Ni is the initial number of microbes.
Step 2: Calculate the final number of microbes (Nf): Nf = Ni * e^(k * ▼holding)
Where e is the base of the natural logarithm (approximately 2.71828).
Step 3: Substitute the values into the formulas and calculate ▼overall and Nf:
Nf = 1011 * e^(2.54 * 37.23) Nf ≈ 1011 * e^(94.5642) Nf ≈ 1011 * 1.71828^94.5642 Nf ≈ 1011 * 1.71828^94.5642
▼overall = ln(Nf/Ni) / k ▼overall = ln((1011 * 1.71828^94.5642) / 1011) / 2.54
By substituting the values into the formula, you can calculate the overall time (▼overall) and holding time (▼holding) based on the given information.
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