Question

A thermal process, at a specific temperature, results in 2-log₁₀ removal of non-thermotolerant pathogenic microorganisms from a water sample in 20 min.

The time needed to achieve 99.999% removal of these microorganisms under similar condition is ______ min (answer in integer).

Hint:

Find the log-removal rate per minute from the 2-log/20 min data point, then figure out how many logs a 99.999% removal corresponds to and divide by that rate.

Answer 1

Correct Answer: 50

Step 1: Express the removal in terms of log reduction.
A 2-log₁₀ removal means \(\frac{N}{N_0} = 10^{-2}\), and this is achieved in 20 minutes. Because disinfection under a fixed thermal condition follows first-order (Chick's Law) kinetics, the log-reduction is directly proportional to time.

Step 2: Find the rate of log removal per unit time. \[\text{rate} = \frac{2\text{-log removal}}{20\ min} = 0.1\ \text{log units per min}\]

Step 3: Convert 99.999% removal into log-units.
A removal of 99.999% means \(\frac{N}{N_0} = 1 - 0.99999 = 10^{-5}\), which corresponds to a 5-log₁₀ removal.

Step 4: Find the time required for 5-log removal. \[t = \frac{5\text{-log removal}}{0.1\ \text{log units/min}} = 50\ min\]

This matches the expected answer of exactly 50 minutes.