Question

The microbial death kinetics for a food suspension follows the equation: \[ \log \frac{N_0}{N} = 1 + \frac{t - t_l}{D} \] where \(N_0 =\) initial microbial load, \(N =\) microbial load after time \(t\), \(t_l =\) lag time, and \(D =\) decimal reduction time. The correct statement for this equation is:

• A. the time required to reduce 10% of the initial population is lag time.
• B. the time required to reduce the initial 90% of population is lag time.
• C. time required to kill the first 90% population is lower than \(D\) value at the same temperature.
• D. lag time approaches \(D\) value as \(N_0\) becomes smaller and temperature decreases.

Hint:

Remember: The \(D\)-value is a measure of microbial heat resistance (time for 90% reduction), while lag time delays the start of death kinetics.

Answer 1

The Correct Option is D

Step 1: Understand the equation. The given microbial death kinetics equation is: \[ \log \frac{N_0}{N} = 1 + \frac{t - t_l}{D} \] This is a modified form of the logarithmic microbial inactivation model. Here, - \(D\) value = time required to reduce the microbial population by 90% (1 log reduction). - \(t_l\) = lag time before exponential inactivation starts.

Step 2: Eliminate wrong options. - (A) Incorrect, because lag time is not the time to reduce 10% population, but the delay before log-linear death begins.
- (B) Incorrect, because lag time is not linked with killing 90% population; that is defined by \(D\) value.
- (C) Incorrect, because the time required to kill 90% population is exactly the \(D\) value, not lower.

Step 3: Correct interpretation. - (D) Correct: At lower temperatures or smaller \(N_0\), microbial reduction is slower, and the lag time effectively approaches the \(D\) value. This matches the given microbial death equation. \[ \boxed{\text{Option (D)}} \]