A continuous Ultra-High Temperature (UHT) steam infusion sterilizer processes liquid dairy dessert at $140.0^\circ\text{C}$. For target bacterial spores of \textit{Geobacillus stearothermophilus}, the thermal death kinetics at $140^\circ\text{C}$ are characterized by $D_{140} = 0.50\text{ seconds}$. To achieve an $8\text{-log}$ spore reduction ($8 D$ process), the required continuous holding time in seconds is ________ (answer in integer).
Answer Key:
4
Step-by-Step Solution & Explanation
Multi-Approach Solution:
**Method 1: Direct Multiple of D-Value**
Total thermal holding time required:
$F = n \times D = 8 \times D_{140}$
$F = 8 \times 0.50\text{ seconds} = 4.0\text{ seconds}$
**Method 2: First-Order Logarithmic Inactivation**
$\log\left(\frac{N_0}{N}\right) = \frac{t}{D} \implies 8 = \frac{t}{0.50} \implies t = 4.0\text{ seconds}$