Question Bank • QB_DFE_PF_001 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Preservation of Food

Subtopic: Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods

Question Statement:

A heat-resistant bacterial spore has a decimal reduction time of $D_{115} = 4.20\text{ minutes}$ at $115.0^\circ\text{C}$. The thermal resistance constant is $z = 10.0^\circ\text{C}$. Using the thermal death relationship $\log(D_1 / D_2) = \frac{T_2 - T_1}{z}$, the decimal reduction time at $121.0^\circ\text{C}$ ($D_{121}$) in minutes is ________ (round off to two decimal places).

Answer Key:

1.06

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Thermal Resistance Equation** $\log\left(\frac{D_{115}}{D_{121}}\right) = \frac{121.0 - 115.0}{z} = \frac{6.0}{10.0} = 0.60$ $\frac{D_{115}}{D_{121}} = 10^{0.60} \approx 3.98107$ $D_{121} = \frac{D_{115}}{3.98107} = \frac{4.20\text{ min}}{3.98107} = 1.055\text{ minutes} \approx 1.06\text{ minutes}$ **Method 2: Direct Exponential Form** $D(T) = D_0 \times 10^{(T_0 - T)/z} = 4.20 \times 10^{-6/10} = 4.20 \times 0.25119 = 1.055\text{ min}$
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