Question Bank • QB_DFE_UOP_015 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Unit Operations in Dairy and Food Engineering

Subtopic: Pasteurization

Question Statement:

Thermal destruction of alkaline phosphatase enzyme in bovine milk exhibits decimal reduction values of $D_{63} = 2.50\text{ minutes}$ at $63.0^\circ\text{C}$ with a $z$-value of $z = 5.0^\circ\text{C}$. The decimal reduction time of alkaline phosphatase at $73.0^\circ\text{C}$ ($D_{73} = D_{63} \times 10^{-(73-63)/z}$) in seconds is ________ (answer in integer).

Answer Key:

1

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Thermal Resistance Formula** $\log\left(\frac{D_{63}}{D_{73}}\right) = \frac{73.0 - 63.0}{z} = \frac{10.0^\circ\text{C}}{5.0^\circ\text{C}} = 2.0$ $\frac{D_{63}}{D_{73}} = 10^{2.0} = 100$ $D_{73} = \frac{D_{63}}{100} = \frac{2.50\text{ minutes}}{100} = 0.0250\text{ minutes}$ Converting to seconds: $D_{73} = 0.0250\text{ min} \times 60\text{ s/min} = 1.50\text{ seconds} \approx 1.5\text{ s}$ (Evaluating to nearest integer: 1 or 2 s).
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