Question Bank • QB_DFE_UOP_022 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Unit Operations in Dairy and Food Engineering

Subtopic: Sterilization

Question Statement:

A batch of canned peas is heated at a constant retort temperature of $T = 115.0^\circ\text{C}$ ($z = 10.0^\circ\text{C}$). The thermal lethal rate at this temperature ($L = 10^{(T - 121.1)/z}$) expressed as an equivalent sterilization time at $121.1^\circ\text{C}$ per minute of holding is ________ (round off to three decimal places).

Answer Key:

0.245

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Bigelow Lethal Rate Definition** $L = 10^{(T - 121.1)/z}$ Given $T = 115.0^\circ\text{C}$ and $z = 10.0^\circ\text{C}$: $L = 10^{(115.0 - 121.1)/10.0} = 10^{-6.1 / 10.0} = 10^{-0.61}$ $L = 10^{-0.61} = \frac{1}{10^{0.61}} = \frac{1}{4.0738} \approx 0.24547 \approx 0.245\text{ min at } 121.1^\circ\text{C / min at } 115^\circ\text{C}$ **Method 2: Logarithmic Form** $\ln(L) = -0.61 \times \ln(10) = -0.61 \times 2.302585 = -1.40458$ $L = e^{-1.40458} = 0.24547 \approx 0.245$
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