Subtopic: D-value change with temperature from z-value
Question Statement:
A bacterial spore has a decimal reduction time of $D_1 = 15.0\text{ min}$ at $T_1 = 111.1^\circ\text{C}$ and a thermal resistance constant $z = 10.0^\circ\text{C}$. The decimal reduction time $D_2$ at $T_2 = 121.1^\circ\text{C}$ is ________ $\text{min}$ (round off to two decimal places).
Answer Key:
1.50
Step-by-Step Solution & Explanation
The relationship between $D$-value and temperature governed by $z$-value is:
$\log_{10}\left( \frac{D_1}{D_2} \right) = \frac{T_2 - T_1}{z}$
$\frac{D_1}{D_2} = 10^{\frac{T_2 - T_1}{z}} = 10^{\frac{121.1 - 111.1}{10.0}} = 10^1 = 10$
$D_2 = \frac{D_1}{10} = \frac{15.0}{10} = 1.50\text{ min}$