In a thin layer grain drying experiment, the moisture ratio ($MR$) follows Page's equation: $MR = \frac{M - M_e}{M_0 - M_e} = \exp(-k t^n)$. For drying cereal grains at $45^\circ\text{C}$, the drying constants are $k = 0.04\text{ min}^{-1}$ and $n = 1.0$. The drying time in minutes required to reduce the moisture ratio to $0.368$ (which equals $e^{-1}$) is ________ (answer in integer).
Answer Key:
25
Step-by-Step Solution & Explanation
Given Page's equation with $n = 1.0$ (which reduces to Newton's thin layer drying model):
$MR = \exp(-k t)$
Substitute $MR = 0.368 = e^{-1}$ and $k = 0.04\text{ min}^{-1}$:
$e^{-1} = e^{-0.04 t} \implies 0.04 t = 1$
$t = \frac{1}{0.04} = 25\text{ minutes}$