Question Bank • QB_APE_EXP_011 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Evaporation and Drying

Subtopic: Drying kinetics

Question Statement:

Grain drying follows Lewis' thin-layer equation $\frac{M - M_e}{M_0 - M_e} = e^{-k t}$. A grain lot with initial moisture content $M_0 = 24\%$ (d.b.) is dried to $M = 16\%$ (d.b.) in $2.0\text{ hours}$. The equilibrium moisture content $M_e = 12\%$ (d.b.). The thin-layer drying constant $k$ in $\text{h}^{-1}$ is ________ (round off to 3 decimal places).

Answer Key:

0.549

Step-by-Step Solution & Explanation

Lewis drying equation: $\frac{M - M_e}{M_0 - M_e} = e^{-k t}$ Given: • $M_0 = 24\%$ • $M = 16\%$ • $M_e = 12\%$ • $t = 2.0\text{ hours}$ Moisture ratio $MR$: $MR = \frac{16 - 12}{24 - 12} = \frac{4}{12} = \frac{1}{3} \approx 0.33333$ $e^{-2 k} = \frac{1}{3} \implies -2 k = \ln(1/3) = -\ln 3 \approx -1.09861$ $k = \frac{1.09861}{2} \approx 0.5493\text{ h}^{-1} \approx 0.549\text{ h}^{-1}$
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