Question Bank • QB_APE_DRY_004 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Evaporation and Drying

Subtopic: Osmotic dehydration and freeze drying

Question Statement:

A batch of fresh apple slices of initial mass $M_0 = 100.0\text{ g}$ and initial moisture content $X_0 = 85.0\%\text{ (wb)}$ is immersed in a $60^\circ\text{Brix}$ sucrose solution for osmotic dehydration. After $3\text{ hours}$, the final mass of the apple slices is $M_t = 62.0\text{ g}$ and the final moisture content is $X_t = 60.0\%\text{ (wb)}$. The Water Loss ($WL$) percentage based on the initial fresh mass of apple slices is ________ % (round off to one decimal place).

Answer Key:

47.8

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Component Mass Tracking** Initial sample ($M_0 = 100.0\text{ g}$): Water $W_0 = 85.0\text{ g}$, Dry solids $S_0 = 15.0\text{ g}$. At time $t$ ($M_t = 62.0\text{ g}$): Water $W_t = 62.0 \times 0.60 = 37.2\text{ g}$, Dry solids $S_t = 62.0 - 37.2 = 24.8\text{ g}$. Water Loss ($WL$): $WL = \frac{W_0 - W_t}{M_0} \times 100\% = \frac{85.0 - 37.2}{100.0} \times 100\% = 47.8\%$ **Method 2: Direct Formula** $WL = \frac{M_0 X_0 - M_t X_t}{M_0} \times 100\% = \frac{100(0.85) - 62(0.60)}{100} \times 100\% = (85.0 - 37.2)\% = 47.8\%$
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