Question

Potatoes are dried from 14% total solids to 93% total solids. What is the product yield in per cent from each 1000 kg of raw potatoes assuming that 9% of the original potatoes are lost in peeling?

• A. 13.6%
• B. 10.6%
• C. 14.6%
• D. 12.6%

Hint:

Always perform material balances on a dry matter basis when dealing with drying, evaporation, or concentration operations.
Because the amount of bone-dry solids does not change, it provides a stable reference point for all calculations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a material balance problem on a dry matter basis.
The mass of total solids remains constant throughout the drying process, as only moisture is removed.

Step 2: Key Formula or Approach:
The overall mass balance can be conducted by:
1. Finding the mass of potatoes after peeling.
2. Calculating the dry solid matter balance across the dryer:
\[ \text{Peeled Potatoes} \times \text{Initial Solids \%} = \text{Dried Product} \times \text{Final Solids \%} \]

Step 3: Detailed Explanation:
- Initial mass of raw potatoes = \(1000\text{ kg}\)
- Peeling loss = \(9\%\) of original mass = \(0.09 \times 1000 = 90\text{ kg}\)
- Mass of peeled potatoes entering the dryer (\(F\)) = \(1000 - 90 = 910\text{ kg}\)
- Initial total solids = \(14\%\)
- Mass of total solids entering the dryer = \(910 \times 0.14 = 127.4\text{ kg}\)
- Final total solids of dried product (\(P\)) = \(93\%\)
Performing the dry solid balance:
\[ 127.4\text{ kg} = P \times 0.93 \]
\[ P = \frac{127.4}{0.93} \approx 136.99\text{ kg} \]
Now, calculating the product yield relative to the original \(1000\text{ kg}\) of raw potatoes:
\[ \text{Product Yield \%} = \frac{\text{Mass of final dried product}}{\text{Mass of original raw potatoes}} \times 100\% \]
\[ \text{Yield \%} = \frac{136.99\text{ kg}}{1000\text{ kg}} \times 100\% \approx 13.7\% \]
Among the given choices, \(13.6\%\) is the closest option (corresponding to minor rounding differences).

Step 4: Final Answer:
The product yield is approximately 13.6%, which corresponds to option (A).