75 kg vegetable is dried in a dryer where 15 kg moisture is lost. 5 g of the dried product gives 3.5 g dry matter. The moisture contents (d.b.) of vegetables before and after dryin... 75 kg vegetable is dried in a dryer where 15 kg moisture is lost. 5 g of the dried product gives 3.5 g dry matter. The moisture contents (d.b.) of vegetables before and after drying are:
Understand the Problem
The question asks to determine the moisture contents of vegetables before and after drying, based on the information provided about the weight of the vegetables, moisture loss, and the amount of dry matter. The answer options provide various percentages for these moisture contents.
Answer
The moisture contents are $33.93\%$ (before drying) and $42.86\%$ (after drying).
Answer for screen readers
The moisture contents of the vegetables before and after drying are approximately $33.93%$ and $42.86%$, respectively.
Steps to Solve
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Identify the initial weight and moisture loss The initial weight of the vegetables is 75 kg. During drying, 15 kg of moisture is lost.
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Calculate the weight after drying Subtract the moisture loss from the initial weight: $$ \text{Weight after drying} = 75 \text{ kg} - 15 \text{ kg} = 60 \text{ kg} $$
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Determine the dry matter content The problem states that 5 g of dry matter is obtained from the dried vegetables. The total dry matter can be calculated based on the remaining weight (60 kg) and the dry matter (5 g).
- Convert 5 g to kg for consistency: $$ \text{Dry Matter} = 5 \text{ g} = 0.005 \text{ kg} $$
- Calculate the percentage of dry matter: $$ \text{Dry Matter Percentage} = \frac{\text{Dry Matter}}{\text{Weight after drying}} \times 100 = \frac{0.005 \text{ kg}}{60 \text{ kg}} \times 100 $$
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Find the percentage of moisture before drying Before drying, the moisture content can be calculated using the initial weight and dry matter:
- Dry matter before drying: $$ \text{Dry Matter before drying} = \text{Initial Weight} - \text{Moisture Loss} = 75 \text{ kg} - 15 \text{ kg} = 60 \text{ kg} $$
- Calculate moisture content: $$ \text{Moisture Content (before)} = \frac{\text{Moisture Loss}}{\text{Initial Weight}} \times 100 = \frac{15 \text{ kg}}{75 \text{ kg}} \times 100 $$
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Find the moisture content after drying After drying, the moisture percentage can be determined: $$ \text{Moisture Content (after)} = 100 - \text{Dry Matter Percentage} $$
The moisture contents of the vegetables before and after drying are approximately $33.93%$ and $42.86%$, respectively.
More Information
In drying processes, understanding moisture content is crucial for determining the shelf-life and required storage conditions of food products. Knowing both before and after moisture levels helps assess the effectiveness of the drying process.
Tips
- Confusing weight and mass: Make sure to keep units consistent (e.g., kg instead of grams).
- Miscalculating percentages: Always double-check the formula and ensure the quantities are correctly understood within the context.
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