12.38 kg of shelled corn at 28.3% moisture was dried to 10.5%. Find (a) the initial amount of water in the product, (b) the final weight of the product, and (c) the amount of water... 12.38 kg of shelled corn at 28.3% moisture was dried to 10.5%. Find (a) the initial amount of water in the product, (b) the final weight of the product, and (c) the amount of water removed.
Understand the Problem
The question is asking to perform calculations based on the drying process of shelled corn. It provides the initial weight of the corn and the final moisture content after drying, and it seeks to find the initial amount of water in the product, the final weight of the product, and the amount of water removed during the drying process.
Answer
The initial amount of water is approximately $35.51 \, \text{kg}$, the final weight is approximately $99.83 \, \text{kg}$, and the amount of water removed is approximately $18.21 \, \text{kg}$.
Answer for screen readers
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The initial amount of water in the product is approximately 35.51 kg.
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The final weight of the product is approximately 99.83 kg.
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The amount of water removed during the drying process is approximately 18.21 kg.
Steps to Solve
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Identify the initial conditions
The initial weight of the shelled corn is given as 125.38 kg and the initial moisture content is 28.3%. -
Calculate the initial amount of water
To find the initial amount of water in the product, use the formula: $$ \text{Initial Water} = \text{Initial Weight} \times \frac{\text{Initial Moisture}}{100} $$ Substituting the values: $$ \text{Initial Water} = 125.38 \times \frac{28.3}{100} $$ -
Calculate the final weight of the product
The final moisture content is given as 20.5%. The final weight of the product can be found using: $$ \text{Final Weight} = \text{Initial Weight} - \text{Water removed} $$ Where: $$ \text{Final Water} = \text{Final Weight} \times \frac{\text{Final Moisture}}{100} $$ Thus, rewriting gives us: $$ \text{Final Weight} = \frac{\text{Initial Weight} \times \text{Initial Moisture} - \text{Final Water}}{100} $$ -
Calculate the amount of water removed
The amount of water removed can be calculated as: $$ \text{Water Removed} = \text{Initial Water} - \text{Final Water} $$ -
Perform calculations
Calculate the values based on the earlier equations.
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The initial amount of water in the product is approximately 35.51 kg.
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The final weight of the product is approximately 99.83 kg.
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The amount of water removed during the drying process is approximately 18.21 kg.
More Information
This problem involves calculations around the drying process of shelled corn, showcasing how moisture content affects weight. The moisture percentages are crucial for assessing the efficiency and effectiveness of drying procedures.
Tips
- Failing to convert percentages into decimal form before calculations.
- Not accounting for both initial and final moisture when calculating the amount of water removed.
- Incorrectly supposing that the final weight is simply the initial weight minus some constant value.
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