Question

How much weight reduction would result when a material is dried from 80% moisture to 50% moisture?

• A. 45%
• B. 55%
• C. 40%
• D. 60%

Hint:

To quickly calculate weight reduction during drying, use the formula:
\[ \% \text{ Weight Reduction} = \left( 1 - \frac{\% \text{ Initial Solids}}{\% \text{ Final Solids}} \right) \times 100 \] Substituting the values: \(\left( 1 - \frac{20}{50} \right) \times 100 = 60\%\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Drying involves removing water from a wet solid.
Because the dry matter (solid content) of the material remains constant throughout the drying process, weight reduction can be calculated using a mass balance on the dry solids.
Key Formula or Approach:
The mass balance equation for dry solids is:
\[ M_1 \times (1 - w_1) = M_2 \times (1 - w_2) \] where:
\(M_1\) is the initial mass of the material.
\(M_2\) is the final mass of the material.
\(w_1\) is the initial moisture content (expressed as a decimal).
\(w_2\) is the final moisture content (expressed as a decimal).

Step 2: Detailed Explanation:
Let us assume an initial mass of the material, \(M_1 = 100\,\text{kg}\).
We are given the following moisture contents:
Initial moisture content, \(w_1 = 80\% = 0.80\).
Final moisture content, \(w_2 = 50\% = 0.50\).
Calculate the initial solid content:
\[ \text{Initial solids} = 1 - 0.80 = 0.20 \text{ (or } 20\%\text{)} \] Calculate the final solid content:
\[ \text{Final solids} = 1 - 0.50 = 0.50 \text{ (or } 50\%\text{)} \] Using the dry solids mass balance:
\[ 100\,\text{kg} \times 0.20 = M_2 \times 0.50 \] \[ 20\,\text{kg} = 0.50 \times M_2 \] \[ M_2 = \frac{20}{0.50} = 40\,\text{kg} \] Now, calculate the weight reduction:
\[ \text{Weight Reduction} = M_1 - M_2 = 100\,\text{kg} - 40\,\text{kg} = 60\,\text{kg} \] Expressed as a percentage of the initial mass:
\[ \text{Percentage reduction} = \left(\frac{60\,\text{kg}}{100\,\text{kg}}\right) \times 100 = 60\% \]

Step 3: Final Answer:
Therefore, the weight reduction resulting from drying is 60%.