Question

At \(16%\) wet basis moisture content, the sample of grain contains \(16\) kg of water and \(84\) kg of dry matter. If the same amount of grain again dried to \(11%\) moisture content, the final weight of water will be ____.

• A. \(9.24\ \text{kg}\)
• B. \(9.13\ \text{kg}\)
• C. \(10.38\ \text{kg}\)
• D. \(4.225\ \text{kg}\)

Hint:

Wet basis moisture content: \[ \boxed{ M_w = \frac{\text{Water mass}} {\text{Total mass}} \times100 } \] Important drying principle: \[ \boxed{ \text{Dry matter remains constant during drying} } \]

Answer 1

The Correct Option is C

Concept: Wet basis moisture content is defined as: \[ \boxed{ M_w = \frac{\text{Mass of water}} {\text{Total mass}} \times 100 } \] During drying:
• Water content changes
• Dry matter remains constant This is the key principle used in grain drying calculations.

Step 1: Understanding the initial condition. Initially: \[ 16%\ \text{moisture content} \] Water mass: \[ W_w = 16\ \text{kg} \] Dry matter: \[ W_d = 84\ \text{kg} \] Total mass: \[ W_t = 16+84=100\ \text{kg} \] Thus: \[ \frac{16}{100}\times100 = 16% \] which verifies the data.

Step 2: Understanding drying process. After drying:
• Dry matter remains unchanged
• Water content decreases Therefore: \[ \boxed{ W_d = 84\ \text{kg remains constant} } \] Final moisture content: \[ 11% \]

Step 3: Using wet basis moisture equation. Let final water mass be: \[ x\ \text{kg} \] Then final total mass becomes: \[ 84+x \] Using wet basis definition: \[ \frac{x}{84+x}\times100 = 11 \] or: \[ \frac{x}{84+x}=0.11 \]

Step 4: Solving the equation carefully. Multiply both sides: \[ x = 0.11(84+x) \] Expanding: \[ x = 9.24 + 0.11x \] Bring like terms together: \[ x-0.11x = 9.24 \] \[ 0.89x = 9.24 \] \[ x = \frac{9.24}{0.89} \] \[ x \approx 10.38\ \text{kg} \] Thus: \[ \boxed{ \text{Final water mass} = 10.38\ \text{kg} } \]

Step 5: Comparing with the options. Calculated value: \[ 10.38\ \text{kg} \] matches: \[ \boxed{ (C)\ 10.38\ \text{kg} } \] Final Conclusion: After drying to \(11%\) moisture content, the final water weight becomes: \[ \boxed{ 10.38\ \text{kg} } \] Hence the correct answer is: \[ \boxed{ (C) } \]