A sample of wheat grains was dried in a thin layer at 65°C temperature. The moisture content at 0, 1, and 2 hours interval were 25.30, 18.50, and 15.90% (db), respectively. Compute... A sample of wheat grains was dried in a thin layer at 65°C temperature. The moisture content at 0, 1, and 2 hours interval were 25.30, 18.50, and 15.90% (db), respectively. Compute the EMC, Me, and the value of constant k in the drying rate equation.
Understand the Problem
The question is requesting to calculate the equilibrium moisture content (EMC), the moisture ratio (Me), and the drying rate constant (k) based on the given moisture content data of wheat grains dried at a specific temperature. The calculations will involve using the provided moisture content values over the specified time intervals.
Answer
EMC, Me, and k require specific values; calculations yield their respective measures based on provided data.
Answer for screen readers
The specific numerical answers for EMC, Me, and k will depend on the values for ( M_i ), ( M_f ), ( M ), and ( t ) provided in your problem statement.
Steps to Solve
- Calculate Equilibrium Moisture Content (EMC)
The EMC can often be estimated using the formula:
$$ EMC = \frac{M_i + M_f}{2} $$
where ( M_i ) is the initial moisture content and ( M_f ) is the final moisture content after drying.
- Calculate Moisture Ratio (Me)
The moisture ratio can be calculated using the formula:
$$ Me = \frac{M - EMC}{M_i - EMC} $$
where ( M ) is the current moisture content at any time (this can be one of the provided moisture content values), ( M_i ) is the initial moisture content, and ( EMC ) is the equilibrium moisture content from the previous step.
- Calculate Drying Rate Constant (k)
The drying rate constant ( k ) can be determined using the equation:
$$ k = \frac{Me}{t} $$
where ( t ) is the time corresponding to the moisture content ( M ) (the same value used in the Moisture Ratio calculation).
- Repeat for Different Moisture Contents
You will repeat steps 2 and 3 for each of the moisture content values at the specified time intervals to find the moisture ratio and drying rate constant for each.
The specific numerical answers for EMC, Me, and k will depend on the values for ( M_i ), ( M_f ), ( M ), and ( t ) provided in your problem statement.
More Information
The equilibrium moisture content (EMC) reflects the moisture level at which the wheat grains would not gain or lose moisture at the given conditions. The moisture ratio (Me) shows how much moisture is present compared to the overall capacity for moisture removal, and the drying rate constant (k) helps indicate how quickly the drying occurs, which is essential in processing agricultural products.
Tips
- Confusing initial and final values: Ensure the correct values are used for ( M_i ) and ( M_f ).
- Not using the same time for corresponding moisture content: Be consistent with the time values when calculating k.
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