Two tonnes of paddy with 22% moisture content (wb) are to be dried to 13% moisture content (db). Calculate the weight of bone-dry product and water evaporated during the drying.

Steps to Solve

1. Define Initial Conditions

We start with 2 tonnes (2000 kg) of paddy which has a moisture content of 25% on a wet basis.

2. Calculate Bone-Dry Weight of Paddy

To find the bone-dry weight, we first need to determine the dry matter in the paddy using the initial moisture content. The formula to convert wet basis moisture content to dry weight is:

$$ \text{Dry Weight} = \text{Wet Weight} \times \left(1 - \text{Moisture Content (wb)}\right) $$

In this case,

$$ \text{Dry Weight} = 2000 \times (1 - 0.25) $$

3. Calculate Water Weight in Initial Paddy

Next, to find the weight of water in the paddy initially, we use:

$$ \text{Water Weight} = \text{Wet Weight} \times \text{Moisture Content (wb)} $$

Thus,

$$ \text{Water Weight} = 2000 \times 0.25 $$

4. Define Final Conditions

We now consider that after drying, the moisture content is reduced to 10% on a wet basis.

5. Calculate Final Bone-Dry Weight with 10% Moisture Content

Using the final moisture content to find the new dry weight:

$$ \text{Final Dry Weight} = \text{Wet Weight Final} \times \left(1 - \text{Moisture Content Final (wb)}\right) $$

Assuming the final weight of the paddy (Wet Weight Final) can be calculated using:

$$ \text{Wet Weight Final} = \frac{\text{Final Dry Weight}}{1 - 0.10} $$

So, we can rearrange this to solve the final dry weight.

6. Calculate Final Water Weight

Now, we can calculate the final water weight using:

$$ \text{Final Water Weight} = \text{Wet Weight Final} \times 0.10 $$

7. Calculate Evaporated Water Weight

Finally, subtract the final water weight from the initial water weight to find the amount of water evaporated.

$$ \text{Evaporated Water} = \text{Initial Water Weight} - \text{Final Water Weight} $$