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. Calculate the initial weight of the moisture in the paddy

First, we determine the weight of the moisture in the paddy. The moisture content is given as 22%, so for 2 tonnes of paddy, we calculate the moisture weight as follows:

[ \text{Moisture weight} = \text{Total weight} \times \text{Moisture content} = 2 \text{ tonnes} \times 0.22 = 0.44 \text{ tonnes} ]

2. Determine the weight of the bone-dry product

Next, we find the weight of the dry matter in the paddy. This is the total weight minus the moisture weight:

[ \text{Dry weight} = \text{Total weight} - \text{Moisture weight} = 2 \text{ tonnes} - 0.44 \text{ tonnes} = 1.56 \text{ tonnes} ]

3. Calculate the target moisture weight when dried to 13%

Now, we need to find out what the total weight will be when the moisture content is reduced to 13%. Let ( W_d ) be the final weight:

We're given that the final moisture content is 13%, which means that 87% of the final weight will be the bone-dry product. We can set up the following equation:

[ W_d \times 0.87 = \text{Dry weight} ]

Substituting the dry weight:

[ W_d \times 0.87 = 1.56 ]

Solving for ( W_d ):

[ W_d = \frac{1.56}{0.87} \approx 1.79 \text{ tonnes} ]

4. Calculate the amount of water evaporated

To find out the amount of water that has evaporated, we subtract the final weight from the initial total weight:

[ \text{Water evaporated} = \text{Initial weight} - \text{Final weight} = 2 \text{ tonnes} - 1.79 \text{ tonnes} \approx 0.21 \text{ tonnes} ]