Question

A 10 kg tomato pulp is concentrated from an initial moisture content of ( 90% ) (wet weight basis) to ( 35% ) (wet weight basis). The weight of the concentrate in kg is _____ (round off to 2 decimal places).

Hint:

The weight of the concentrate can be calculated using the formula: [ {Final weight} = frac{{Initial dry matter}}{{Final dry matter fraction}}. ] Ensure proper rounding to match the required precision.

Answer 1

To determine the weight of the concentrate, let us calculate the dry matter in the tomato pulp before and after concentration: Step 1: Calculate the weight of dry matter.

The weight of dry matter in the tomato pulp remains constant during the concentration process. The initial dry matter content is:

\[ \text{Dry matter} = \text{Total weight} \times (1 - \text{Moisture fraction}) \]

Substituting the given values:

\[ \text{Dry matter} = 10 \, \text{kg} \times (1 - 0.90) = 10 \, \text{kg} \times 0.10 = 1.0 \, \text{kg}. \] Step 2: Determine the final weight of the concentrate.

At **35%** moisture content, the dry matter fraction is:

\[ \text{Dry matter fraction} = 1 - 0.35 = 0.65. \]

The final weight of the concentrate is:

\[ \text{Final weight} = \frac{\text{Dry matter}}{\text{Dry matter fraction}} = \frac{1.0 \, \text{kg}}{0.65} \approx 1.54 \, \text{kg}. \] Step 3: Round off the result.

The weight of the concentrate is approximately **1.54 kg**, which lies within the range **1.50 to 1.60 kg**.