Question

The composition and energy content of a representative solid waste sample are given in the table. If the moisture content of the waste is 26%, the energy content of the solid waste on dry-weight basis is \underline{\hspace{2cm} MJ/kg (round off to one decimal place).} \includegraphics[width=0.75\linewidth]{image698.png}

Hint:

To convert energy content from wet weight to dry weight, divide by the dry mass fraction (1 - moisture content).

Answer 1

Correct Answer: 18

Let the total mass of the waste be 1 kg. The composition by mass and energy content is given in the table: \[ \begin{array}{|c|c|c|} \hline Component & Percent by mass & Energy content (MJ/kg)
\hline \text{Food waste} & 20% & 4.5
\text{Paper} & 45% & 16.0
\text{Cardboard} & 5% & 14.0
\text{Plastics} & 10% & 32.0
\text{Others} & 20% & 8.0
\hline \end{array} \] Now, calculate the energy content on a wet basis by multiplying the mass fractions with the corresponding energy content: \[ \text{Energy on wet basis} = \left(0.20 \times 4.5 \right) + \left(0.45 \times 16.0 \right) + \left(0.05 \times 14.0 \right) + \left(0.10 \times 32.0 \right) + \left(0.20 \times 8.0 \right) \] \[ = 0.9 + 7.2 + 0.7 + 3.2 + 1.6 = 13.6 \text{ MJ} \] Next, calculate the dry mass by subtracting the moisture content (26%) from the total mass: \[ \text{Dry mass fraction} = 1 - 0.26 = 0.74 \] Now, calculate the energy content on a dry-weight basis: \[ \text{Energy content on dry-weight basis} = \frac{\text{Energy on wet basis}}{\text{Dry mass fraction}} = \frac{13.6}{0.74} = 18.38 \text{ MJ/kg} \] Thus, the energy content on dry-weight basis is approximately 18.0 to 19.0 MJ/kg. \boxed{18.38\, \text{MJ/kg}}