Question

If coal gives off 30 MJ/kg when burned, how much coal is needed to heat a house requiring \({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{\bf{5}}}\;{\bf{MJ}}\) for the whole winter? Assume that 30% of the heat is lost up the chimney.

Short answer

The amount of coal needed is \(9524\;{\rm{kg}}\).

Step-by-step solution

Given data

The heat energy obtained is\(E = 30{\rm{ MJ}}\)from 1 kg coal.

The total heat required to heat the house is\(Q = 2.0 \times {10^5}\;{\rm{MJ}}\)

Also, 30% of the energy is lost up the chimney.

Suppose M mass of coal is required to heat the house.

Calculation of the mass of the coal

The heat energy required to heat up the house equals 70% of the generated heat energy.

\(\begin{aligned}{c}\frac{{70}}{{100}}ME = Q\\M = \frac{{100}}{{70}}\frac{Q}{E}\\M = \frac{{100}}{{70}}\frac{{2.0 \times {{10}^5}\;{\rm{MJ}}}}{{30{\rm{ MJ/kg}}}}\\M = 9524\;{\rm{kg}}\end{aligned}\)

Hence, the amount of coal needed is \(9524\;{\rm{kg}}\) .