Determine the mass of copper that was melted in a furnace with an efficiency of 50%, while burning 2 tons of coal.

Data: η (efficiency of the furnace in which the copper was melted) = 50% (0.5); m2 (mass of coal burnt in the furnace) = 2 tons (2 * 10 ^ 3 kg); for the calculation, we assume that copper was at the melting temperature.

Constants: q (specific heat of combustion of coal) = 27 * 10 ^ 6 J / kg; λ (specific heat of fusion of copper) = 2.1 * 10 ^ 5 J / kg.

We determine the mass of molten copper from the formula: η = λ * m1 / (q * m2), whence m1 = η * q * m2 / λ.

Calculation: m1 = 0.5 * 27 * 10 ^ 6 * 2 * 10 ^ 3 / (2.1 * 10 ^ 5) = 128 571 kg ≈ 128.6 tons.