What is the efficiency of a smelting furnace, in which 400 g of coal is consumed to melt 1 kg

What is the efficiency of a smelting furnace, in which 400 g of coal is consumed to melt 1 kg of copper taken at a temperature of 85 ºС?

Data: m1 (copper mass) = 1 kg; t0 (initial copper temperature) = 85 ºС; m2 (mass of coal) = 400 g = 0.4 kg.

Reference values: t (melting point of copper) = 1085 ºС; C (specific heat of copper) = 400 J / (kg * K); λ (specific heat of melting of copper) = 2.1 * 10 ^ 5 J / kg; q (specific heat of combustion of coal) = 2.7 * 10 ^ 7 J / kg.

Melting furnace efficiency: η = (С * m1 * (t – t0) + λ * m1) / (q * m2) = (400 * 1 * (1085 – 85) + 2.1 * 10 ^ 5 * 1) / (2.7 * 10 ^ 7 * 0.4) = 0.0565 or 5.65%.