How much steel, taken at a temperature of 20C, can be melted in a furnace with an efficiency of 50%, burning 2 webs of coal?

Data: t0 (initial steel temperature) = 20 ºС; η (furnace efficiency) = 50% = 0.5; m2 (mass of coal) = 2 t = 2000 kg.

Reference data: C (specific heat capacity of steel) = 500 J / (K * kg); λ (specific heat of melting of steel) = 0.84 * 10 ^ 5 J / kg; tmelt (average steel melting temperature) = 1450 ºС; q (specific heat of combustion of coal) = 2.7 * 10 ^ 7 J / kg.

η = m1 * (С * (tmelt – t0) + λ) / (m2 * q).

m1 = η * m2 * q / (С * (tmelt – t0)) = 0.5 * 2000 * 2.7 * 10 ^ 7 / (500 * (1450 – 20)) = 37 762 kg.