How much copper can be smelted in a smelting furnace with an efficiency of 40% by burning 2.2

How much copper can be smelted in a smelting furnace with an efficiency of 40% by burning 2.2 tons of A-1 grade coal? initial temperature of copper 289k?

Given: qа – heat of combustion of coal A – 1 (anthracite; qа = 3 * 10 ^ 7 J / kg); mа is the mass of anthracite (ma = 2.2 * 10 ^ 3 kg); η – furnace efficiency (η = 40% = 0.4); λ – heat of fusion (λ = 2.1 * 10 ^ 5 J / kg); Cm – heat capacity (Cm = 400 J / (kg * K)); t – temp. melting (t = 1084.5 ºС); t0 – early. pace. (t0 = 289 K = 16 ºС).

Formula: η = mm * (λ + Cm * (tmelt – t0)) / (qа * ma); mm = qa * ma * η / (λ + Cm * (tmelt – t0)).

Calculation: mm = 3 * 10 ^ 7 * 2.2 * 10 ^ 3 * 0.4 / (2.1 * 10 ^ 5 + 400 * (1084.5 – 16)) = 41 418 kg.