How much ice, taken at -20C, can be melted in a 10 kg aluminum pan. When burning 0.5 kg of dry wood?

t (ice temperature, pots) = -20 ºС; m1 (pan) = 10 kg; m3 (firewood) = 0.5 kg.

q (combustion of firewood) = 10 ^ 7 J / kg; C1 (aluminum) = 920 J / (kg * K); C2 (ice) = 2100 J / (kg * K); λ (melting ice) = 3.4 * 10 ^ 5 J / kg; C3 (water) = 4200 J / (kg * K); L (steam) = 2.3 * 10 ^ 6 J / kg.

q * m3 = C1 * m1 * (100 – t) + m2 * (C2 * (0 – t) + λ + C3 * 100).

m2 = (q * m3 – C1 * m1 * (100 – t)) / (C2 * (0 – t) + λ + C3 * 100) = (10 ^ 7 * 0.5 – 920 * 10 * (100 – (-20))) / (2100 * (0 – (-20)) + 3.4 * 10 ^ 5 + 4200 * 100) = 4.86 kg.