Forging a sword requires 10 kg of steel to be melted. This required 8.24 MJ. Find the starting temperature of the steel.

Initial data: m (steel mass) = 10 kg; Q (required heat) = 8.24 MJ = 8.24 * 10 ^ 6 J.

Reference data: C (specific heat) = 500 J / (K * kg); λ (specific heat of fusion) = 84 * 10 ^ 3 J / kg; tmelt (melting point) = 1500 ºС.

Formula for calculating the required heat:
Q = C * m * (tpl – tn) + λ * m.

C * m * (tpl – tн) = Q – λ * m.

tmelt – tн = (Q – λ * m) / (C * m).

tн = tpl – (Q – λ * m) / (C * m) = 1500 – (8.24 * 10 ^ 6 – 84 * 10 ^ 3 * 10) / (500 * 10) = 1500 – 1480 = 20 ºС …