In an electric furnace with a power of 100 kW, a steel ingot was completely melted in 2.3 hours.

In an electric furnace with a power of 100 kW, a steel ingot was completely melted in 2.3 hours. What is the mass of the ingot if it is known that before the start of melting, the steel had to be heated to 1500C? Neglect the loss of energy.

N = 100 kW = 100000 W.

T = 2.3 h = 8280 s.

Δt = 1500 ° C.

C = 500 J / kg * ° C.

λ = 84000 J / kg.

m -?

Let us express the amount of heat Q, which is released in the electric tile according to the formula: Q = N * T, where N is the power of the tile, T is the operating time of the tile.

Steel must first be heated to its melting point and then melted. The amount of heat Q, which is necessary for steel melting, is expressed by the formula: Q = C * m * Δt + λ * m = (C * Δt + λ) * m, where C is the specific heat capacity of steel, Δt is the change in steel temperature during heating, λ is the specific heat of fusion, m is the mass of steel.

N * T = (C * Δt + λ) * m.

The mass of steel m will be determined by the formula: m = N * T / (C * Δt + λ).

m = 100000 W * 8280 s / (500 J / kg * ° C * 1500 ° C + 84000 J / kg) = 993 kg.

Answer: the mass of molten steel was m = 993 kg.