In an electric furnace, a steel ingot with a mass of 1 t was completely melted in 2.3 hours.

In an electric furnace, a steel ingot with a mass of 1 t was completely melted in 2.3 hours. What is the power of an electric furnace if it is known that before the start of melting, the steel had to be heated by 1500 degrees. Neglect the loss of energy.

m = 1 t = 1000 kg.

T = 2.3 h = 8280 s.

C = 500 J / kg * ° C.

λ = 84000 J / kg.

Δt = 1500 ° C.

N -?

The amount of heat Q that is released in an electric furnace can be expressed by the formula: Q = N * T, where N is the power of the furnace, T is the operating time of the furnace.

For heating and melting steel, the required amount of heat Q is expressed by the formula: Q = C * m * Δt + λ * m, where C, λ is the specific heat and the heat of melting of steel, m is the mass of molten steel, Δt is the heating temperature of steel.

N * T = C * m * Δt + λ * m.

N = (C * Δt + λ) * m) / T.

N = (500 J / kg * ° C * 1500 ° C + 84000 J / kg) * 1000 kg / 8280 s = 100725 W.

Answer: the power of the electric oven is N = 100725 W.