How long will it take to melt 3500 kg of steel in a 50 kW oven operating at 65% efficiency from room temperature to 1600°C?

71195 seconds or 19.8 hours

Explanation:

Because the steel will be melted, beginning from room temperature, energy is needed to heat it from room temperature to 1600°C and another to melt it at 1600°C.

We take room temperature to be 27°C, the specific heat capacity of steel to be 420 J/kg/K and the specific latent heat of fusion of steel to be 440 J/kg.

The heat required to heat the steel from room temperature to 1600°C is given by

is the mass, is the specific heat capacity and is the change in temperature.

The heat required to melt it at 1600°C is

is the mass and is the specific latent heat of fusion of steel.

Adding both, the heat required is

Because the oven is 65% efficient, its output power =

Now, energy = power * time

Time = Energy/power

the second one and the forth one are in the purple because they are opinions and the rest are in the yellow

explanation: