Answer:
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
[tex]H_S = mc_S\delta\theta[/tex]
[tex]m[/tex] is the mass, [tex]c_S[/tex] is the specific heat capacity and [tex]\delta\theta[/tex] is the change in temperature.
[tex]H_S = 3500\times420\times(1600-27) = 2312310000[/tex]
The heat required to melt it at 1600°C is
[tex]H_L = ml_S[/tex]
[tex]m[/tex] is the mass and [tex]l_S[/tex] is the specific latent heat of fusion of steel.
[tex]H_L = 3500\times440 = 1540000[/tex]
Adding both, the heat required is [tex]2312310000+1540000=2313850000\text{ J}[/tex]
Because the oven is 65% efficient, its output power = [tex]65\%\times50000 = 32500 \text{ W}[/tex]
Now, energy = power * time
Time = Energy/power
[tex]t = \dfrac{2313850000}{32500}=71195 \text{ seconds} = 19.8 \text{ seconds} [/tex]
