Answer:
The heat required, to burn a hole 15 cm in diameter through the iron door is 34,370.050 kJ
Step-by-step explanation:
The information given on the door are;
The thickness of the door, t = One-meter
The diameter of the hole to be burnt out, d = 15 cm = 0.15 m
The latent heat of fusion of iron,
= 247 kJ/kg
The density of iron, ρ = 7.874 g/cm³ = 7874 kg/m³
The volume of the iron to be melted off, V = π·d²/4 × t
∴ V = (π × 0.15²/4) × 1 ≈ 0.01767145867
The volume of the iron to be melted off, V ≈ 0.01767145867 m³
The mass of the iron to be melted off, m = ρ × V
∴ m = 7874 kg/m³ × 0.01767145867 m³ ≈ 139.145066 kg
The mass of the iron to be melted off, m ≈ 139.15 kg
The heat required, to melt the mass of iron at the melting point temperature and burn a hole 15 cm in diameter, ΔH, is given as follows;
ΔH =
× m
∴ ΔH = 139.15 kg × 247 kJ/kg = 34,370,050 J = 34,370.050 kJ
The heat required, to burn a hole 15 cm in diameter through the iron door ΔH = 34,370.050 kJ.