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A door is made of solid iron and this one-meter stick. How many kilojoules would it take to be to burn a hole 15 centimeters in diameter?

User Jasonbogd
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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,
H_f = 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 =
H_f × 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.

User Howl
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