Answer
The amount of energy required to melt a hole through the steel can be calculated as follows:
First, we need to find the mass of the steel that needs to be melted. The volume of the hole is given by:
V = πr²h = π(1.00 cm)²(12.5 cm) = 392.7 cm³
where r is the radius of the hole and h is the thickness of the steel. The density of the steel is given as 7970 kg/m³, which is equivalent to 7.97 g/cm³. Therefore, the mass of the steel that needs to be melted is:
m = Vρ = 392.7 cm³ × 7.97 g/cm³ = 3.13 kg
The energy required to melt this amount of steel can be found using the heat of fusion of the steel:
Q = mΔH_f = 3.13 kg × 268 kJ/kg = 838.84 kJ
The time it takes for the torch to deliver this amount of energy can be found using the thermal power of the torch:
P = ΔQ/Δt
Δt = ΔQ/P = 838.84 kJ / (0.45 × 2.35 kW) = 799.7 s
Therefore, it would take approximately 800 seconds or 13.3 minutes for the torch to melt a 2.00-cm-diameter hole through a 12.5-cm-thick piece of stainless steel.
Work Step by Step
The amount of energy required to melt a hole through the steel can be calculated as follows:
First, we need to find the mass of the steel that needs to be melted. The volume of the hole is given by:
V = πr²h = π(1.00 cm)²(12.5 cm) = 392.7 cm³
where r is the radius of the hole and h is the thickness of the steel. The density of the steel is given as 7970 kg/m³, which is equivalent to 7.97 g/cm³. Therefore, the mass of the steel that needs to be melted is:
m = Vρ = 392.7 cm³ × 7.97 g/cm³ = 3.13 kg
The energy required to melt this amount of steel can be found using the heat of fusion of the steel:
Q = mΔH_f = 3.13 kg × 268 kJ/kg = 838.84 kJ
The time it takes for the torch to deliver this amount of energy can be found using the thermal power of the torch:
P = ΔQ/Δt
Δt = ΔQ/P = 838.84 kJ / (0.45 × 2.35 kW) = 799.7 s
Therefore, it would take approximately 800 seconds or 13.3 minutes for the torch to melt a 2.00-cm-diameter hole through a 12.5-cm-thick piece of stainless steel.
