Consider a 1000-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024-T6 (rho = 2770 kg/m3 and cp = 875 J/kg·°C). The base plate has a surface area of 0.03 m2. Initially, the iron is in thermal equilibrium with the ambient air at 22°C. Assuming 90 percent of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 220°C.

Question

Marely Evans

Engineering

1 May, 13:16

Consider a 1000-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024-T6 (rho = 2770 kg/m3 and cp = 875 J/kg·°C). The base plate has a surface area of 0.03 m2. Initially, the iron is in thermal equilibrium with the ambient air at 22°C. Assuming 90 percent of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 220°C.

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Answers (1)

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Esther Quinn · Answer 1

Answer: 79.98sec

Explanation:

Power received by plate = 0.9x1000

= 900W

Volume of metal = area x thickness

V = 0.5x10^-2 x 0.03 = 1.5x10^-4m3

Mass of metal = density x volume

= 2770kg/m3 x 1.5x10^-4 = 0.4155kg

Electrical heat energy = power x time = mass x specific heat capacity (Cp) x temperature change

900 x t = 0.4155 x 875 x (220-22)

900t = 71985.375

t = 79.98s