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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.

Respuesta :

tochjosh

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

batolisis

The minimum time needed for the plate temperature to reach 220°C is :

  • 80 secs

Given data :

Power rating of Iron = 1000 watts

base thickness = 0.5 cm

rho = 2770 kg/m³

cp = 875 j/kg°C

Surface area of base plate = 0.03 m²

Determine the minimum time needed for plate to reach 220°C

The power received by the plate = 1000 * 0.9 = 900 watts

next step : calculate the volume of the metal

volume = area * thickness

             = 0.5 * 10⁻² * 0.03

             = 1.5 * 10⁻⁴ m³

next step : calculate the mass of metal

mass of metal = 2770 * 1.5 * 10⁻⁴ m³

                        = 0.4155kg

Final step : Calculate the minimum time required

applying the formula for calculating electrical heat energy

= power * time = mass * Cp * temperature change

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

solve for  t ( minimum time required )

t = 79.98 secs ≈ 80 secs

Hence we can conclude that The minimum time needed for the plate temperature to reach 220°C is :

  • 80 secs

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