1) A 500 W iron has a base plate of thickness Lp = 0.5 cm, made...

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1) A 500 W iron has a base plate of thickness Lp = 0.5 cm, made of aluminum alloy (p = 3000 kg/m; Cp = 900 J/(kg-K)) with a high thermal conductivity (k = 180 W/(m K)). One side of the base plate is in contact with resistance wires that generate heat; the other side of the base plate is exposed to air and has a surface area Ap = 0.03 m. The convective heat transfer coefficient between the base plate and the air is h = 12 W/(m-K). Initially, the iron has the same temperature as the surrounding air, Tair = 20C. A/ Derive the differential equation that describes the rate of change of the plate temperature, dT/dt. B/ Assuming that the resistance wires are delivering the maximum power and that 90% of the heat generated is transferred to the plate, how long does it take for the plate to reach 140C? Normally, the temperature of an iron is maintained at the desired level by switching the electric current through the resistance wires on and off. In our case, the control system is broken and full power is delivered to resistance wires continuously. C/ Calculate the equilibrium temperature that the plate of the defective iron would reach at steady state, if it is left on. Ignore the effects of radiation. D/ Was it reasonable to ignore radiation in C/? Support your answer with a simple calculation. 1) A 500 W iron has a base plate of thickness Lp = 0.5 cm, made of aluminum alloy (p = 3000 kg/m; Cp = 900 J/(kg-K)) with a high thermal conductivity (k = 180 W/(m K)). One side of the base plate is in contact with resistance wires that generate heat; the other side of the base plate is exposed to air and has a surface area Ap = 0.03 m. The convective heat transfer coefficient between the base plate and the air is h = 12 W/(m-K). Initially, the iron has the same temperature as the surrounding air, Tair = 20C. A/ Derive the differential equation that describes the rate of change of the plate temperature, dT/dt. B/ Assuming that the resistance wires are delivering the maximum power and that 90% of the heat generated is transferred to the plate, how long does it take for the plate to reach 140C? Normally, the temperature of an iron is maintained at the desired level by switching the electric current through the resistance wires on and off. In our case, the control system is broken and full power is delivered to resistance wires continuously. C/ Calculate the equilibrium temperature that the plate of the defective iron would reach at steady state, if it is left on. Ignore the effects of radiation. D/ Was it reasonable to ignore radiation in C/? Support your answer with a simple calculation.