Consider a 1000-w iron whose base plate is made of 0.5-cm-thick aluminum alloy (ρ = 2770 kg/m3, cp = 875 j/kg·°c, α = 7.3x10-5 m2/s). 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. taking the heat transfer coefficient at the surface of the base plate to be 12 w/m2·°c and assuming 85 percent of the energy generated in the resistance wires is transferred to the plate, determine how long it will take for the plate temperature to reach 140°c. is it realistic to assume the plate temperature to be uniform at all times? note: use an energy balance and come up with a differential equation to solve for this problem.