Consider a 1000 w iron whose base plate is made of 0.5 cm thick aluminum alloy (ρ = 2770 kg/m^3, 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?