Consider the base plate of a 1200 W household iron that has a thickness of L= 0.5 cm, base area of A = 300 cm^2, and properties of ? = 7.3 e-5 m^2/s, ?=2770 kg/m^3 and Cp = 875 J/kgK. The inner surface of the base plate is in contact with the resistance heaters inside, and the outer surface losses heat to the surrounds at 20°C with a convection coefficient of h=80 W/m^2k. The base plate is initially in equilibrium with the ambient air. Assuming 85% of the energy generated by the resistance heaters is transferred to the base plate, determine how long it will take for the exterior of the plate to reach 140°C.