Question $1$: Consider a $800-$W iron whose base plate is made of $0\mathrm{.}5-$ cm$-$thick aluminum alloy $2024-T6(=2770k\frac{g}{m^3},c_p=875\frac{J}{k}g*K,=7\mathrm{.}3{10}^{-5}\frac{m^2}{s}).$ The base plate has a surface area of $0\mathrm{.}03m^2.$ Initially, the iron is in thermal equilibrium with the ambient air at $22C.$ Taking the heat transfer coefficient at the surface of the base plate to be $12\frac{W}{m^2}*K$ and assuming $85\%$ of the heat generated in the resistance wires is transferred to the plate, determine how long it will take for the plate temperature to reach $140C.$ Is it realistic to assume the plate temperature to be uniform at all times?