Consider a $1000-$W iron whose base plate is made of $0\mathrm{.}5-$cm$-$thick aluminum alloy $2024-$T$6$

and $\{$:$c_p=875\frac{J}{k}g*C).$ The base plate has a surface area of

$0\mathrm{.}03m^2.$ Initially, the iron is in thermal equilibrium with the ambient air at $22C.$ Assuming

$90$ percent of the heat generated in the resistance wires is transferred to the plate,

determine the minimum time needed for the plate temperature to reach $190\mathrm{.}0C.($Round

the final answer to three decimal places.$)$