Q$2.$ A tile$-$iron is designed with a large plate that is heated to $150C$ by an embedded electrical heater. This heated iron presses against a tile to weaken the adhesive underneath, making it easier to remove the tile from the subfloor. The adhesive will become pliable if its temperature exceeds $50C$ for at least $2$ minutes, but it must not reach temperatures higher than $120C$ to prevent damage. Assume that the tile and subfloor start at a temperature of $25C$ and have similar thermal properties characterized by thermal conductivity $k=0\mathrm{.}1\frac{W}{m}*K$ and volumetric heat capacity $C_p=1\mathrm{.}00{10}^6\frac{J}{m^3}*K.$

a$)$ How much time is required for a worker to successfully lift the tile using the tile$-$iron? Will the temperature of the adhesive go beyond $120C?(3$ points assumptions $+4$ points calculation$)$

b$)$ If the tile$-$iron has a square surface area measuring $254$ mm on each side, how much energy is extracted from it during the time taken to lift the tile? $(3$ points calculation$)$

$($Please consider that tile and subflooring have same thermophysical properties$)$