(Solved): A cubical piece of heat-shield-tile from the space shuttle measures \( 0.13 \mathrm{~m} \) on a sid ...

A cubical piece of heat-shield-tile from the space shuttle measures \( 0.13 \mathrm{~m} \) on a side and has a thermal conductivity of \( 0.065 \mathrm{~J} /\left(\mathrm{s} \cdot \mathrm{m} \cdot \mathrm{C}^{\circ}\right) \). The outer surface of the tile is heated to a temperature of \( 1110^{\circ} \mathrm{C} \), while the inner surface is maintained at a temperature of \( 17^{\circ} \mathrm{C} \). (a) How much heat flows from the outer to the inner surface of the tile in \( 5.0 \) minutes? (b) If this amount of heat were transferred to \( 3.8 \) liters ( \( 3.8 \mathrm{~kg}) \) of liquid water, by how many Celsius degrees would the temperature of the water rise?