A hollow square box is made from $1$ ft$2$ sheets of a prototype insulating material that is $1$ inch thick. Engineers are performing a test to measure the new material$$s thermal conductivity. A $100$ W electrical heater is placed inside the box. Over time, thermocouples attached to the box show that the interior and exterior surfaces of one face have reached the constant temperatures of $150$F and $90$F$.($a$)$ Calculate the thermal conductivity in USCS units of Btu$/$hr ft$$F $.($b$)$ Calculate the thermal conductivity in SI units of W m$$C