Two rooms, each a cube 4.0 m per side, share a 14-cm-thick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at $30 ^\circ \textrm{C}$, while in the other room it is at $10 ^\circ \textrm{C}$. How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. These two rooms are separated by a brick wall of thickness 0.14 meters. And 1 room is 30 degrees Celsius and the other one is 10 degree Celsius. So, the rate of heat transfer across this wall due to conduction is the thermal conductivity of brick, 0.84 joules per second meter Celsius degree, times the area of the wall which is 4 meters squared since we're told each room is a cube of side length 4 meters. And then multiplied by the temperature difference, 30 degrees Celsius minus 10 degrees Celsius divided by the thickness of the wall, 0.14 meters. And this gives 1,920 watts is the rate of heat transfer. So, the number of bulbs needed to maintain this rate of heat transfer, we need to supply this amount of power. There's going to be 1,920 watts times 1 bulb for every 100 watts. And this gives us 19.2 bulbs. But since you can't have 0.2 bulbs, we'll have to round this up to 20 bulbs.