Change the chapter
Question
(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is $120\textrm{ m}^2$ and their inside surface is at $18.0^\circ\textrm{C}$, while their outside surface is at $5.00^\circ\textrm{C}$ . (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?
Question by OpenStax is licensed under CC BY 4.0.
  1. $1.01\times 10^{3}\textrm{ W}$
  2. One kilowatt heater is needed to offset the rate of heat loss.
Solution Video

OpenStax College Physics Solution, Chapter 14, Problem 30 (Problems & Exercises) (1:10)

Sign up to view this solution video!

Rating

1 vote with a rating of 2

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 14, Problem 30 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. Walls that are 13.0 centimeters thick which is 13.0 times 10 to the minus 2 meters thick have a thermal conductivity 2 times that of glass wool which is 0.042 joules per second per meter per Celsius degree and that works out to 0.084. The walls have an area of 120 square meters and the temperature inside is 18.0 degrees Celsius and the temperature outside is 5.00 degrees Celsius. So these are all the pieces of data that we need to plug into our formula for the rate of heat transfer due to thermal conductivity. So this is the thermal conductivity here and we multiply it by the area of the wall times the temperature difference between the two sides of it divided by the thickness of the wall. So that's 0.084 times 120 square meters times 18.0 minus 5.00 divided by the thickness and that gives 1.01 times 10 to the 3 watts. This is 1 kilowatt and so there's only 1 kilowatt heater needed to offset this rate of heat loss.