Change the chapter
Question
The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly the windows transfer heat by conduction, calculate the rate of conduction in watts through a $3.00 \textrm{ m}^2$ window that is 0.635 cm thick (1/4 in) if the temperatures of the inner and outer surfaces are $5.00^\circ\textrm{C}$ and $-10.0^\circ\textrm{C}$, respectively. This rapid rate will not be maintained—the inner surface will cool, and even result in frost formation.
Question by OpenStax is licensed under CC BY 4.0.

$6.0 \times 10^3 \textrm{ W}$

Solution Video

OpenStax College Physics Solution, Chapter 14, Problem 31 (Problems & Exercises) (2:21)

Sign up to view this solution video!

Rating

2 votes with an average rating of 5.

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 31 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. We have a window pane which is made up of glass and the glass is a quarter inch thick which is 0.635 cm thick which we write in meters as 0.635 times 10 to the minus 2 meters. The area of this window pane if you were to look at it face on is 3 meter squared and we have the inside of the house here, here's the floor and this temperature inside which is T2. Because this formula for the rate of heat conduction is the rate of heat conduction from body 2 towards body 1 and so the heat is going from the inside of the house which is at 5 degrees and its going to the outside which is T1 which is negative 10 degrees Celsius and the thermal conductivity of glass is 0.84 Joules per second per meter squared per Celsius degree squared. OK. So maybe that's not squared there. Yeah, OK. And it’s actually not squared because we have a meter squared here but one of the meter squared in that area gets canceled by this thickness so leaving only 1 meter to the power of 1 in this denominator. OK. So let’s, well, we have written down our formula for the rate of heat conduction and this is the thermal conductivity of the material times with area divided by its thickness and we just plug in numbers. So it’s 0.84 Joules per second per meter per Celsius degree and then times up by 3 square meters area of the window times temperature inside 5 degree Celsius minus the temperature outside which is negative 10 and pay attention to the minus negative 10 which makes a plus in the end and divided by the thickness of the window and you end up with six point O times 10 to the 3 watts is the rate of heat conduction through the window pane.