Double-paned window heat transfer

[aoc0708]

Homework Statement

Consider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of 0.745 m2, separated by a layer of air with a thickness of 1.95 cm. The temperature on one side of the window is 0.00°C; the temperature on the other side is 20.0°C. In addition, note that the thermal conductivity of glass is roughly 36 times greater than that of air.

(a) Approximate the heat transfer through this window by ignoring the glass. That is, calculate the heat flow per second through the 1.95 cm of air with a temperature difference of 20.0 C°. (The exact result for the complete window is 17.6 J/s.) Express your answer with three significant digits.


(b) Use the approximate heat flow found in part (a) to find an approximate temperature difference across each pane of glass. (The exact result is 0.141 C°.) Express your answer with three significant digits.

Homework Equations

H = (kAdeltaT)/L

The Attempt at a Solution

I've only gotten as far as A; I've tried setting up the equation like this:

30.5L = [36k(air)*2(.745)*20] + [k(air)*A(air)*20]

but there are too many variables to work with. My main goal was to find the area so I could find the heat transfer through air separately, but for some reason even when I plug in the actual values of k for glass and air it doesn't work. Assistance is welcome!

 

[danago]

I think you can assume that the area of the air section is the same as the area of the glass panels.

By the looks of your working, it seems as if you are assuming that there is a 20 degree temperature difference across each pane of glass, as well as 20 degrees across the air. The question is saying that the outside of one of the glass panes is 0 degrees, and the outside of the OTHER glass panes is at 20 degrees. The temperature gradient across each individual pane and the air gap will be less than 20 degrees, but they will sum to a total of 20.