- #1

diegzumillo

- 173

- 18

## Homework Statement

The attached image shows the temperature as a function of the distante to a glass window. The window dimensions are given ( 60cm, 60cm, 0.5cm) and the thermal conductivity of the air and glass are, respectively, [tex]1W/(m.K)[/tex] and [tex]0,025W/(m.K)[/tex]. What is the energy transfer to the exterior through the window?

## Homework Equations

I believe this is the 'rate of energy transfer', it mentions above:

[tex]\frac{Q}{\Delta T}=\frac{A(T_{2}-T_{1})}{\sum_{i} d_{i} / k_{i}}[/tex]

This equation is generalized for any number of materials joined together. the [tex]d_i[/tex] are the thickness and [tex]k_i[/tex] the thermal conductivity of each material and [tex]A[/tex] is the area of the surface the exchange is being made.

## The Attempt at a Solution

So, I tried to solve this problem in all possible ways.. none of them gave me the right answer!

The one that seems more reasonable is to consider the 'interior' as one material in which the left extremity is at a high temperature, the exterior also as a material in which the right extremity is at a low temperature. In the middle is, of course, the glass. So the above equation should look something like this:

[tex]\frac{Q}{\Delta T}=\frac{3600cm^{2}30K}{(7,75+0,5/0,025+7,75)cm/\frac{W}{m.K}}[/tex]

Simplifying, using meters we have - if I didn't screwd up- this:

[tex]\frac{Q}{\Delta T}=31,3W[/tex]

Wich is NOT the correct answer. The correct answer is [tex]1,75W[/tex]... :uhh:

Also, this illustration is really troubling me. I don't really undestand the physics behind it. Except the fact that the temperature gets lower. But why is it constant in the glass?