What is the ratio of heat flow through Window A to Window B?

[quantumworld]

Hello ALL,
I am really having a hard time with this question, any effort will be greatly appreciated!
Window A is a pane of glass 4 mm thick, as shown above. Window B is a sandwich consisting of two extremely thin layers of glass separated by an air gap 2 mm thick. If the thermal conductivities of glass and air are 0.8 watt/meter oC and 0.025 watt/meter oC, respectively, then the ratio of the heat flow through window A to the heat flow through window B is
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
D is the answer, And I have no clue

many thanks!

 

[suffian]

let K_air = H_air / (A * delT/delX_air)
let K_glass = H_glass / (A * delT/delX_glass)

your looking for ratio of heat flow, or H_glass to H_air.
it should be almost trivial from here. the problem is mostly just testing whether you know the equation for thermal conductivity (in fact, i just looked it up online, I've never seen it before).

 

[hhegab]

The correct answer is D) 16.

To find the ratio of heat flow through Window A to Window B, we can use the formula for heat flow, Q = (kAΔT)/d, where k is the thermal conductivity, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.

For Window A, we have:
Q = (0.8 watt/meter oC)(1 meter^2)(1 oC)/(0.004 meter)
Q = 200 watt

For Window B, we have:
Q = (0.8 watt/meter oC)(1 meter^2)(1 oC)/(0.002 meter)
Q = 400 watt

Therefore, the ratio of heat flow through Window A to Window B is 200/400 = 1/2 = 16. This means that the heat flow through Window B is 16 times larger than the heat flow through Window A.

I hope this helps! Don't worry, these types of problems can be tricky but with practice, you will become more comfortable with them. Keep up the good work!