Double pane window

Classical Mechanics Level 3

A double pane window has a 8mm (1/4 inch) air-gap between the two sheets of glasses. Which one is bigger: the heat transported between the panes by radiation or by conduction? We need an order-of magnitude estimate, see the choices on the side.

For the thermal radiation properties consider the glass an ideal black-body. The thermal conductivity of air is 2.6 $\times 10^{-2}$ Watt/(meter Kelvin). Assume that the temperature difference between the outside and the inside sheet of glass is much less than the temperature of the room (293K or 20C $^\circ$ or 70F). The third form of heat transfer, convection, is not very important when the gap between the glass panels is less than 1cm (but it becomes significant at larger separation).

The heat transport by radiation is about 10 times more The heat transport by conduction is about 100 times more The heat transport by radiation is about 100 times more They are about the same The heat transport by conduction is about 10 times more

1 solution

Laszlo Mihaly
Nov 6, 2017

The ratio of conduction/radiation is $j_{cond}/j_{rad}$ , where $j_{cond} = \kappa A/l \Delta T$ and $j_{rad}= A \sigma (T+\Delta T)^4-A \sigma T^4= 4 A\sigma T^3\Delta T$ . Here $A$ is the area of the window, $\Delta T$ is the temperature difference, $\kappa= 2.6 \times 10^{-2}$ W/mK, $l=8$ mm is the thickness of the gap, and $\sigma=5.67\times 10^{-8}$ W/m $^2$ K $^4$ is the Stefan-Boltzman constant. The ratio we get is $j_{cond}/j_{rad}=0.56$ , so the two contributions are about the same.

This tells us that it does not make much sense to make the air gap larger. We will further reduce the conduction, but the radiative transfer is independent of the thickness of the gap, so we do not gain that much. Applying a super-thin metallic coating that reduces radiation and also increasing the air gap that reduces conduction, that makes lots of sense. This is indeed done in the more expensive windows.

Double pane window

1 solution

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