Stefan's Radiation Law with Boxes

[Fireworks]

I performed my own experiment, with one roof of one box painted white, another black and a third covered with plants. Temperatures were recorded inside of the boxes every 30 minutes. How could Stefan's radiation law be used with the temperatures to reflect the white box having cooler temperatures then the black box?

I am trying to use P_net = $$\sigma$$Ae(T⁴ - T_O⁴) ; where P is power, $$\sigma$$is the Stefan-Boltzmann constant (5.6696 x 10 W/m2∙K4), A is surface area, e is the emissivity of the object, T is temperature of the object, and TO is the surrounding temperature.

Any suggestions on how to use Stefan's radiation law to support/explain my data?

 

[wywong]

I guess all the boxes receives the same amount of sunlight.

From the Stefan's Law you can tell that radiation heat loss is proportional to emissivity. On the other hand, the heat absorbed from sunlight is also proportional to emissivity. For steady temperature, heat absorbed = heat loss so you should expect all the boxes to reach the same temperature in the absence of other means of heat loss (e.g. when hung in a vacuum). The other means include conduction and convection which are independent of emissivity so a darker surface loses *comparatively* less heat through the other means, resulting in a higher temperature.

Plants can lose significant amount of heat through evaporation and larger surface area. I hope you are not required to justify why such factors are small compared with the low emissivity of the white surface. In extreme conditions (low light, high ambient temperature), plants can be cooler than the surrounding!

Wai Wong