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

 

[astrokreng]

Great question! Stefan's radiation law can definitely be used to support and explain your data. Let's break down the equation and see how it applies to your experiment.

First, we have Pnet, which represents the net power emitted by the object. In this case, the object is the box. The net power emitted is the difference between the power emitted by the box and the power absorbed by the box.

Next, we have the Stefan-Boltzmann constant, which is a fundamental constant in physics that relates the temperature of an object to the amount of thermal radiation it emits.

Then, we have A, which is the surface area of the box. This is important because the larger the surface area, the more radiation can be emitted.

Next, we have e, which is the emissivity of the object. Emissivity is a measure of how well an object emits thermal radiation. In your experiment, the white box has a higher emissivity compared to the black box, as white surfaces tend to emit more thermal radiation.

Finally, we have T and TO, which represent the temperature of the box and the surrounding temperature, respectively. This is where your data comes in. By plugging in the temperatures you recorded for each box, you can calculate the net power emitted by each box.

According to Stefan's radiation law, the higher the temperature of the object, the more thermal radiation it emits. So, in your experiment, the white box with a higher temperature should emit more thermal radiation compared to the black box with a lower temperature. This aligns with your data showing that the white box had cooler temperatures compared to the black box.

In summary, Stefan's radiation law can be used to explain your data by considering the emissivity and temperature of each box. The white box, with a higher emissivity and temperature, emitted more thermal radiation and therefore had cooler temperatures compared to the black box. I hope this helps to support your findings in your experiment!