 #1
AppleiPad556
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 1
 Homework Statement:

Hi!
For my Physics IB Extended Essay, I’m interested in exploring the correlation between the colour of a surface (using albedo) and the temperature of the surface (after reading articles about white roofs and the urban heat island). Currently I’m hoping to execute an experiment and correlate the data points with an equation, and I have a few questions that I hope to gain more insight on below.
 Relevant Equations:

General formula for Albedo: ##\alpha = \frac{\text{total scattered power}}{\text{total incident power}}##
StefanBoltzmann equation: ##P = \varepsilon\sigma A(T^4T_s^4)##
Combining the two: $$T = \sqrt[4]{\frac{\alpha P_{incident}}{\varepsilon\sigma A}+T_s^4}$$
 As mentioned above, I wanted to devise an equation that can relate the colour of a surface to the temperature on the surface. I tried using the general definition of albedo and combining it with the StefanBoltzmann equation (see above, Relevant Equations). However this means that the higher the albedo value, the higher the temperature, which goes against the fact that higher albedo has more energy reflected (which should cause lower temperature).
Is this correct, or did I misuse these equations (am I able to relate the two powers together?), and are there other equations or values that might work better in this case?  Along these lines, is albedo a good value to use in my case? I chose albedo originally as it appeared to have a good correlation with energy and colour, but it seems that albedo tends to be used more for planetary bodies instead of specific surfaces. Is there something else that I can use that can relate colour and reflected energy, or is albedo okay for this situation?
 With the lack of laboratories/detailed equipment, my current plan for the experiment is to create model structures with the top of the structure being flat with differentcoloured construction paper. With an infrared lightbulb as a heat source, I would fill the structure with water and use a thermometer to calculate the energy reflected (power from bulb – energy in water), and I can also use an infrared thermometer to determine the temperature of the roof itself. This experiment can be easily done at home, but is it too simple to get accurate data? Are there better materials that I can substitute that are readily available?
 Thinking about my discussion, another goal I wanted to achieve in this experiment was to see if I could also mix in surface area of the roof into the relationship and to try to see how accurate it is using real case studies of cool roofs. I can factor this into my experiment (keep volume but change dimensions of structure), and it seems to be included in the StefanBoltzmann equation. Is this too ambitious? I am aware that there are a plethora of factors that need to be factored into the real world, and this is only something that I want to use as further exploration.
Thank you for reading, and have a good day,
Eric