Blackbody Rooftop Homework | Emissivity 0.9, Absorbtivity 0.8

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In summary, we are given a black roof with an emissivity of 0.9 and an absorbtivity of 0.8 for solar radiation. The sun's intensity is 300 BTU/hr ft2 at midday. Considering a temperature of 68 °F for air and surroundings and using q/A = 0.38 (∆T)^1.25 for the rate of conduction/convection, we can calculate the equilibrium temperature of the roof. Additionally, assuming an effective sky temperature of -10 °F and using WolframAlpha, we can determine the fraction of heat lost to radiation from the roof.
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Homework Statement


The black roof of a building has an emissivity of 0.9 and an absorbtivity of 0.8 for solar radiation. The sun beats down at midday with an intensity of 300 BTU / hr ft2.

a) If the temperature of the air and the surroundings is 68 °F, if the wind velocity is negligible, and if no heat penetrates the roof, what is the equilibrium temperature of the roof ? For the rate of conduction / convection use q/A = 0.38 (T) 1.25, where T is the temperature drop between the roof and air in degrees F.

b) What fraction of the heat from the roof is lost to radiation.


Homework Equations





The Attempt at a Solution


For this problem, assume the effective sky temperature on that day is -10F. also, the "rate of conduction / convection" just means the overall rate of conduction + convection away from the roof.

I am wondering if I approached this correctly. I used wolframalpha to solve the equation.
 

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1. What is a blackbody rooftop?

A blackbody rooftop is a theoretical construct used in physics to represent an idealized surface that is a perfect absorber and emitter of radiation at all wavelengths. It is often used as a model for real-world objects, such as rooftops, to study their behavior in terms of radiation.

2. What is emissivity?

Emissivity is a measure of the efficiency with which a surface emits thermal radiation. It is often represented as a decimal between 0 and 1, with 1 being a perfect emitter and 0 being a perfect reflector. A blackbody rooftop, by definition, has an emissivity of 1.

3. What is absorptivity?

Absorptivity is a measure of the efficiency with which a surface absorbs thermal radiation. It is also represented as a decimal between 0 and 1, with 1 being a perfect absorber and 0 being a perfect reflector. In the case of a blackbody rooftop, it has an absorptivity of 0.9.

4. How are emissivity and absorptivity related?

Emissivity and absorptivity are directly related to each other, as they both measure the ability of a surface to emit and absorb thermal radiation. In general, a surface with a high emissivity will also have a high absorptivity, and vice versa.

5. Why are emissivity and absorptivity important for a blackbody rooftop?

For a blackbody rooftop, emissivity and absorptivity are important because they determine the behavior of the rooftop in terms of thermal radiation. A blackbody rooftop, with its high emissivity and absorptivity, absorbs and emits thermal radiation at a high rate, making it an efficient model for studying the behavior of real-world rooftops in terms of heat transfer.

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