Temperature of a body exposed to sunlight

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Discussion Overview

The discussion revolves around determining the temperature evolution of a black-painted aluminum object exposed to sunlight, considering factors such as solar radiation, heat absorption, and heat loss mechanisms. The scope includes theoretical and conceptual aspects of heat transfer and thermodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Jaimie seeks to understand how to calculate the temperature evolution of a black-painted aluminum object exposed to solar radiation of 1 kW-hr/m².
  • One participant suggests that the aluminum will reach an equilibrium temperature when it radiates 1 kW/m², using Stefan's law to estimate the temperature at approximately 90°C.
  • Another participant questions the unit of solar radiation provided and emphasizes the need to consider the cross-sectional area of the aluminum to calculate energy absorption accurately.
  • Jaimie clarifies that the solar energy received is 1 kW per square meter over one hour and expresses interest in understanding the relationship between paint absorption, aluminum heat capacity, and other factors.
  • A participant advises Jaimie to list all relevant variables to identify which can be neglected and which require assumptions, indicating that there are more factors to consider than just absorption and heat capacity.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and assumptions regarding the calculation of temperature evolution, with no consensus reached on the methodology or the significance of various factors involved.

Contextual Notes

Participants highlight the importance of considering various assumptions and variables, such as the area of the aluminum object and the specifics of heat loss mechanisms, which remain unresolved.

jc.int
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hello,
If I have a black painted aluminium exposed to sunlight (being it and the atmosfere at 27ºC), and I have the total solar radiation it is exposed to (lets say 1 ° KW-hr/m²), how can I know the evolution of its temperature?
(if there is any free simulator on the internet I would be glad if someone could give it, but I haven't found any).

Thank you,
Jaimie
 
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If you only consider heat loss by radiation then I would say that the blackened Aluminium would reach an equilibrium temperature when it is radiating 1kW/m^2
Then use Stefan's law
E = σT^4 to find T (in Kelvin)
I got about 90C using your figures...seems reasonable
 
Hi Jaimie,

I don't understand this unit here below. What you will need to do is find the cross sectional area of your aluminum bucket and use that to find the energy per unit time being absorbed by the bucket.

jc.int said:
(lets say 1 ° KW-hr/m²)

The other answer given to you will be very approximate because the entire bucket will be radiating heat, while only the side facing the sun will be acquiring heat.

You have a few assumptions to make.
 
I mean that the solar energy received in one m2 in 1hour is 1 ° KW (metric units for solar energy radiatio, see http://www.raws.dri.edu/cgi-bin/rawMAIN.pl?nmXHAC , equivalent to the Langley, ºly). What I'd like to know what is the relation between the painting absorbion, aluminum heat capacity, etc

Thank you,
Jaimie
 
I was confused previously because your first unit was not a rate.

I think it would help for you to write down a list of variables that you have to consider. That way you can decide which ones are "negligible" and which ones you'd like to make assumptions for. I assure you that there are more variables than absorption and heat capacity.
 

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