How Do Surface Properties Affect Heat Absorption and Emission in Copper Discs?

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The experiment involves measuring the Stefan Boltzmann constant using two copper discs, one normal and one painted black, with temperature measurements taken electronically. The black disc shows a consistent temperature rise of about 10 degrees before tapering off, while the normal disc only rises by 5 degrees in the same time frame. The discussion raises a question about whether the normal disc would eventually reach the same temperature as the black disc if given more time, assuming both are in contact with a heated container. It is noted that if the discs are not fully inside the container, conduction may affect the temperature outcomes. Ultimately, the precise behavior of the normal disc remains uncertain without further experimentation.
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I'm doing an experiment to measure the Stefan Boltzmann constant with two small copper discs, one normal copper and one with a painted black surface. Both are covered with a a heated container and the termperature of the discs electronically measured. The black disc's temperature rises at a fairly constant rate, then tails off after a temperature rise of about 10 degrees. For the normal disc, a rise of 5 degrees was measured in the same time period and didn't tail off.

My question is had I allowed more time for the normal disc, would it have reached the same temperature as the other did and then tail off, or will this temperature be different?
 
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If the heated container is maintained at exactly the same temperature and the disc is in contact with only the container, both discs must eventually reach thermal equilibrium with the container. It seems, from your description, that the discs aren't completely inside the container. In that case, conduction comes into play and it's hard to say what will happen without doing the experiment.
 
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