Rate of EM emission based on surface characteristics

[druscilla]

Homework Statement

Given a scenario where there is a black painted surface at a temperature of 15 degrees Celsius and a polished aluminum plate at 20 degrees Celsius, could you determine which of these objects experiences a higher rate of emission of electromagnetic radiation per unit area?

Relevant Equations

None

I would think the black painted surface is

 

[hmmm27]

I would think the black painted surface is

And, why do you think that ?

 

[druscilla]

Since dark matt surfaces are better emitters of em radiation because of higher emissivity

 

[hutchphd]

You are correct but the fact that it is black to your eye speaks only to its emissivity/absorbance behavior for radiation in the visible spectrum. What is the peak black body emission for ~300K?
Also how are these objects being heated? They will not maintain a temperature difference unless differentially heated.

 

[haruspex]

Since dark matt surfaces are better emitters of em radiation because of higher emissivity

Right, but the aluminium plate is hotter. So the question is, is the temperature difference enough to overcome the emissivity difference? How will you assess that?

Also how are these objects being heated? They will not maintain a temperature difference unless differentially heated.

I think we are supposed to assume those temperatures are maintained somehow.

 

[druscilla]

No other variables were stated in the question, so now I think the Al plate must be the answer given Stephan-Boltzmann's law

 

[haruspex]

No other variables were stated in the question, so now I think the Al plate must be the answer given Stephan-Boltzmann's law

I see no reason to jump to the opposite conclusion.
If the emissivities were the same, what would the power ratio be?
What emissivity ratio would balance that?