Black bodies, perfect reflection and heat transfer

[Carlos de Meo]

Hi Guys
While studying physics for my masters (doing it in material science engineering), huge amount of questions appeared.
First, let's imagine two experiments
1) One enclosure with perfect reflective walls (R=1 over the entire thermal radiation spectra) at a temperature T1 and a body inside with Temperature T2 (T2 higher than T1). Let's say there is vacuum inside so energy can only be exchanged through radiation
After some time, since the reflected photons have the same energy of the incoming ones, there is no energy left for increasing temperature of the wall? If that statement is true, this system will never eventually reach thermal equilibrium
2) The same enclosure but now the walls are perfect black bodies. The walls will absorb thermal radiation until it reaches the same temperature of the body inside. Is that true so the system will reach thermal equilibrium?

 

[mfb]

If the walls are perfectly reflective, the wall does not absorb or emit any energy, it does not change its temperature, not even initially (assuming there are no effects from the outside). The system never reaches equilibrium because you removed heat transfer completely.

2) The same enclosure but now the walls are perfect black bodies. The walls will absorb thermal radiation until it reaches the same temperature of the body inside. Is that true so the system will reach thermal equilibrium?

Right.

 

[Carlos de Meo]

Well, since reflection and absorption are opposite events (i think), returning to the real world
Let´s study a metal. Since transmittance is pretty low, we can say R + A = 1 (R stands for reflection and A for absorption)
The extinction coefficient (K) is usually high in metals. So we think about the Absorptivity= A= 4πK/λ + scattering and R= ((n+1²+K²)/((n+1)²+k²) assuming a electromagnetic wave traveling from air to a conductor. Increasing K raises the values of both A and R
So, in the end, metal absorbs radiation, reflects, they are similar things or none of above?

 

[mfb]

R=1 directly leads to T=A=0, as their sum is 1 and they cannot be negative.

Such a material does not exist in reality, but metals are good reflectors for everything below their plasma frequency (that makes them shiny), and superconductors are even better reflectors, at least a lower frequencies.

 

[Carlos de Meo]

But how can the same coefficient (K) increases both R and A at the same time and R= 1 -A?

 

[mfb]

Your formula for the absorption is the absorption length in the material, it is not the fraction of light that gets absorbed by the surface.

 

[Carlos de Meo]

And the amount of absorbed light would be evaluated through Beer Lambert law, correct?

 

[mfb]

After you take surface reflection into account, you can use that law to calculate absorption while radiation passes through the material. Then you can consider reflection at the end of the material to find the amount transmitted to whatever comes behind.

 

[Carlos de Meo]

Ahhh, now it makes sense. Vielen dank Herr mfb, sie sind sehr freundlich