Black Body and the colored objects around us

[fog37]

Hello Forum,

A quick discussion about blackbody theory. As a premise, this is what I know:

A blackbody is an ideal body that absorbs all types of radiation incident on it, no matter its wavelength. Once absorbed, the energy is used to increase the blackbody's temperature and when the temperature is nonzero, the blackbody will also start emitting a portion of that same radiation (energy) that it previously absorbed. The emitted energy is distributed over all wavelengths (the emission spectrum depends on the temperature $T$).

• When steady-state is reached, the rate of energy absorption is perfectly matched by the rate of energy emission and the temperature stops increasing and remains fixed. Is it possible to know how much of the absorbed energy goes into raising the blackbody's temperature $T$ and how much of the absorbed energy becomes emitted radiation before steady-state is reached? For example, at steady-state, if the absorbed power is 100W, the emitted power would be also 100W. But before reaching steady-state, if the absorbed power is 100W, the emitted power may be just 30W and the remaining 70W should solely go, I believe, into increasing the temperature (i.e. average kinetic energy of the composing molecules). What happens to the molecules and their average kinetic energy when steady-state is reached?

• Ordinary objects have a certain color because they absorb sunlight energy of all wavelengths except for the energy at the wavelength that corresponds to their color which gets instead reflected. Does that mean that ordinary colored objects are far from being blackbodies and are far from following blackbody theory? Which objects resemble blackbodies or greybodies? The sun is yellowish but seems to be a good example of a blackbody...

Thanks!

 

[scottdave]

The sun emits radiation because of the nuclear reactions taking place, releasing energy.

It's been awhile since I studied this, but ordinary colored objects should behave much differently than a blackbody.

 

[Bystander]

See "cavity radiator/radiation," https://www.google.com/search?q="ca...ome..69i57.29212j0j7&sourceid=chrome&ie=UTF-8

 

[fog37]

Well, as a follow-up to my own question, I think there are always the following three processes involved when an opaque object (not transparent, so no transmission) has radiation falling on it:

a) Absorption
b) Reflection
c) Emission

Ideal blackbodies don't reflect any energy at all. They only absorb and emit. But teal life objects that have color do absorb, reflect and emit radiation when some radiation is incident on them. Example: a red apple in sunlight. The apple reflects energy at about 650nm (red color) and absorbs all the energy at the remaining wavelengths. Because of this absorbed energy, the apple's temperature is raised and at steady-state the energy is emitted with a peak wavelength in the emission spectrum that is in the infrared (not visible to the human eye)...Does that sound correct?

The apple's temperature is not due to absorbed energy in sunlight only but also to the energy absorbed by other objects (air, etc.). Is that correct?

 

[scottdave]

The apple's temperature is not due to absorbed energy in sunlight only but also to the energy absorbed by other objects (air, etc.). Is that correct?

Yes the apple can receive direct radiation of heat from the sunlight, as well as from the air molecules (Convection, I believe), and the table or other object that it is resting on (Conduction)

 

[Stavros Kiri]

Does that mean that ordinary colored objects are far from being blackbodies and are far from following blackbody theory?

Generally yes. But there is a certain energy density/ wavelength-temperature (or frequency-temperature) distribution that is followed (in equilibrium) [see ahead (cf. 'Planck's law [of black body radiation]')].

Which objects resemble blackbodies or greybodies? The sun is yellowish but seems to be a good example of a blackbody...

Model for 'black body' serves a small opening (or hole) in a cavity, which follows Planck's law (see also section "Derivation" and the quote:)
"Consider a cube of side L with conducting walls filled with electromagnetic radiation in thermal equilibrium at temperature T. If there is a small hole in one of the walls, the radiation emitted from the hole will be characteristic of a perfect black body. We will first calculate the spectral energy density within the cavity and then determine the spectral radiance of the emitted radiation."

The sun is just a 4π (solid angle) opening (or cavity) [taken as integral], that's why it's considered a black body ! ...

I hope that helps.
[P.S. looking at the proof (of a theory etc.) I think always helps to understand it better.
Note: your other (i.e. 1st) question is a non-equilibrium question and the answer I think depends on the system, but it is not generally described via black body theory.]

 

[Stavros Kiri]

I wish the OP came back to tell us what he thinks ...

 

[fog37]

So sorry, my apologies. I had too much homework to do.

I am now comfortable with the idea that a blackbody is a perfect absorber ( in the sense that it absorbs all the energy that is incident on it). The absorbed energy will eventually be emitted but not necessarily in the same spectral region in which it was absorbed which means that the absorption coefficient at wavelength $\lambda$ will not be necessarily equal to the emission coefficient at the same wavelength $\lambda$, correct? However, Kirchhoff's law states that the two coefficients are equal at every wavelength for a blackbody...where is the problem?

 

[Khashishi]

The absorbed energy will eventually be emitted but not necessarily in the same spectral region in which it was absorbed which means that the absorption coefficient at wavelength λ will not be necessarily equal to the emission coefficient at the same wavelength λ, correct?

No. As you said next, Kirchhoff's law says that the coefficients are equal. But that doesn't mean the absorption and emission brightnesses are equal, since the temperatures of the body and incoming radiation are not necessarily equal. If the body is colder than the light source, the object will absorb light and preferentially reradiate at higher wavelengths due to the T^4 term.

The Sun is a pretty good black body because it is really big (and therefore rather opaque) and has many degrees of freedom. The mean free path for photons in the upper solar atmosphere is small compared to the length scale of the atmosphere. Photons will continually scatter between various particles (mostly electrons and protons), picking up random Doppler shifts with each collision.