The formation of blackbody radiation

[jauram]

I am puzzled about the formation of blackbody emission (Planck's law). Specifically, we know that such things like incandescent lamps, an electric arc in a gas at high pressure etc. produce a nearly blackbody spectrum of corresponding temperature. Does this mean that in these cases a nearly equilibrium state between radiation and matter is set up? Or how do you explain why the spectra are close to that of a cavity?

 

[lalbatros]

Consider first a cavity with a small hole: the emission is low enough as to not perturb the BB radiation.

Consider now a very large volume of gas. Since the volume is very large, most of the radiations emitted inside the volume will be reabsorbed, only a tiny fraction has chance to escape.

Consider now a small volume of a solid.
This is exactly similar to the large volume of gas, as long as this volume of solid does not become transparent (like a gold foil).
That's why hot iron from a blast furnace also shows a nice BB spectrum.

The key point is "transparency".
See the full theory of radiation heat exchanges for more details.
These notions of emissivity, absorptivity have many applications, for example in combustion modeling.

Michel

 

[astrokreng]

The formation of blackbody radiation is a fundamental concept in physics and is described by Planck's law. This law states that the intensity of radiation emitted by a blackbody at a given temperature is a function of the wavelength and the temperature, and it follows a specific distribution known as the Planck distribution.

In order to understand the formation of blackbody radiation, it is important to first understand what a blackbody is. A blackbody is an idealized object that absorbs all radiation incident upon it, without reflecting or transmitting any of it. This means that a blackbody also radiates at all wavelengths, making it a perfect emitter of radiation. Real objects, such as incandescent lamps and electric arcs, may not be perfect blackbodies, but they can still emit radiation that closely follows the blackbody spectrum.

The reason for this is that in these cases, a nearly equilibrium state between radiation and matter is set up. This means that the energy absorbed by the material is quickly re-emitted as radiation, and this process continues until an equilibrium is reached. This equilibrium state is what allows these objects to emit radiation that closely follows the blackbody spectrum.

In the case of incandescent lamps, the filament is heated to a high temperature, causing it to emit radiation in the visible spectrum. This radiation is then absorbed and re-emitted by the surrounding gas, creating a nearly equilibrium state between the radiation and matter. Similarly, in an electric arc, the high temperature of the gas causes it to emit radiation, which is then absorbed and re-emitted, again resulting in a nearly equilibrium state.

In summary, the reason why these objects emit radiation that closely follows the blackbody spectrum is due to the establishment of a nearly equilibrium state between radiation and matter. This phenomenon is a fundamental aspect of blackbody radiation and is crucial in understanding the behavior of objects that emit radiation, such as stars and other celestial bodies.