Radiation heat transfer rate, q [W/m2], from a body (e.g. a black body) to its surroundings is proportional to the fourth power of the absolute temperature and can be expressed by the following equation:
q = εσT4
where σ is a fundamental physical constant called the Stefan–Boltzmann constant, which is equal to 5.6697×10-8 W/m2K4. The Stefan–Boltzmann constant is named after Josef Stefan (who discovered the Stefa-Boltzman law experimentally in 1879) and Ludwig Boltzmann (who derived it theoretically soon after). As can be seen, radiation heat transfer is important at very high temperatures and in a vacuum.
Q = εσA1-2(T41 −T42) [J/s]
q = εσ(T41 −T42) [J/m2s]
The area factor A1-2, is the area viewed by body 2 of body 1, and can become fairly difficult to calculate.
It is known that the amount of radiation energy emitted from a surface at a given wavelength depends on the material of the body and the condition of its surface as well as the surface temperature. Therefore, various materials emit different amounts of radiant energy even whhen they are at the same temperature. A body that emits the maximum amount of heat for its absolute temperature is called a blackbody.
A blackbody is an idealized physical body, that has specific properties. By definition, a black body in thermal equilibrium has an emissivity of ε = 1.0. Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a black body and therefore are called gray bodies.
The surface of a blackbody emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature (25 °C, 298.15 K). Real objects with emissivities less than 1.0 (e.g. copper wire) emit radiation at correspondingly lower rates (e.g. 448 x 0.03 = 13.4 W/m2). Emissivity plays important role in heat transfer problems. For example, solar heat collectors incorporate selective surfaces that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation.
Since the absorptivity and the emissivity are interconnected by the Kirchhoff’s Law of thermal radiation, a blackbody is also a perfect absorber of electromagnetic radiation.
Kirchhoff’s Law of thermal radiation:
For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.
emissivity ε = absorptivity α
A blackbody absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. Its absorptivity is therefore equal to unity, which is also the highest possible value. That is, a blackbody is a perfect absorber (and a perfect emitter).
Note that visible radiation occupies a very narrow band of the spectrum from 0.4 to 0.76 nm, we cannot make any judgments about the blackness of a surface on the basis of visual observations. For example, consider white paper that reflects visible light and thus appear white. On the other hand it is essentially black for infrared radiation (absorptivity α = 0.94) since they strongly absorb long-wavelength radiation.