# Black body

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Radiating evacuated enclosure containing a blackbody.

To define a benchmark of the ability of a material to emit EM thermal energy, consider a thermodynamic argument. Suppose that a material can absorb EM energy that is incident upon it, converting the EM radiation into internal energy of the absorbing substance. Most real surfaces reflect some of the EM energy that is incident. For example, if radiation from a lecturer's laser pointer is directed onto a blackboard, the spot is easily seen, because the blackboard reflects a portion of the beam energy. If the blackboard surface were a perfect absorber, none of the laser energy would be reflected, and the laser spot would not be visible to the class. A material that absorbs 100 percent of the energy incident on it from all directions and at all wavelengths (i.e., has no reflection at all) is defined as a blackbody.

Now, consider such a blackbody element suspended within an evacuated enclosure at uniform temperature T (see figure). Let G be the total rate of radiant energy incident on the blackbody that originates by emission from the surface of the enclosure. By definition, the blackbody will absorb all of this energy. As with any mode of heat transfer, this absorbed thermal radiant energy will increase the internal energy (and thus temperature) of the blackbody element. However, this process can only continue until the blackbody reaches the temperature of the enclosure surface T; otherwise the system would violate the Second Law by having energy transfer from a colder to a hotter material. Because the blackbody is in an evacuated enclosure, it cannot have heat transfer by conduction or convection. Thermal radiation emission must therefore balance the absorbed radiation. The blackbody will come to equilibrium at temperature T when the absorbed radiation is balanced by the emitted radiation.

Suppose now that the absorbing element is not a perfect absorber, so that some incident energy is reflected and not absorbed. It follows that to maintain thermal equilibrium at temperature T, the element must emit less thermal energy than the perfectly absorbing blackbody element. Therefore, the perfectly absorbing blackbody must also be the best possible emitter of thermal radiation. It remains to quantify the amount of radiative energy emitted by the blackbody at a given temperature, as well as to prescribe how this energy is distributed among wavelengths.

## References

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.