Radiation from a black body

Black body It is an ideal body that absorbs all incident thermal radiation. It is therefore a perfect absorber since its absorption power is equal to 1.

Although it is an idealization, there are several ways to obtain bodies with behavior similar to that of a black body. For example, we can coat any body with an irregular layer of black pigments.

Since emissivity and absorbance are equal, according to Kirchhoff's law, a blackbody will also have emissivity equal to 1. Thus, in addition to an ideal absorber, a blackbody is also an ideal emitter.

Stefan-Boltzmann's law for a blackbody becomes:

Any blackbody at the same temperature emits thermal radiation of the same full intensity. Each radiation of a given wavelength at the same temperature is also emitted to the same intensity by all black bodies, regardless of the material they are made of.

The study of black bodies is of great importance to physics, since the thermal radiation they emit has universal behavior. The emission spectrum analysis of these bodies was key to the development of the theories of energy quantization.

The graph below shows the intensity of radiation emitted by a blackbody as a function of wavelength at a given temperature.

Looking at the chart above, it is important to note that:

  • The emitted thermal radiation is composed of numerous radiations, distributed in a continuous range of wavelengths;
  • There is a radiation of a certain wavelength that is emitted at maximum intensity.
  • Wien Displacement Law

    In the graph below, we can observe the behavior of radiation emitted by a blackbody at two different temperatures.

    Over temperature T1 for T2, it is important to note that:

    • the intensity of each emitted radiation of a given wavelength increases as well as the total intensity of the emitted radiation and the total radiated power;
    • the maximum point of the curve shifts as the wavelength for which the intensity is maximum decreases.

    In 1893, Wilhelm Wien demonstrated that the maximum point of the curve I x λ shifts according to the expression below, called wien displacement law:

    Where B and the Wien dispersion constant, whose value is b = 2,898x10-3 m.K