This dependence is called square of distances law

,

where Е ₁ – density of radiant heat flux at the distance of 1m from the emitter;

E _r –the same value at the distance of r meters.

This law holds true for the case when dimensions of emitting body or element are very small as compared with distance. But if emitting body surface is characterized by dimensions comparable with distance this law cannot be used.

Lambert’s law. It is possible to determine total quantity of energy E emitted in all the directions using Stefan-Bolzmann law. But distribution of this energy in different directions is not uniform. Emissitive ability in normal direction is

where Е – density of integral hemispherical radiation of blackbody determined with Stefan-Boltzmann law, W/m²;

В –brightness of integral radiation, W/m².

It can be seen from this dependence that brightness in normal direction is in p times smaller than density of integral hemispherical radiation.

For monochromatic radiation

where J –spectral radiation intensity determined with Plank’s law, W/m³;

В _l – brightness of monochromatic radiation, W/m³.

According to Lambert’s law energy quantity Е _j emitted in direction that forms angle j with normal to the surface is determined like follows (figure 7.8)

.

Therefore the most energy is emitted in normal direction with j =0, it diminishes with angle j increase and equals zero if j =90°.

Density of integral hemispherical radiation

then or .

It is known from experiments that Lambert’s law holds absolutely true for blackbody only. For grey bodies it is confirmed only for angle values j =0...60°.

Дата добавления: 2015-08-17