Relating Radiancy to Energy Density?

[eck]

I'm looking through some of my physics notes where we derived radiancy equations for black body radiation (Rayleigh-Jeans and Planck), and I have a quick question. In class, we went through the derivation for the energy density as a function of frequency and temperature. However, I can't find anything in my notes about how radiancy is related to energy density. I tried to look online, and didn't find anything helpful, other than the equation that relates them: $$R(\nu ,T) = c/4 u(\nu ,T)$$, where u is the energy density and R is the radiancy. From the units it looks like radiancy is the power per area per time, but I am totally mystified by the factor c/4. Can anyone quickly go over where this comes from?

 

[eck]

Sorry, the TeX came out wrong. It should be one-fourth times c times u (nu, T).

 

[sir-pinski]

Radiancy and energy density are two important concepts in the study of black body radiation. Radiancy, also known as spectral radiance, is the amount of electromagnetic radiation emitted from a surface in a particular direction and at a particular frequency. It is measured in units of power per unit area per unit solid angle per unit frequency. On the other hand, energy density is the amount of energy per unit volume of a material.

The relationship between radiancy and energy density can be understood through the concept of radiative transfer. This is the process by which energy is transferred from one location to another via electromagnetic radiation. In the case of black body radiation, the energy emitted by a surface is absorbed and re-emitted by neighboring surfaces, thus creating a continuous exchange of energy. The energy density at a particular frequency and temperature is related to the radiancy at that frequency and temperature through the equation R(\nu ,T) = c/4 u(\nu ,T).

The factor c/4 in this equation is known as the Stefan-Boltzmann constant, which relates the energy density to the temperature of the black body. It is derived from the Planck's law of black body radiation and represents the maximum amount of energy that can be emitted by a black body at a given temperature. This is why it is also referred to as the black body radiation constant.

In summary, radiancy and energy density are two important concepts related to the emission and transfer of energy via electromagnetic radiation. Radiancy represents the amount of energy emitted per unit area, while energy density represents the amount of energy per unit volume. The relationship between these two quantities is described by the Stefan-Boltzmann constant, which takes into account the temperature of the black body.