41 - Radiation

For most solids, the transmissivity is zero, and thus they may be called opaque to thermal radiation. For an opaque body, \(\rho + \alpha = 1\).

A black body is one for which \(\alpha = 1\). A black body neither reflects nor transmits any thermal radiation.

Kirchhoff’s law: it is a relation between absorptivity and emissivity at a given wavelength (\(\lambda\)) as given below: \[{\varepsilon_\lambda = \alpha_\lambda}\]

A gray body is defined as one which has a constant value of emissivity, so that for any temperature range, it radiates the same proportion of energy radiated by a black body. Similarly it will have a constant absorptivity. With the application of Kirchhoff’s law, for gray body \(\varepsilon = \alpha\).

A black body absorbs all incoming radiation and emits the maximum possible, \(\alpha = \varepsilon = 1\); where \(\varepsilon\) is emissivity.

Since we see reflected light (radiation), a so-called black body will appear black, no light being reflected from it. A small hole in a large cavity closely approaches a black body. Radiation incident to the hole has very little opportunity to be reflected back out of the hole.

Highly polished and white surfaces generally have lower emissivities than rough or black surfaces.