$$\require{cancel}$$

# 1.11: Exitance M

The exitance of an extended surface is the rate at which it is radiating energy (in all directions) per unit area. The usual symbol is $$M$$ and the units are $$\text{W m}^{-2}$$. It is an intrinsic property of the radiating surface and is not dependent on the position of an observer.

Most readers will be aware that some property of a black body is equal to $$\sigma T^4$$. Technically it is the exitance (integrated over all wavelengths, with no subscript on the $$M$$) that is equal to $$\sigma T^4$$, so that, in our notation, the Stefan-Boltzmann law would be written

$M=\sigma T^4 \tag{1.11.1}, \label{1.11.1}$

where $$\sigma$$ has the value $$5.7 \times 10^{-8} \text{W m}^{-2} \text{K}^{-4}$$.

Likewise the familiar Planck equation for a black body:

$M_\lambda=\frac{2\pi hc^2}{\lambda^5 \left( e^{hc/kT}-1 \right)} \tag{1.11.2} \label{1.11.2}$

gives the exitance per unit wavelength interval.

The word "emittance" is an older word for what is now called exitance.

The emissivity of a radiating surface is the ratio of its exitance at a given wavelength and temperature to the exitance of a black body at that wavelength and temperature.