# 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.