What we learn in this chapter

A photon gas in perfect thermal equilibrium with its surroundings at some temperature T will exhibit an energy spectrum of a specific amplitude and shape known as the blackbody spectrum, which was first proposed by Max Planck in 1901. In its form as a specific intensityI(ν) (W m−2 Hz−1 sr−1), the blackbody spectrum peaks at a frequency proportional to its temperature. At low frequencies (the Rayleigh–Jeans approximation), it increases linearly with temperature and quadratically with frequency. At high frequencies (the Wien approximation), it decreases quasi-exponentially. The energy density, ∝ T4, and photon number density, ∝ T3, follow directly from I(ν). The former is closely related to the pressure of a photon gas, whereas the latter is closely related to the distribution function, the number density in six-dimensional phase space. Calculation of the average photon energy yields 2.70 kT.

The total energy flux (W) passing in one direction through a unit surface is proportional to T4. A normal gaseous (spherical) star emits a spectrum that approximates (roughly) that of a blackbody, which allows the luminosity to be expressed in terms of the stellar radius and an effective temperature. Momentum transfer by the photons to a hypothetical surface yields a pressure that is one-third the energy density. The blackbody flux is the maximum intensity that can be obtained from a thermal body. […]