Thermodynamics of radiation modes

We study the equilibrium thermodynamics of the electromagnetic radiation in a cavity of a given volume and temperature. We found three levels of description, the thermodynamics of one mode, the thermodynamics of the distribution of frequencies in a band by summing over the frequencies in it and the global thermodynamics by summing over all the frequencies. One equation relating frequency and volume is used to define the thermodynamics of one mode, and to explain the mystery of the frequency-dependent quantities having a similar behaviour to the non-frequency-dependent quantities for some thermodynamic equations and different behaviour for others. Besides, this frequency-volume relation is used to count the number of modes in a band of frequency.