Plancks law for black body radiation explains the color of a glowing hot object, the light from our sun, and even the energy radiated by the Earth. This post offers a complete derivation of that famous equation for black body radiation, starting from the foundational principles of thermodynamics. We build the formula from the ground up, relying on just a few clearly stated postulates. You will see how a profound physical result emerges from a surprisingly simple and direct thermodynamical approach.

The fundamental mathematical ideas behind thermodynamics

My goal is to derive Maxwell’s equations of electromagnetism with almost no effort at all. As often in mathematics, things look simpler when there is less structure. Here, as in mechanics, we do not assume any prior metric, so the geometry of the space at hand is very simple.