Consider a non-relativistic electron bath that is at an equilibirum temperature T e , i.e., k B T e ≪ ≪ m e c 2 , where m e is the electron mass. Let there be a low-frequency radiation field that satisfies the soft-photon approximation, i.e., ℏ ℏ ω ω ≪ ≪ m e c 2 where ω ω is the photon frequency. Then, the enery exchange in any collision between photon and electron will be small. Assuming homogeneity and isotropy and expanding the collision integral of the Boltzmann equation in terms of small energy exchange, one obtains the Kompaneyets equation.