# Kirchhoff law of thermal radiation

Kirchhoff's law of thermal radiation states that for thermal equilibrium for a particular surface the monochromatic emissivity $\epsilon_{\lambda}$ equals the monochromatic absorptivity $\alpha_{\lambda}$: $$\alpha_{\lambda} = \epsilon_{\lambda}$$ I wonder how this can be only valid for thermal equilibrium, because $\epsilon_{\lambda}$ and $\alpha_{\lambda}$ seem to depend only on the temperature of the surface under consideration, and it seems to me that they don't depend on the other bodies around the surface. So according to this, it should follow that they are equal always, when they are equal in thermal equilibrium, which isn't correct. So I wonder how the lack of thermal equilibrium can change the values of $\alpha$ and $\epsilon$?

Think of those not as a capacity to absorb/emit but as simply absorption/emission. Imagine you put a cold metal cube next to a hot identic cube. The hot one will emit a lot of heat but receive a very little amount of heat from the cold one. Therefore $α_λ<ϵ_λ$, and vice-versa for the other cube. After a while, they will reach the same temperature, and at that moment, the radiation from cube A will be equal as cube B's. At that moment $α_λ$ will equal $ϵ_λ$ since the "output" radiation and "input" radiation are equal.