Savchenko Problem 5.11.4

The key insight is that at thermal equilibrium, a body must absorb and emit thermal radiation at equal rates—otherwise its temperature would change. By comparing the radiation each body emits (proportional to its emissivity $\varepsilon$) with what it absorbs from its surroundings (proportional to its absorption coefficient $\alpha$), you'll see these must be identical for the system to stay in balance. This is Kirchhoff's law in action: the body's "greyness" for emitting heat must match its "greyness" for absorbing it.

The key insight is that at thermal equilibrium, a body must absorb and emit thermal radiation at equal rates—otherwise its temperature would change. By comparing the radiation each body emits (proportional to its emissivity $\varepsilon$) with what it absorbs from its surroundings (proportional to its absorption coefficient $\alpha$), you'll see these must be identical for the system to stay in balance. This is Kirchhoff's law in action: the body's "greyness" for emitting heat must match its "greyness" for absorbing it.