How’s this square up the the Stefan Bolztmann law? I.e., for a black body, the power radiated is proportional to T4. So if you had two black bodies radiating all their energy at each other, with one acting as a resevoir, you’d get a net outward flux of power of the form Pα(T4−T4env), right?
Yeah, as Shankar says, this is only for conduction (and maybe convection?). The assumption about transition probabilities is abstractly saying there’s a lot of contact between the subsystems. If two objects contact each other in a small surface area, this post doesn’t apply and you’ll need to model the heat flow with the heat equation. I suppose radiative cooling acts abstractly like a narrow contact region, only allowing photons through.
Newton’s law of cooling, which this is proposed as a correction to, only describes conduction. It’s motivated by kinetic energies transferring via collisions.
How’s this square up the the Stefan Bolztmann law? I.e., for a black body, the power radiated is proportional to T4. So if you had two black bodies radiating all their energy at each other, with one acting as a resevoir, you’d get a net outward flux of power of the form P α (T4−T4env), right?
Yeah, as Shankar says, this is only for conduction (and maybe convection?). The assumption about transition probabilities is abstractly saying there’s a lot of contact between the subsystems. If two objects contact each other in a small surface area, this post doesn’t apply and you’ll need to model the heat flow with the heat equation. I suppose radiative cooling acts abstractly like a narrow contact region, only allowing photons through.
Newton’s law of cooling, which this is proposed as a correction to, only describes conduction. It’s motivated by kinetic energies transferring via collisions.