# Thermodynamics: heat transfer

I hope this question isn't too simplistic but I've been in a discussion with someone who claims that no energy is transferred between a cool object and a warm one (either by radiation or conduction) because the 2nd Law of Thermodynamics states that heat always flows from hot to cold.

My intuitive understanding is that energy actually flows in both directions, but the net flow conforms to the 2nd Law as more goes from hot to cold than vice-versa. In effect, the 2nd Law is an emergent property of many interactions. Is this the case?

EDIT: I should add that I've researched as much as possible, but no sources seem to explicitly state anything but the standard 2nd Law statement. If the answer is can be found in a resource I can be pointed towards, I'd be hugely grateful and apologise for wasting anyone's time.

• No time to write a detailed answer, but in short you're 100% correct, energy flows in both directions, always. The second law applies to the net transfer of hot-to-cold minus cold-to-hot, averaged over time. Commented Sep 18, 2014 at 13:00
• @Nathaniel Agreed. The directionality of heat transfer is not imposed by some universal law which demands it to be in one direction or another. It is the emergent result of billions of individual interactions that, curiously enough, can be predicted in advance based on the initial temperatures of the two bodies. Commented Sep 18, 2014 at 14:06

To see that you are correct, look to radiative heat transfer amongst black bodies. Consider two black bodies, call them bodies A and B, arranged as flat plates facing one another. Suppose body A has a temperature $T_A$ and body B has a temperature $T_B$. Both plates are black bodies, so each radiates energy at a rate given by the Stefan-Boltzmann law: $dE/dt = A\sigma T^4$, where $A$ and $T$ are the surface area and temperature of the body in question.
Since a black body absorbs all incoming radiation, body A transfers energy to body B, even if $T_A<T_B$, and body B transfers energy to body A, even if $T_B<T_A$.