Question about thermal radiation and the 2nd Law

Question

I am studying thermal radiation and considering two radiating black bodies. The book describes the net heat flux as the difference between the flux from object 1 to object 2, and the flux from object 2 to object 1. But if there is a net flux then one object must be hotter than the other. Say object 1 is hotter. Since object 1 is hotter, there should be no flux from object 2 to object 1 as per the 2nd Law prohibition on the transfer of heat from a cold object to a hot object. So why does my book say there is when calculating the net heat flux?

Answer 1

The second law says the net flow of heat occurs spontaneously from a higher temperature body to a lower temperature body. This applies to conduction and convection as well as radiation. But that does not preclude the possibility of some energy transfer from the lower temperature body to the higher temperature body. It is perhaps easiest to explain using a microscopic description of heat transfer by conduction.

The average translational kinetic energy of the atoms and molecules of a higher temperature body is greater than the average of a loweri temperature body. When the two bodies are in contact with one another collisions between the atoms and molecules of the two bodies result in a net transfer of kinetic energy from the higher temperature body to the lower temperature body.

However some individual atoms and molecules of the lower temperature body may have higher kinetic energy than individual atoms and molecules of the higher temperature body. When they collide kinetic energy is transferred from the lower temperature body to the higher temperature body. There is no violation of the second law because the net transfer of kinetic energy is from the higher temperature body to the lower temperature body due to the fact that the average kinetic energy of the atoms and molecules is higher in the higher temperature body.

So for radiation there is heat flux from the lower temperature body to the higher temperature body, as there is kinetic energy transfer from the lower temperature body to the higher temperature body for conduction. However the net heat flux is from the higher temperature body to the lower temperature body.

Can you point to a source that explicitly states this? None of my textbooks say "net" heat flow in any 2nd Law statement.

While it is true the statements of the second law do not explicitly use the term "net", that it because the statements apply to the overall macroscopic effect of heat transfer and not to the microscopic details of energy transfer. I would like to quote the following from the Hyperphysics web site, bold face is mine. It is from the third slide in the link that follows:

"It is important to note that when it is stated that energy will not spontaneously flow from a cold object to a hot object, that statement is referring to net transfer of energy. Energy can transfer from the cold object to the hot object either by transfer of energetic particles or electromagnetic radiation, but the net transfer will be from the hot object to the cold object in any spontaneous process. Work is required to transfer net energy to the hot object"

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw.html#:~:text=Second%20Law%3A%20Refrigerator%20Second%20Law%20of%20Thermodynamics%3A%20It,higher%20temperature%20object.%20This%20precludes%20a%20perfect%20refrigerator.

Hope this helps

Answer 2

All objects that have some temperature radiate energy. This radiant energy leaving the body is solely a function of its temperature and emissivity.

The second law statement - heat can not flow from a cold body to hot body spontaneously - is referring to the net heat flux. In other words, it is saying that net heat gained by the cold body and the net heat lost by the hot body is always positive. (When these bodies are in isolated system)

Let us assume two bodies are maintained at T1 and T2 (with T1>T2). for example.. assume that these bodies are so large that any net heat flux into or out of them would hardly alter their temperature. If these two body comprise the system, the net heat flux is always from hot to the cold body.

Hope this helps.