- #1
pastro
- 15
- 0
Hi,
I feel extremely stupid for having to have this explained to me, but I am really confused by it. I recently encounter a proof of the fact that the brightness (energy/(time x area x solid angle x frequency)) of a black body can only depend on its temperature, not the properties of the enclosure itself. Here is the argument:
"Two black body cavities at the same temperature are brought near each other. They each have a tiny hole so that they can exchange radiation with each other. A filter which only allows radiation of frequency [tex]\nu[/tex] to pass between them is placed between the holes. If the brightness function of the two is not the same, energy will spontaneously flow from one cavity to another, which violates the second law of thermodynamics. Thus, the brightness functions of the two black bodies must be the same at a given temperature."
The part I don't understand is why the spontaneous flow of energy between two systems in thermal equilibrium violates the second law of thermodynamics. If I casually think to myself, "the second law gives the time arrow of energy, and energy only flows from hot to cold, then heat flow between bodies at equal temperatures must be a violation," then I get what is meant. But, if I write,
[tex]\frac{\delta Q_{total}}{T}\geq 0[/tex] and [tex]\delta Q_{body1}[/tex]=-[tex]\delta Q_{body2}[/tex], then the second law reads [tex]\frac{\delta Q_{body1}+\delta Q_{body2}}{T}\geq 0[/tex] so [tex]\delta Q_{body1} \times 0 \geq 0[/tex]
I don't see the contradiction, or how this puts a constraint on [tex]\delta Q_{body1}[/tex]
pastro
I feel extremely stupid for having to have this explained to me, but I am really confused by it. I recently encounter a proof of the fact that the brightness (energy/(time x area x solid angle x frequency)) of a black body can only depend on its temperature, not the properties of the enclosure itself. Here is the argument:
"Two black body cavities at the same temperature are brought near each other. They each have a tiny hole so that they can exchange radiation with each other. A filter which only allows radiation of frequency [tex]\nu[/tex] to pass between them is placed between the holes. If the brightness function of the two is not the same, energy will spontaneously flow from one cavity to another, which violates the second law of thermodynamics. Thus, the brightness functions of the two black bodies must be the same at a given temperature."
The part I don't understand is why the spontaneous flow of energy between two systems in thermal equilibrium violates the second law of thermodynamics. If I casually think to myself, "the second law gives the time arrow of energy, and energy only flows from hot to cold, then heat flow between bodies at equal temperatures must be a violation," then I get what is meant. But, if I write,
[tex]\frac{\delta Q_{total}}{T}\geq 0[/tex] and [tex]\delta Q_{body1}[/tex]=-[tex]\delta Q_{body2}[/tex], then the second law reads [tex]\frac{\delta Q_{body1}+\delta Q_{body2}}{T}\geq 0[/tex] so [tex]\delta Q_{body1} \times 0 \geq 0[/tex]
I don't see the contradiction, or how this puts a constraint on [tex]\delta Q_{body1}[/tex]
pastro