# Violation of the second law of thermodynamics? [closed]

Here is a machine which seems to violate the second law of thermodynamics:

• $A$ and $B$ are point black bodies of the same temperature (initially).
• everything is rotationally symmetric around the axis $AB$
• $e$ and $f$ are ellipsoids with foci $A$ and $B$, made of a reflective material
• $CD$ and $EF$ are sections of a reflective annulus
• there is no air

The stable state of the machine is $A$ having higher temperature than $B$ because

• The heat radiated by $B$ is all absorbed by $A$ (via paths $B\rightarrow K\rightarrow A$ and $B\rightarrow J\rightarrow A$).
• The heat radiated by $A$ is either absorbed by $B$ (via paths $A\rightarrow K\rightarrow B$ and $A\rightarrow J\rightarrow B$) OR by $A$ (via paths $A\rightarrow G\rightarrow I\rightarrow A$)

This seems to violate the 2nd law.

So, where is the hole here?

PS. While point bodies and perfect mirrors do not exits, note that we have quite a lot of margin here: a huge left ellipsoid and a tiny right ellipsoid will lead to almost 50% of all radiation from $A$ reflecting back to $A$. So, "small" bodies and 90%-efficient mirrors should be fine.

• Why downvote? Please explain! – sds Oct 6 '14 at 16:22
• Perfect mirrors and point blackbodies are not physical. However, to your point, there may be a more "fundamental" reason. Someone smarter than I will have to address that. – garyp Oct 6 '14 at 16:38
• Could you explicitly explain why this would contradict the second law? No word games please, calculate the entropies that you claim are violating the law - i.e. where does entropy decrease here? (Note that, though you have found a stable state, it is not granted that any initial configuration will actually reach that state) – ACuriousMind Oct 6 '14 at 16:59
• Voting to close. This is yet another variant of the ellipsoid paradox in thermodynamics. The resolution is simple: You are assuming point particles. Non-point sources will bathe the entire structure in light. See, for example Yoder & Adkins, "Resolution of the ellipsoid paradox in thermodynamics." American Journal of Physics 79.8 (2011): 811-818.. – David Hammen Oct 6 '14 at 19:40
• @David Hammen - asking a question about how a setup avoids violating some law is not the same as saying confidently that it does violate that law, I assumed the question was sincere and not a rhetorical way of saying "look, I've violated the 2nd law!" Physics textbooks often present "puzzler" questions like these for the purpose of aiding understanding. – Hypnosifl Oct 8 '14 at 22:37

• Can you actually do the calculation with a finite radius $R$ for the black bodies and check that the energy transfer balances out? What about the limit $R\to 0$? – Steven Mathey Oct 6 '14 at 17:10
• @StevenMathey In the limit that $R\rightarrow 0$ Stefan-Boltzmann Law has the emitted power tend to 0. Since this is a universal law for all black bodies, there is no parameter you can tune to keep the finite answer in the limit of zero surface area. – By Symmetry Oct 6 '14 at 17:33