heating two identical spheres

Heating two identical balls

De Palma & Sormani , Am.J.Phys,83,723 [ADS link]

The following physics puzzle was given at the very first International Physical Olympiad (IPhO) in 1967:

"Consider two identical homogeneous balls, A and B, with the same initial temperatures. One of them is at rest on a horizontal plane, while the second one hangs on a thread. The same quantities of heat have been supplied to both balls. Are the final temperatures of the balls the same or not? Justify your answer. (All kinds of heat losses are negligible.)"

This problem became very popular due to the elegance and simplicity of the official solution, and it can now be found in several problem books and collections. However, after being around for almost half a century, we re-analysed it and found that the official solution is wrong! It turns out that this solution violates the second law of thermodynamics. We worked our the correct solution, and found that answer goes in the opposite direction of the incorrect solution. Check out our paper on the American Journal of Physics for the details.