Counterintuitive effect of gravity on the heat capacity of a solid sphere: Re-examination of a well-known problem

A well-known high-school problem asking the final temperature of two identical spheres that are given the same amount of heat, one lying on a table and the other hanging from a thread, is re-examined. The conventional solution states that the sphere on the table ends up colder, because thermal expansion raises its center of mass. This solution violates the second law of thermodynamics and is therefore incorrect. Two different new solutions are proposed. The first uses statistical mechanics, while the second is based on purely classical thermodynamical arguments. Gravity produces a counterintuitive effect on the heat capacity, and the new answer to the problem goes in the opposite direction of what has been traditionally thought.