  A well-known high-school problem asking the final temperature of two 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, since thermal expansion raises its
center of mass. It is found that 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. It is found that gravity produces a
counterintuitive effect on the heat capacity, and the new answer to the problem
goes in the opposite direction of what traditionally thought.
