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

TL;DR

This paper re-examines a classic physics problem and finds that gravity has a counterintuitive effect on a metal sphere's heat capacity, challenging traditional solutions and proposing new approaches using statistical mechanics and thermodynamics.

Contribution

It introduces two novel solutions to a well-known problem, demonstrating that gravity's effect on heat capacity is opposite to traditional expectations.

Findings

Gravity influences heat capacity in a counterintuitive way

Traditional solutions violate the second law of thermodynamics

New solutions align with thermodynamic principles

Abstract

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.