Archimedes' principle for ideal gas

TL;DR

This paper proves Archimedes' principle for a macroscopic object in an ideal gas, demonstrating asymptotic behavior and deriving properties like exponential density and inverse temperature.

Contribution

It introduces an asymptotic theorem for a macroscopic ball in ideal gas and analyzes the gas's density and temperature in the limit of many particles.

Findings

Gas density is exponential with height

Asymptotic inverse temperature is derived

Phase space volume estimated accurately

Abstract

We prove Archimedes' principle for a macroscopic ball in ideal gas consisting of point particles with non-zero mass. The main result is an asymptotic theorem, as the number of point particles goes to infinity and their total mass remains constant. We also show that, asymptotically, the gas has an exponential density as a function of height. We find the asymptotic inverse temperature of the gas. We derive an accurate estimate of the volume of the phase space using the local central limit theorem.