Obtaining Laws of Thermodynamics for Ideal Gases using Elastic Collisions

TL;DR

This paper explores deriving ideal gas laws from Newtonian mechanics through elastic collisions, using simulations and mathematical proofs to validate thermodynamic principles.

Contribution

It provides a novel approach to deriving thermodynamic laws directly from Newtonian mechanics using simple one-dimensional models.

Findings

Numerical simulation demonstrates the second law of thermodynamics.

Mathematical proof of the adiabatic law of expansion.

Validation of ideal gas laws from elastic collision models.

Abstract

The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws. The first section describes a numerical simulation that demonstrates the second law of thermodynamics. The second section mathematically demonstrates the adiabatic law of expansion of ideal gases.