Stephen Montgomery-Smith and Hannah Morgan, Obtaining Laws of Thermodynamics for Ideal Gases using Elastic Collisions.
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.
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