On a Link between Classical Phenomenological Laws of Gases and Quantum Mechanics

TL;DR

This paper establishes a link between classical gas laws and quantum mechanics, deriving the adiabatic law PV^5/3=const from quantum principles, thus revealing a quantum basis for macroscopic thermodynamic behavior.

Contribution

It demonstrates, for the first time, a quantum mechanical derivation of a classical thermodynamic law for ideal gases.

Findings

Derived the adiabatic law PV^5/3=const from quantum mechanics.

Showed a quantum basis for macroscopic gas behavior.

Discussed physical implications of quantum-classical connection.

Abstract

In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered independently on all other molecules, and thus the macroscopic parameters of ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of molecules. It is shown that for an ideal gas enclosed in a macroscopic cubic box of volume V, the constant, in the classical law of adiabatic expansion, i.e.PV^5/3=const, can be derived, based on quantum mechanics. Physical implications of the result we disclose are discussed. In any case, our finding proves, seemingly for the first time, a macroscopic manifestation of a quantum mechanical behavior, and this in relation to classical thermodynamics.