The Classical Adiabatic Constancy of ? for an Ideal Gas Turns out to be a Quantum Mechanical Occurence
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of non-interacting particles confined in a box, in fact constituting an ideal gas. In such a gas, the motion of each individual molecule can be considered independently from 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 expression, i.e. PV5/3 can be derived, based on quantum mechanics. Physical implications of the result we disclose are discussed. In any case, our finding proves, seemingly, a macroscopic manifestation of a quantum mechanical behavior, and this in relation to classical thermodynamics.