Quantum Mechanical Disclosure of the Classical Adiabatic Constancy of PVg for an Ideal Gas, and for a Photon Gas

TL;DR

This paper demonstrates that the classical adiabatic law PV^{5/3} = constant for ideal gases and photon gases can be derived from quantum mechanics, linking macroscopic constants to fundamental quantum constants like h and c.

Contribution

It extends the quantum mechanical derivation of the adiabatic constant from ideal gases to photon gases, revealing their dependence on universal constants.

Findings

The adiabatic constant for an ideal gas is proportional to h^2/m.

For a photon gas, the constant is proportional to hc.

The constants are rooted in universal quantum constants, h and c.

Abstract

Previously, we established a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules of an ideal gas (T. Yarman et al. arXiv:0805.4494). In such a gas, the motion of each molecule can be considered independently on all other molecules, and thus the macroscopic parameters of the ideal gas, like pressure P and temperature T, can be introduced as a result of simple averaging over all individual motions of the molecules. It was shown that for an ideal gas enclosed in a macroscopic cubic box of volume V, the constant, arising along with the classical law of adiabatic expansion, i.e. PV5/3=constant, can be explicitly derived based on quantum mechanics, so that the constant comes to be proportional to h^2/m; here h is the Planck Constant, and m is the relativistic mass of the molecule the gas is made of. In this article we show that the same holds for a photon gas, although the related setup is quite different than the previous ideal gas setup. At any rate, we come out with PV5/3 hc=constant, where c is the speed of light. No matter what the dimensions of the constants in question are different from each other, they are still rooted to universal constants, more specifically to h2 and to hc, respectively; their ratio, i.e. V1/3 h/mc, interestingly pointing to the de Broglie relationship's cast.