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. PV^5/3 = constant, can be explicitly derived based on quantum mechanics, so that the instant comes to be proportional to h²/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 PV^5/3 ~ 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. V^1/3 ~ h/mc, interestingly pointing to the de Broglie relationships cast.