Quantum mechanical disclosure of the classical adiabatic constancy of pγ for both an ideal and a photon gas

Abstract

In our recent paper (Yarman et al., 2010), we established a connection between the macroscopic adiabatic transformation law (Pressure × Volume5/3= Constant) of an ideal gas and the quantum mechanical description of its molecules. This connection was unique in embodying just the Planck contant and quantum numbers, instead of the classical temperature quantity and Boltzmann constant. 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, comes to be proportional to h2/m; here h is the Planck constant and m is the rest mass of the molecule the gas is made of. In this paper, we first check the relationship of concern in general parallelepiped geometry, displaying how the quantum numbers are affected throughout. We then show that our results hold for a photon gas, too, although the related setup is quite different from the previous ideal gas setup. At any rate, for a photon gas we come out with PV4/3 ~ hc = Constant, where c is the speed of light in vacuum. No matter what, the dimensions of the two constants in question are different from each other; they are still rooted to universal constants, more specifically to h2 and to hc, respectively, while their ratio, that is, V1/3 ~h/mc, interestingly points to the de Broglie relationship's cast. © 2011 Academic Journals.