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

Year: 2008 Pages: 7

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*, can be explicitly derived based on quantum mechanics, so that the instant comes to be proportional to^{5/3}= constant*h*here^{2}/m*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*, where^{5/3}~ hc = constant*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*h*and to^{2}*hc*, respectively; their ratio, i.e.*V*interestingly pointing to the^{1/3}~ h/mc,*de Broglie relationships*cast.