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

Tolga Yarman
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. PV5/3 = 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 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 relationships cast.