International Journal of the Physical Sciences Vol. 5(10), pp. 1524-1529, 4 September, 2010 Available online at http://www.academicjournals.org/IJPS ISSN 1992 - 1950 ©2010 Academic Journals Full Length Research Paper The classical adiabatic constancy of PV γ for an ideal gas as a quantum mechanical occurrence Tolga Yarman 1 , Alexander L. Kholmetskii 2,3 * and Önder Korfali 4 1 Department of Engineering, Okan University, Akfirat, Istanbul, Turkey and Savronik, Eskisehir, Turkey. 2 Department of Physics, Belarus State University, 4 Nezavisimosti Avenue, 220030 Minsk, Belarus. 3 Okan University, Akfirat, Istanbul, Turkey. 4 Galatasaray University, Ortaköy, Istanbul, Turkey. Accepted 29 June, 2010 In this paper, a connection between the long lasting macroscopic classical laws of gases and the quantum mechanical description of non-interacting particles confined in a box was found, thus constituting an ideal gas. In such a gas, the motion of each individual molecule can be considered to be independent of all other molecules, and the macroscopic parameters of an ideal gas, mainly, pressure P and temperature T, can be defined as simple average quantities based on individual motions of all molecules in consideration. It is shown that for an ideal gas enclosed in a macroscopic box of volume V, the constant γ γ γ appearing in the classical law of adiabatic expansion law, that is, t cons PV tan = γ , can be derived based on quantum mechanics. Physical implications of the result we disclose are discussed. Key words: Adiabatic transformation, quantum mechanics, kinetic theory of gases. INTRODUCTION From time to time, most of us, no doubt, just like many scientists of the 20th century, were puzzled with the question of finding a link between the Boltzmann Constant k and the Planck Constant h. In particular, one can refer to the de Broglie doctorate thesis, where he brilliantly has applied his relationship (associating a wave length with the momentum of a moving particle) to the statistical equilibrium of gases (de Broglie, 1925), but did not advance his idea, to see whether one can along such a line, obtain anything related to the law of gases, established long ago, in 1650. At the second half of the past century a possible relationship between k, h as well as the light velocity in vacuum c has been explored in details by Dannenhower (1977). However, he concluded that the existence of a solution is not evident; thus according to him the issue remains unresolved. We will see below that this is actually a vain effort. *Corresponding author. E-mail: khol123@yahoo.com. Let us assume that the gas is made of just one kind of molecule. The Boyle-Mariotte law of ideal gas is given as usual by kNT RT n PV m = = (1) where P is the pressure of the gas, V the volume of the gas, T the temperature of the gas, n m the number of moles the gas is made of, N the number of molecules making the gas, R= 8.31 J/K is the gas constant, A N R k / = (2) is the Boltzmann constant, and A N the Avagadro number. The kinetic theory of gases allows us to derive the same casing as that of Equation (1) via considering the momentum change of each molecule separately, when bouncing back from a wall of the given container