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Macroscopic equations for the adiabatic piston

AutorCencini, Massimo; Palatella, Luigi; Pigolotti, Simone; Vulpiani, Angelo
Palabras claveDifferential equations
Statistical mechanics
Fecha de publicación7-nov-2007
EditorAmerican Physical Society
CitaciónPhysical Review E 76, 051103 (2007)
ResumenA simplified version of a classical problem in thermodynamics -the adiabatic piston- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained in the left and right chambers of the piston are always in equilibrium that is, the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution after any collision with the piston. Then by using kinetic theory we derive the collision statistics, from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables namely, the piston average velocity and position, the velocity variance, and the temperatures of the two compartments. The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of a gas devised to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables that catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache, and Lesne [J. Stat. Phys. 108, 669 (2002); 112, 1177 (2003)].
Descripción12 pages.-- PACS numbers: 05.70.Ln, 05.40.-a.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.76.051103.
Auxiliary material available at: http://netserver.aip.org/cgi-bin/epaps?ID=E-PLEEE8-76-106710.
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