2001/09/28 by C. Gruber, Gruber, Christian, S. Pache +3
Engineering · Physics and Astronomy · #Advanced Thermodynamic Systems and Engines #Dynamics and Control of Mechanical Systems #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.cond-mat/0109542
openalex publication_date 2001/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the evolution of a system composed of N non-interacting point particles of mass m in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area A of the cross-section, the mass M of the piston, and the number N of particles go to infinity keeping A/M and N/M fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption.