A close examination of the motion of an adiabatic piston

The adiabatic piston problem involves two ideal gases contained in a horizontal cylinder and separated by an insulated piston that moves without friction. Initially, the piston is held in place, and the pressures of the two gases are different. When the piston is released, it undergoes oscillations that are damped due to frictional effects caused by the gases, and its motion finally ceases. The final pressures of the two gases are equal, but the final temperatures are typically different. Approximate solutions are developed for the time dependence of the piston motion, the temperatures of the gases, and the entropy changes of the gases. These results are compared with exact solutions of the coupled differential equations derived by Crosignani ["Approach to thermal equilibrium in a system with adiabatic constraints," Am. J. Phys. 64, 610-613 (1996)]. (C) 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3480028]