We consider a three-dimensional system composed of point particles of mass m enclosed in a cylinder of length 2L. The cross section of the cylinder is a circle of area A. We choose the coordinate system whose X-axis coincides with the symmetry axis of the cylinder. The cylinder extends from X = L to X=L. At time t=0, the total volume 2LA is divided into two equal subvolumes La by a circular piston with vanishing width, situated at the origin X=0. The mass m of the piston is equal to the mass of the point particles filling the cylinder. The number of the particles to the left and to the right of the piston are N{sup}- and N{sup}+, respectively. The piston is assumed to move along the X-axis without friction. Its collisions with the gas particles are perfectly elastic, and consist in instantaneous exchanges of velocities. As the piston has no internal degrees of freedom it represents a mobileadi abatic wall.
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