20 80 140 200 M/m 0.02 0.04 0.06 0.08 $_{Z}$/L FIG. 3: (Color online) Dimensionless relative standard deviation σ$_{Z}$/L of the position of the movable piston as a function of the mass ratio M/m , for several values of the coefficient of normal restitution of the gas α , as indicated in the insert. The curves are guides for the eye. In all the cases, the coefficient of restitution for the gas-movable piston collisions is α$_{P}$ = 0 . 99. III. COMPRESSIBILITY AND EFFECTIVE TEMPERATURE where p$_{L}$ is the pressure of the granular gas in the vicinity of the movable piston and V is the volume (area) of the system. The derivative in the above equation is computed at constant value of all the parameters defining the system, α , α$_{P}$ , N$_{z}$ and v$_{W}$ , except p$_{L}$ = Mg 0 /W , as it follows from the definition of the pressure. In the following, p$_{L}$ will be modified by changing the mass of the piston M , keeping g 0 and W unchanged. The reason for this choice is twofold. First, changing g 0 is equivalent to modifying v$_{W}$ and, second, increasing k ≡ − 1 < V > ( ∂ < V > ∂p$_{L}$ )$_{v}$$_{W}$ , (7) 11 To measure the facility of the system to be compressed, define a coefficient of compress- ibility k by