system. The first obvious candidate to be considered is the granular temperature of the gas, defined from the second moment of the velocity distribution of the grains. Actually, this parameter is known to play in the hydrodynamic description of granular gases a role similar to the usual temperature in molecular hydrodynamics [13]. But there is another temperature parameter that is relevant for the description of the system, the one defined from the second moment of the velocity distribution of the movable piston. Both temperatures, defined from the velocity of the gas and of the piston, respectively, are the same in equilibrium systems, but they can differ strongly in granular systems, as a manifestation of the violation of energy equipartition [14]. Clarifying the relationship between the effective temperature defined from the volume fluctuations, the granular temperature, and the temperature parameter of the piston, is one of the aims of this work. The structure of the remaining of this paper is as follows. In Sec. II, the system is described and the macroscopic steady state to be considered is characterized. Also, the parameter region to be investigated is specified. It is shown than when the mass of the piston is much larger than the mass of the grains, the volume fluctuations of the system exhibit a Gaussian distribution. The second moment of this distribution depends much stronger on the inelasticity of collisions between particles than on the elastic or inelastic character of the collisions of the particles with the piston. In Sec. III, a compressibility factor is defined for the granular gas. As usual, it is a measurement of the change in the volume of the system as a consequence of a change in the external pressure under well defined constrains. From the values of the second moment of the volume fluctuations and of the compressibility factor, an effective temperature is defined, as indicated above. This temperature turns out to be quite simply related with the temperature parameter of the piston, but its relationship with the granular temperature of the gas appears to be very intricate. Finally, Sec. IV contains a short summary of the main results in the paper and some general comments. Consider a system composed by N smooth inelastic hard disks of mass m and diameter d , in presence of gravity, and confined by a movable piston of mass M located on the top. By definition, the piston can only move in the direction of the gravity field. Moreover, II. STEADY FLUCTUATIONS OF THE POSITION OF THE PISTON 3