  The volume fluctuations in the steady state reached by a vibrated granular
gas of hard particles confined by a movable piston on the top are investigated
by means of event driven simulations. Also, a compressibility factor, measuring
the response in volume of the system to a change in the mass of the piston, is
introduced and measured. From the second moment of the volume fluctuations and
the compressibility factor, an effective temperature is defined, by using the
same relation as obeyed by equilibrium molecular systems. The interpretation of
this effective temperature and its relationship with the granular temperature
of the gas, and also with the velocity fluctuations of the movable piston, is
discussed. It is found that the ratio of the temperature based on the volume
fluctuations to the temperature based on the piston kinetic energy, obeys
simple dependencies on the inelasticity and on the piston-particle mass ratio.
