  Thermal quantities, including the the entropy density and gluon spectrum, of
quark matter within a box that is finite in the longitudinal direction are
calculated using a bag model. Under the assumption of entropy conservation, the
corresponding gluon dissociation rate of J/psi is studied. It reaches a maximum
at a certain longitudinal size L_m, below which the suppression is weak even if
the temperature becomes higher than that without the finite size effect, and
above which the dissociation rate approaches to the thermodynamic limit
gradually with increasing longitudinal size of the fireball.
