  In this paper we calculate the entropy of a thin spherical shell that
contracts reversibly from infinity down to its event horizon. We find that, for
a broad class of equations of state, the entropy of a non-extremal shell is
one-quarter of its area in the black hole limit. The considerations in this
paper suggest the following operational definition for the entropy of a black
hole: $S_{BH}$ is the equilibrium thermodynamic entropy that would be stored in
the material which gathers to form the black hole, if all of this material were
compressed into a thin layer near its gravitational radius. Since the entropy
for a given mass and area is maximized for thermal equilibrium we expect that
this is the maximum entropy that could be stored in the material before it
crosses the horizon. In the case of an extremal black hole the shell model does
not assign an unambiguous value to the entropy.
