  We evaluate how much energy can be converted into gravitational radiation in
head-on collision of black holes. We estimate it by the area theorem of black
hole horizon incorporating merging entropy of colliding black holes from a
viewpoint of black hole thermodynamics. Then we obtain an upper bound of energy
ratio of the gravitational radiation which is smaller than the upper bound
originally derived by Hawking. The fact that this estimation is not
inconsistent with the results of both numerical investigations in low- and
high-energy head-on collision implies that thermodynamics of coalescing black
holes requires the contribution of the merging entropy.
