  We define the Bondi energy for two-dimensional dilatonic gravity theories by
generalizing the known expression of the ADM energy. We show that our
definition of the Bondi energy is exactly the ADM energy minus the radiation
energy at null infinity. An explicit calculation is done for the evaporating
black hole in the RST model with the Strominger's ghost decoupling term. It is
shown that the infalling matter energy is completely recovered through the
Hawking radiation and the thunderpop.
