  The discovery of extended, approximately spherical weak shock waves in the
hot intercluster gas in Perseus and Virgo has precipitated the notion that
these waves may be the primary heating process that explains why so little gas
cools to low temperatures. This type of heating has received additional support
from recent gasdynamical models. We show here that outward propagating,
dissipating waves deposit most of their energy near the center of the cluster
atmosphere. Consequently, if the gas is heated by (intermittent) weak shocks
for several Gyrs, the gas within 30-50 kpc is heated to temperatures that far
exceed observed values. This heating can be avoided if dissipating shocks are
sufficiently infrequent or weak so as not to be the primary source of global
heating. Local PV and viscous heating associated with newly formed X-ray
cavities are likely to be small, which is consistent with the low gas
temperatures generally observed near the centers of groups and clusters where
the cavities are located.
