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 outwardly 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 Gyr, 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.
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