We examine the spectrum of diffuse emission detected in the 17 by 17 field around Sgr A* during 625 ks of Chandra observations. The spectrum exhibits He-like and H-like lines from Si, S, Ar, Ca, and Fe, that are consistent with originating in a two-temperature plasma, as well as a prominent low-ionization Fe line. The cooler, kT=0.8 keV plasma differs in surface brightness across the image by a factor of 9. This soft plasma is probably heated by supernovae. The radiative cooling rate of the plasma within the inner 20 pc of the Galaxy could be balanced by 1% of the kinetic energy of one supernova every 300,000 y. The hotter, kT=8 keV component is more spatially uniform, ranging over a factor of 2 in surface brightness. The intensity of the hard plasma is correlated with that of the soft, but they are probably only indirectly related, because supernova remnants are not observed to produce thermal plasma hotter than kT=3 keV. Moreover, a kT=8 keV plasma is too hot to be bound to the Galactic center, and therefore would form a slow wind or fountain of plasma. The energy required to sustain such a freely-expanding plasma within the inner 20 pc of the Galaxy is ~10^40 erg/s, which corresponds to the entire kinetic energy of one supernova every 3000 y. This rate is unreasonably high. However, alternative explanations for the kT=8 keV diffuse emission are equally unsatisfying. We are left to conclude that either the diffuse emission is heated by an unanticipated source of energy, or that a population of faint (< 10^31 erg/s), hard X-ray sources that are a factor of 10 more numerous than CVs remains to be discovered. (Abridged)
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