  Type Ia supernovae (SNe Ia) provide unique and important feedback in
quiescent galaxies, but their impact has been underappreciated. In this paper,
we analyze a series of high-resolution simulations to examine the energetics
and turbulence of the medium under SNe Ia. We find that when SN remnants are
resolved, their effects differ distinctly from a volumetric heating term, as is
commonly assumed in unresolved simulations. First, the net heating is
significantly higher than expected, by 30$\pm$10\% per cooling time. This is
because a large fraction of the medium is pushed into lower densities which
cool inefficiently. Second, the medium is turbulent; the root-mean-squared
(RMS) velocity of the gas to 20-50 km s$^{-1}$ on a driving scale of tens of
parsec. The velocity field of the medium is dominated by compressional modes,
which are larger than the solenoidal components by a factor of 3-7. Third, the
hot gas has a very broad density distribution. The ratio between the density
fluctuations and the RMS Mach number, parameterized as $b$, is 2-20. This is in
contrast to previous simulations of turbulent media, which have found
$b\lesssim$ 1. The reason for the difference is mainly caused by the
\textit{localized} heating of SNe Ia, which creates a large density contrast.
Last, the typical length scale of a density fluctuation grows with time,
forming increasingly larger bubbles and filamentary ridges. These underlying
density fluctuations need to be included when X-ray observations are
interpreted.
