  The dissipation of energy from sound waves and weak shocks is one of the most
promising mechanisms for coupling AGN activity to the surrounding intracluster
medium (ICM), and so offsetting cooling in cluster cores. We present a detailed
analysis of the weak shock found in deep Chandra observations of the Perseus
cluster core. A comparison of the spectra either side of the shock front shows
that they are very similar. By performing a deprojection analysis of a sector
containing the shock, we produce temperature and density profiles across the
shock front. These show no evidence for a temperature jump coincident with the
density jump. To understand this result, we model the shock formation using 1D
hydrodynamic simulations including models with thermal conduction and gamma <
5/3 gas. These models do not agree well with the data, suggesting that further
physics is needed to explain the shock structure. We suggest that an
interaction between the shock and the H-alpha filaments could have a
significant effect on cooling the post-shock gas.
  We also calculate the thermal energy liberated by the weak shock. The total
energy in the shocked region is about 3.5 times the work needed to inflate the
bubbles adiabatically, and the power of the shock is around 6x10^44 erg/s per
bubble, just over 10^45 erg/s in total.
