The thermodynamic behavior of conventional chillers (generalized air conditioning and refrigeration systems) is acutely sensitive to internal dissipation. Previous chiller analyses have excluded entropy production in the evaporator and condenser heat exchangers, on the assumption of its being negligible. With experimental measurements from a commercial chiller, we demonstrate that heat exchanger internal dissipation is not inconsequential, and that ignoring its contribution can lead to substantial errors in chiller diagnostics and in the prediction of chiller performance curves. To evaluate the impact of this dissipation on chiller efficiency, one needs to define a proper process average temperature (PAT). In addition to discussing the fundamental significance of the correct PAT, we will show that earlier conventional definitions of PAT, where internal irreversibilities in chiller heat exchangers have been overlooked, result in inaccurate and sometimes unphysical predictions.