  (Abridged) Far-infrared Herschel-PACS spectra of 18 low-mass protostars of
various luminosities and evolutionary stages are studied. We quantify their
far-infrared line emission and the contribution of different atomic and
molecular species to the gas cooling budget during protostellar evolution. We
also determine the spatial extent of the emission and investigate the
underlying excitation conditions. Most of the protostars in our sample show
strong atomic and molecular far-infrared emission. Water is detected in 17
objects, including 5 Class I sources. The high-excitation H2O line at 63.3
micron is detected in 7 sources. CO transitions from J=14-13 up to 49-48 are
found and show two distinct temperature components on Boltzmann diagrams with
rotational temperatures of ~350 K and ~700 K. H2O has typical excitation
temperatures of ~150 K. Emission from both Class 0 and I sources is usually
spatially extended along the outflow direction but with a pattern depending on
the species and the transition. The H2O line fluxes correlate strongly with
those of the high-J CO lines, as well as with the bolometric luminosity and
envelope mass. They correlate less strongly with OH and not with [OI] fluxes.
The PACS data probe at least two physical components. The H2O and CO emission
likely arises in non-dissociative (irradiated) shocks along the outflow walls
with a range of pre-shock densities. Some OH is also associated with this
component, likely resulting from H2O photodissociation. UV-heated gas
contributes only a minor fraction to the CO emission observed by PACS, based on
the strong correlation between the shock-dominated CO 24-23 line and the CO
14-13 line. [OI] and some of the OH emission probe dissociative shocks in the
inner envelope. The total far-infrared cooling is dominated by H2O and CO, with
[OI] increasing for Class I sources.
