  We report the first large, systematic study of the dynamics and energetics of
a representative sample of FRII radio galaxies with well-characterized
group/cluster environments. We used X-ray inverse-Compton and radio synchrotron
measurements to determine the internal radio-lobe conditions, and these were
compared with external pressures acting on the lobes, determined from
measurements of the thermal X-ray emission of the group/cluster. Consistent
with previous work, we found that FRII radio lobes are typically
electron-dominated by a small factor relative to equipartition, and are
over-pressured relative to the external medium in their outer parts. These
results suggest that there is typically no energetically significant proton
population in the lobes of FRII radio galaxies (unlike for FRIs), and so for
this population, inverse-Compton modelling provides an accurate way of
measuring total energy content and estimating jet power. We estimated the
distribution of Mach numbers for the population of expanding radio lobes,
finding that at least half of the radio galaxies are currently driving strong
shocks into their group/cluster environments. Finally, we determined a jet
power--radio luminosity relation for FRII radio galaxies based on our estimates
of lobe internal energy and Mach number. The slope and normalisation of this
relation are consistent with theoretical expectations, given the departure from
equipartition and environmental distribution for our sample.
