We have identified and studied a sample of 151 FR?IIs found in brightest cluster galaxies (BCGs) in the MaxBCG cluster catalog with data from FIRST and NVSS. We have compared the radio luminosities and projected lengths of these FR?IIs to the projected length distribution of a range of mock catalogs generated by an FR?II model and estimate the FR?II lifetime to be 1.9 × 108?yr. The uncertainty in the lifetime calculation is a factor of two, primarily due to uncertainties in the intracluster medium (ICM) density and the FR?II axial ratio. We furthermore measure the jet power distribution of FR?IIs in BCGs and find that it is well described by a log-normal distribution with a median power of 1.1 × 1037?W and a coefficient of variation of 2.2. These jet powers are nearly linearly related to the observed luminosities, and this relation is steeper than many other estimates, although it is dependent on the jet model. We investigate correlations between FR?II and cluster properties and find that galaxy luminosity is correlated with jet power. This implies that jet power is also correlated with black hole mass, as the stellar luminosity of a BCG should be a good proxy for its spheroid mass and therefore the black hole mass. Jet power, however, is not correlated with cluster richness, nor is FR?II lifetime strongly correlated with any cluster properties. We calculate the enthalpy of the lobes to examine the impact of the FR?IIs on the ICM and find that heating due to adiabatic expansion is too small to offset radiative cooling by a factor of at least six. In contrast, the jet power is approximately an order of magnitude larger than required to counteract cooling. We conclude that if feedback from FR?IIs offsets cooling of the ICM, then heating must be primarily due to another mechanism associated with FR?II expansion.
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