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We present the first results of our study of a sample of 101 X-ray galaxygroups and clusters, which is volume-limited in each of three X-ray luminositybins. The aim of this work is to study the properties of the innermost ICM inthe cores of our groups and clusters, and to determine the effect ofnon-gravitational processes, such as active galactic nucleus (AGN) feedback, onthe ICM. The entropy of the ICM is of special interest, as it bears the imprintof the thermal history of a cluster, and it also determines a cluster's globalproperties. Entropy profiles can therefore be used to examine any deviationsfrom cluster self-similarity, as well as the effects of feedback on the ICM. Wefind that the entropy profiles are well-fitted by a simple powerlaw model, ofthe form $K(r) = \alpha\times(r/100 \rm{kpc})^{\beta}$, where $\alpha$ and$\beta$ are constants. We do not find evidence for the existence of an "entropyfloor", i.e. our entropy profiles do not flatten out at small radii, assuggested by some previous studies.

A volume-limited sample of X-ray galaxy groups and clusters - I. Radial entropy and cooling time profiles