  Semi-analytic models of X-ray clusters and groups of galaxies, relying on the
idea that there was a non-gravitational energy injection in these systems, are
able to reproduce many observed correlations, in particular the L_X-T relation
and the ``central entropy floor'' in groups. Limiting models exist which
describe the behaviour of clusters and groups separately, but no analytic
modeling has yet been found to unify both mass ranges. {\it It is the aim of
this paper to provide such an analytic model.} Our description relies on a now
standard description of the shock thought to occur in these systems near the
virial radius (Cavaliere et al., 98), the isothermality and spherical symmetry
of the intracluster medium, as well as the reinterpretation of observed
quantities (like the X-ray luminosity, the gas mass M_{ICM} and the central SZ
effect y_0) in terms of the specific entropy. This allows the derivation of
analytic expressions for several observed correlations (L_X-T, M_{ICM}-T,
y_0-T,...) and their normalisation encompassing \emph{both the group and the
cluster regimes}. The analytic predictions compare very well with observations,
as well as with more elaborated semi-analytic schemes. This agreement allows a
reinterpretation of the L_X-T relation (via the quantity L_X/T^{7/2}) and the
y_0-T relation (via y_0/T^{5/2}) as indirect measures of the non-gravitational
entropy content of groups and clusters of galaxies. Finally, we emphasize the
need for shock heating, even in the group mass range : \emph{shocks can not be
completely supressed in groups} (and thus groups can not be entirely
isentropic) unless an unacceptably high entropy floor is needed in order to
break the self-similarity in the L_X-T relation.
