  Self-gravitating systems such as elliptical galaxies appear to have a
constant specific entropy and obey a scaling law relating their potential
energy to their mass. These properties can be interpreted as due to the
physical processes involved in the formation of these structures. Dark matter
haloes obtained through numerical simulations have also been found to obey a
scaling law relating their potential energy to their mass with the same slope
as ellipticals. Since the X-ray gas in clusters is weakly dissipative, we have
checked the hypothesis that it might verify similar properties.
  We have analyzed ROSAT-PSPC images of 24 clusters, and also found that: 1)
the S\'ersic law parameters (intensity, shape and scale) describing the X-ray
gas emission are correlated two by two; 2) the hot gas in all these clusters
roughly has the same specific entropy; 3) a scaling law linking the cluster
potential energy to the mass of the X-ray gas is observed, with the same slope
as for elliptical galaxies and dark matter haloes.
