  If the mean properties of clusters of galaxies are well described by the
entropy-driven model, the distortion induced by the cluster population on the
blackbody spectrum of the Cosmic Microwave Background radiation is proportional
to the total amount of intracluster gas while temperature anisotropies are
dominated by the contribution of clusters of about 10^{14} solar masses. This
result depends marginally on cluster parameters and it can be used to estimate
the number density of clusters with enough hot gas to produce a detectable
Sunyaev-Zel'dovich effect. Comparing different cosmological models, the
relation depends mainly on the density parameter Omega_m. If the number density
of clusters could be estimated by a different method, then this dependence
could be used to constrain Omega_m.
