  The angular power spectrum of the Sunyaev-Zeldovich (SZ) effect is calculated
in the $\Lambda$CDM cosmological model with the aim of investigating its
detailed dependence on the cluster population, gas morphology, and gas
evolution. We calculate the power spectrum for three different mass functions,
compute it within the framework of isothermal and polytropic gas distributions,
and explore the effect of gas evolution on the magnitude and shape of the power
spectrum. We show that it is indeed possible to explain the `excess' power
measured by the CBI experiment on small angular scales as originating from the
SZ effect without (arbitrary) rescaling the value of $\sigma_8$, the mass
variance parameter. The need for a self-consistent choice of the basic
parameters characterizing the cluster population is emphasized. In particular,
we stress the need for a consistent choice of the value of $\sigma_8$ extracted
from fitting theoretical models for the mass function to the observed cluster
X-ray temperature function, such that it agrees with the mass-temperature
relation used to evaluate the cluster Comptonization parameter. Our treatment
includes the explicit spectral dependence of the thermal component of the
effect, which we calculate at various frequencies. We find appreciable
differences between the non-relativistic and relativistic predictions for the
power spectrum even for this superposed contribution from clusters at the full
range of gas temperatures.
