  The upcoming generation of SZE surveys will shed fresh light onto the study
of clusters. What will this new observational window reveal about cluster
properties? What can we learn from combining X-ray, SZE, and optical
observations? How do variations in the gas entropy profile, dark matter
concentration, accretion pressure, and intracluster medium (ICM) mass fraction
affect SZE observables? We investigate the signature of these important cluster
parameters with an analytic model of the ICM. Given the current uncertainties
in ICM physics, our approach is to span the range of plausible models motivated
by observations and a small set of assumptions. We find a tight relation
between the central Compton parameter and the X-ray luminosity outside the
cluster core, suggesting that these observables carry the same information
about the ICM. The total SZE luminosity is proportional to the thermal energy
of the gas, and is a surprisingly robust indicator of cluster mass: $L_{SZ}
\propto f_{ICM} M^{5/3}$. We show that a combination of $L_{SZ}$ and the
half-luminosity radius $r_{SZ}$ provides a measure of the potential energy of
the cluster gas, and thus we can deduce the total energy content of the ICM. We
caution that any systematic variation of the ICM mass fraction will distort the
expected $L_{SZ} - M$ calibration to be used to study the evolution of cluster
number density, and propose a technique using kSZ to constrain $f_{ICM}(M,z)$.
