  Unitary Fermi gases, where the scattering length is large compared to the
interparticle spacing, can have universal properties, which are independent of
the details of the interparticle interactions when the range of the scattering
potential is negligible. We prepare an optically-trapped, unitary Fermi gas of
$^6$Li, tuned just above the center of a broad Feshbach resonance. In agreement
with the universal hypothesis, we observe that this strongly-interacting
many-body system obeys the virial theorem for an ideal gas over a wide range of
temperatures. Based on this result, we suggest a simple volume thermometry
method for unitary gases. We also show that the observed breathing mode
frequency, which is close to the unitary hydrodynamic value over a wide range
of temperature, is consistent with a universal hydrodynamic gas with nearly
isentropic dynamics.
