  In- and out-of-plane optical spectra and specific heat measurements for the
single layer cuprate superconductor Hg-1201 at optimal doping (Tc = 97 K) are
presented. Both the in-plane and out-of-plane superfluid density agree well
with a recently proposed scaling relation rho_{s}=sigma_{dc}T_{c}. It is shown
that there is a superconductivity induced increase of the in-plane low
frequency spectral weight which follows the trend found in underdoped and
optimally doped Bi-2212 and optimally doped Bi-2223. We observe an increase of
optical spectral weight which corresponds to a change in kinetic energy of
approximately 0.5 meV/Cu which is more than enough to explain the condensation
energy. The specific heat anomaly is 10 times smaller than in YBCO and 3 times
smaller than in Bi-2212. The shape of the anomaly is similar to the one
observed in YBCO showing that the superconducting transition is governed by
thermal fluctuations.
