In- and out-of-plane optical spectra and specific heat measurements for thesingle layer cuprate superconductor Hg-1201 at optimal doping (Tc = 97 K) arepresented. Both the in-plane and out-of-plane superfluid density agree wellwith a recently proposed scaling relation rho_{s}=sigma_{dc}T_{c}. It is shownthat there is a superconductivity induced increase of the in-plane lowfrequency spectral weight which follows the trend found in underdoped andoptimally doped Bi-2212 and optimally doped Bi-2223. We observe an increase ofoptical spectral weight which corresponds to a change in kinetic energy ofapproximately 0.5 meV/Cu which is more than enough to explain the condensationenergy. The specific heat anomaly is 10 times smaller than in YBCO and 3 timessmaller than in Bi-2212. The shape of the anomaly is similar to the oneobserved in YBCO showing that the superconducting transition is governed bythermal fluctuations.
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