  Using a differential technique, we have measured the specific heats of
polycrystalline Ba1-xKxFe2As2 samples with x=0, 0.1 and 0.3, between 2K and
380K and in magnetic fields 0 to 13 Tesla. From this data we have determined
the electronic specific heat coefficient, gamma, over the entire range for the
three samples. The most heavily doped sample (x=0.3) exhibits a large
superconducting anomaly Delta gamma(Tc)~48mJ/molK^2 at Tc=35K, and we determine
the energy gap, condensation energy, superfluid density and coherence length.
In the normal state for the x=0.3 sample, gamma~47 mJ/molK^2 is constant from
Tc to 380K. In the parent compound (x=0) there is a large almost first order
anomaly at the spin density wave (SDW) transition at To=136K. This anomaly is
smaller and broader for x=0.1. At low T, gamma is strongly reduced by the SDW
gap for both x=0 and 0.1, but above To, gamma for all three samples are
similar.

Superconductivity