  We report the specific heat (SH) measurements on single crystals of hole
doped $FeAs$-based superconductor $Ba_{0.6}K_{0.4}Fe_2As_2$. It is found that
the electronic SH coefficient $\gamma_e(T)$ is not temperature dependent and
increases almost linearly with the magnetic field in low temperature region.
These point to a fully gapped superconducting state. Surprisingly the sharp SH
anomaly $\Delta C/T|_{T_c}$ reaches a value of 98 $mJ/mol K^2$ suggesting a
very high normal state quasiparticle density of states ($\gamma_n \approx 63
mJ/mol K^2$). A detailed analysis reveals that the $\gamma_e(T)$ cannot be
fitted with a single gap of s-wave symmetry due to the presence of a hump in
the middle temperature region. However, our data indicate that the dominant
part of the superconducting condensate is induced by an s-wave gap with the
magnitude of about 6 meV.
