  We report on specific heat measurements in Ba$_{1-x}$K$_x$Fe$_{2}$As$_{2}$
($x\le 0.6$). For the underdoped sample with $x=0.2$ both the spin-density-wave
transition at $T = 100$ K and the superconducting transition at 23 K can be
identified. The electronic contribution to the specific heat in the
superconducting state for concentrations in the vicinity of optimal doping
$x=0.4$ can be well described by a full single-gap within the BCS limit.
