  An analysis of relations between the tunneling rate and the unified first law
of thermodynamics at the trapping horizons of two kinds of spherically
symmetric dynamical black holes is investigated. The first kind is the
Vaidya-Bardeen black hole, the tunneling rate $\Gamma \sim e^{\triangle S}$ can
be obtained naturally from the unified first law at the apparent horizon, which
holds the form $dE_{H}=TdS+WdV$. Another is the McVittie solution, the action
of the radial null geodesic of the outgoing particles does not always has a
pole at the apparent horizon, while the ingoing mode always has one. The
solution of the ingoing mode of the radiation can be mathematically reduced to
the case in the FRW universe smoothly. However as a black hole, the physical
meaning is unclear and even puzzling.
