  Superconducting condensation energy $U_0^{int}$ has been determined by
integrating the electronic entropy in various iron pnictide/chalcogenide
superconducting systems. It is found that $U_0^{int}\propto T_c^n$ with $n$ = 3
to 4, which is in sharp contrast to the simple BCS prediction
$U_0^{BCS}=1/2N_F\Delta_s^2$ with $N_F$ the quasiparticle density of states at
the Fermi energy, $\Delta_s$ the superconducting gap. A similar correlation
holds if we compute the condensation energy through
$U_0^{cal}=3\gamma_n^{eff}\Delta_s^2/4\pi^2k_B^2$ with $\gamma_n^{eff}$ the
effective normal state electronic specific heat coefficient. This indicates a
general relationship $\gamma_n^{eff} \propto T_c^m$ with $m$ = 1 to 2, which is
not predicted by the BCS scheme. A picture based on quantum criticality is
proposed to explain this phenomenon.
