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 $U_0^{BCS}=1/2N_FDelta_s^2$ 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 $U_0^{cal}=3gamma_n^{eff}Delta_s^2/4pi^2k_B^2$ 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.
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