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We present the evolution of the initial (up to ~ 10 kbar) hydrostatic,pressure dependencies of T_c and of the ambient pressure jump in the heatcapacity associated with the superconducting transition as a function of Na -doping in the Ba(1-x)NaxFe2As2 family of iron-based superconductors. For Naconcentrations 0.15 <= x <= 0.9, the jump in specific heat at T_c, Delta C_p,follows the Delta C_p ~ T^3 scaling found for most BaFe2As2 - basedsuperconductors. Pressure dependencies are non-monotonic for x = 0.2 and x =0.24. For other Na concentrations T_c decreases under pressure in almost linearfashion. The anomalous behavior of the x = 0.2 and x = 0.24 samples underpressure are possibly due to the crossing of the phase boundaries of the narrowantiferromagnetic tetragonal phase, unique for the Ba(1-x)NaxFe2As2 series,with the application of pressure.

Heat capacity jump at T_c and pressure derivatives of superconducting transition temperature in the Ba(1-x)NaxFe2As2 (0.1 <= x <= 0.9) series