Comparison of thermodynamic quantities between the MHD and FreeEOS. Left panel: Relative differences between the MHD and FreeEOS in thermal pressure, computed via (P_ther,Free– P_ther,MHD)/P_ther,MHD. Data used in the comparison are generated directly from the corresponding EOS code and based on identical (ρ, T) values, therefore no interpolation is involved in the comparison. The mean structure of our reference 3D solar model atmosphere is over-plotted in the red line, indicating the area of most interest. Both EOSs are computed assuming the same chemical composition, which includes 15 elements with the AGSS09 solar abundance value. Densities and temperatures are in cgs units. Right panel: Relative differences between the MHD and FreeEOS in internal energy per mass.