The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method is developed around two equations of state currently used to construct solar models, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. The results reveal the existence of a subtle effect of the presence of excited states in hydrogen in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized. This effect has an important bearing on the astrophysically relevant helioseismic helium-abundance determination in the solar convection zone.
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