Recently, Asplund et al. (2004) and Asplund et al. (2005) (AGS hereafter), using a refined model for the solar atmosphere, announced the new solar chemical composition with the heavy-element abundance (Z = 0.0122) being about 30% lower than the previously determined value (Z = 0.0171; Grevesse & Sauval (1998); GS98 hereafter). In this study, we use the adiabatic index, Γ1 ≡ (∂ ln P/∂ ln ρ)s, to examine and isolate the effects of different chemical compositions. Specifically, we exploited the fact that Γ1 deviates from the isentropic value of 5/3 in the element ionization zones, which are determined by the equation-of-state (EOS) formalism and the element abundance and are independent of the macrophysical properties (e.g., P, ρ). The results of our study can provide an independent test of the newly determined solar composition.