A novel approach is presented for interpreting and potentially predicting values of the isothermal, isobaric transfer free energy, entropy, and enthalpy (Delta mu(tr)(2), Delta s(2)(tr), and Delta h(2)(tr)) for a solute between water and water- cosolvent mixtures. The approach explicitly accounts for volumetric properties of the solvent and solute (the equation of state, EoS) and casts the overall transfer process as a thermodynamic cycle with two stages: (1) isothermal solvent exchange from pure water to the cosolvent composition of interest at fixed mass density; (2) isothermal expansion or compression at the final solvent composition to recover the pressure of the initial state. Using molecular simulations with methane as the solute, the analysis is illustrated over a wide range of cosolvent concentrations for sorbitol-, ethanol-, and methanol-water binary mixtures. The EoS contribution semiquantitatively or quantitatively captures Delta mu(tr)(2), Delta s(2)(tr), and Delta h(2)(tr) and Ah tr in almost all cases tested, highlighting the importance of considering the effects of changes in solvent density on the overall transfer process. The results also indicate that apolar solvation at these length scales is dominated by the work of cavity formation across a range of cosolvent species and concentrations.