A thermodynamic analysis of the temperature sensitivity of the ratio (λ) between volume thermal expansivity (α V ) and isobaric specific heat (C P ) is presented. By invoking the temperature independence of the thermal Gruneisen parameter (γ G ), some simple approximations are derived for the isobaric volume dependence of the ratio α V /C P . In addition, the temperature dependence of γ G has also been investigated under the condition that there exists a linear scaling relation between bulk modulus (B S ) and enthalpy increment (ΔH). The relations suggested in this study form a consistent thermodynamic framework that serves to relate thermal and elastic properties on a general system-independent basis. As an illustrative application, the isobaric volume dependence of α V /C P has been estimated for MgO and the results are found to be in good agreement with experiment.