The Cubic Relationship of the Molar Heat Capacity Cv and Debye's Temperature for Ethyl Fluoride (C2H5F)

Abstract

This study employs Debye’s theory to compute the constant-volume molar heat capacity (Cv) of solid ethyl fluoride (C2H5F) across cryogenic temperatures (5–140 K). Utilizing numerical integration of the reduced Debye integral implemented in MatLab, the theoretically derived Cv​ curve demonstrates the characteristic temperature-dependent behavior observed experimentally: enhanced heat absorption at low temperatures and an asymptotic approach to the classical limit near the melting point (129.95 K). The model rigorously validates the cubic temperature dependence (Cv​ ∝ T3) near absolute zero, exhibiting close agreement between Debye-derived values and the cubic function below the separation temperature (14.75 K). Beyond this threshold, deviations progressively increase with rising temperature. Crucially, calibration via the empirical approximation θD​ ≈ 10⋅Tsp ​ yields a Debye temperature θD ​≈147.5 K, aligning within 1.67% of the experimental value (θD​=150 K) obtained from sound velocity measurements. This attests to the accuracy of the model parameters.