The polytropic indices of solar flares are studied by means of a semiempirical model of flare thermodynamic structure that utilizes soft X-ray measurements of the Sun and two scaling laws: (1) relating the product of plasma pressure and temperature to spatial scale; and (2) relating spatial scale to flare duration. The model and the main summary results of a survey of ≈1100 flares were described in two previous papers, cited herein. The principal result of the present study is that the polytropic indices, derived from the computed macro-thermodynamic structure of individual flares, are distributed about a value of 1.66 ± 0.02 for moderate flares and trend uniquely toward the value of the ratio of specific heats of a non-relativistic ideal gas, 5/3, for the most intense flares. The main conclusion is that magnetically contained, mostly thermalized plasma manifested in soft X-rays responds quasi-adiabatically to large energy fluxes that are absorbed and released by the flare in a few tens of minutes. This finding is consistent with the hypothesis that energy deposition is exactly balanced by conductive and (mostly) radiative losses over relatively short time intervals.