A small-scale adiabatic calorimeter has been constructed as part of a larger project to study nano-particles and to facilitate specific heat measurements on samples where it is difficult to obtain enough material to run on the current large-scale adiabatic apparatus. This calorimeter is designed to measure sample sizes of less than 0.8 cc over a temperature range from 13 K to 350 K. Specific heat results on copper, sapphire, and benzoic acid show the accuracy of the measurements to be better than ±0.4% for temperatures higher than 50 K. The reproducibility of these measurements is generally better than ±0.25%. Experimental specific heat data was collected on this new apparatus for synthetic akaganeite, β-FeOOH, for samples with varying degrees of hydration. Our results yield values for Δ_0^298.15S°m of 79.94 ±0.20 J•K^-1•mol^-1 and 85.33 ±0.021 J•K^-1•mol^-1 for samples of β-FeOOH0.551H2O and β-FeOOH0.652H2O, respectively. From this data, we were able to determine the standard molar entropy for bare β-FeOOH, as Δ_0^298.15S°m = 53.8 ±3.3 J•K^-1•mol^-1, based on subtractions of the estimated contribution of water from the hydrated species. Additionally, the specific heats of α-uranium, titanium diboride, and lithium flouride have been measured on a low-temperature, semi-adiabatic calorimeter down to 0.5 K. For the α-uranium, the specific heat of a polycrystalline sample was compared to that of a single crystal, and it was found that there was a significant difference in the specific heats, which has been attributed to microstrain in the polycrystal. The third law entropy for the polycrystal at 298.15 K, Δ_0^298.15S°m, calculated from these heat capacities is 50.21 ±0.1 J•K^-1•mol^-1, which is good in agreement with previously published values of polycrystal samples. For the single crystal Δ_0^298.15S°m, calculated using the thermodynamic microstrain model, is 49.02 ±0.2 J•K^-1•mol^-1. The low-temperature specific heats of titanium diboride and lithium fluoride have been measured from 0.5 K to 30 K as part of a larger project in the construction of a neutron spectrometer. For this application, the measured specific heats were used to extrapolate the specific heats down to 0.1 K with lattice, electronic, and Schottky equations for the respective samples. The resultant specific heat values at 0.1 K for TiB2 and 6LiF are 4.08E-4 ±0.27E-4 J•K^-1•mol^-1 and 9.19E-9 ±0.15E-9 J•K^-1•mol^-1, respectively.