The internal energy and free energy are also considered. For each version of the finite-temperature Thomas-Fermi model, the pressure, the kinetic energy, and the entropy are calculated. The equation of state is considered in detail. The relativistic finite-temperature Thomas-Fermi model matches the two asymptotic regimes, i.e., the non-relativistic and the ultra-relativistic finite-temperature Thomas-Fermi models. A formula for the nuclear radius is chosen to treat any element. Assuming a constant distribution of protons inside the nucleus of finite size avoids severe divergence of the electron density with respect to a point-like nucleus. We investigate the relativistic finite-temperature Thomas-Fermi model, which has been proposed recently in an astrophysical context. Relativistic finite-temperature Thomas-Fermi model
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