Thermal contribution to thermodynamic functions in the Thomas–Fermi model

We propose a method of calculation of thermodynamic functions in the Thomas–Fermi model at finite temperature θ. Expressions for first and second derivatives of the free energy are analytically obtained in the framework of the model. A special treatment of thermodynamic functions at low temperatures is provided by asymptotic series expansion at θ → 0. A special algorithm is used to ensure required accuracy for all values in a wide range of volumes and temperatures. We compare the results of our computations with ideal Boltzmann and Fermi gas models.