Low Temperature Physics: 43, 144 (2017); https://doi.org/10.1063/1.4975807
Chemical potentials and thermodynamic characteristics of the ideal Bose and Fermi gases in the region of quantum degeneracy
A.G. Sotnikov1,2,3, K.V. Sereda2, and Y.V. Slyusarenko1,2
1National Science Center “Kharkov Institute of Physics and Technology” 1 Akademicheskaya Str., Kharkov 61108, Ukraine
2V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
3Institute of Physics, ASCR, Na Slovance 1999/2, Prague 8, 18221Czech Republic
Received Jule 29, 2016
We determine dependencies of chemical potentials on the temperature for ideal monatomic gases obeying the Bose–Einstein and Fermi–Dirac statistics in the region of temperatures where the collective effects of quantum degeneracy have a significant impact. With-out applying any additional approaches we perform numerical calculations and study dependencies of chemical potentials on the temperature at the fixed density of particles of gases. We obtain approximate polynomial dependencies of chemical potentials on the temperature that allow to use the obtained dependencies in further studies without applying the used numerical procedures. A convenience of using these representations is shown for the case of deformation of distributions for occupation of energy states with decreasing temperature and also for studying the influence of quantum statistics (exchange interaction) on the equations of state of ideal gases and their thermodynamic characteristics. The results of the present paper bridge two opposite limits in a description of the equilibrium state of ideal gases that are well-known for a long time from the statistical mechanics courses, therefore, they are also valuable from the pedagogical point of view.
PACS: 05.30.–d Quantum statistical mechanics;
Key words: quantum statistics, ideal gas, Bose–Einstein distribution, the Fermi–Dirac distribution, chemical potentials, quantum degeneracy, thermodynamic characteristics of gas.
Published online: November 25, 2016