Semantic Apparatus – Thermodynamic Properties of an Ideal q-deformed Fermi Gas

Cited by Lee Sonogan

Solved Pressure and entropy of degenerate Fermi gas. (a) |

Abstract by Aram Bahroz Brzo1,a, Peshwaz A. Abdoul2,b, Mir Hameeda3,4,5,c,

In this paper, a recently proposed q−deformed Fermi-Dirac distribution function is employed to investigate the thermodynamic properties of an ideal free electron Fermi gas. From our calculations, the total num-ber of particles, total energy of the system, specific heat capacity, chemical potential and entropy are all calculated. As a practical application of our calculations, we have considered the electronic contribution to the specific heat capacity of various metals. Due to significant contribution from the atomic vibration at ordinary or high temperatures, we have limited ourselves to low temperature range at which the role of free electrons are dominant. At low temperatures, very small compared to Fermi temperature, we have used the so-called Sommerefeld expansion technique to derive analytic expression for the specific heat capacity of several metals together with the q−deformed Sommerfeld parameter γ(q). An immediate conclusion to be drawn from our calculations is that; at q = 1, we have reproduced the corresponding results from the conventional (or classical) Fermi-Dirac statistics. For the purpose of comparison, the experimental data for specific heat capacity of various metals is used. We have found that, by proper choice of the q-parameter, the q-deformed calculated values for Sommerfeld parameter can be arranged to obtain excellent agreement with the experimental results. Finally, when temperature tends to absolute zero, the chemical potential is equal to the Fermi energy, entropy and specific heat capacity of the system both approach zero, revealing that, at this extreme situation, the q parameter become irrelevant.

Publication: Many Schools of Physics (Peer-Reviewed Journal)

Pub Date: 19 Aug, 2021 Doi:

Keywords: Probability, Distribution functions, q-Calculus, Tsallis statistics, Rubayata Entropy (Plenty more sections and references in this research article)

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