ESTIMATION OF THERMODYNAMIC PROPERTIES OF IDEAL FERMI GASES THROUGH THE APPLICATION OF QUANTUM MECHANICS

Abstract

In ideal Fermions system, at high temperature limit, quantum effects are small but when the temperature is lowered, quantum effects start becoming important. The main purpose of this study was to formulate thermodynamic properties of an ideal Fermi gases in low temperature limit through the application of quantum Mechanics. The research work involved the evaluation of partition function, using estimated mean values of the internal energy, specific heat, entropy, chemical potential and equation of state of ideal Fermi gases in terms of the Fermi-Dirac function. Numerical results were generated using Matlab R2016a programming language. At low temperature limit of the ideal Fermi gas both specific heat and entropy showed the same numerical value that vanished at absolute zero. However, as the temperature increased above such strong dependence of the two quantities on temperature disappeared and they almost become constant (temperature independent). It shows the classical effect of the gas. The ground-state pressure of an ideal Fermi gas arises because there must be moving particles at absolute zero. At T = 0, the particles are distributed among the single particle states so that the total energy of the gas is minimum because no more than one particle occupies each single state due to the quantum effect called the Pauli exclusion principle. At higher temperature, the chemical potential becomes negative where the system behaves like an ideal classical gas. The results of thermodynamic properties of the ideal Fermi gas near are unrealistic as the approximate calculations are only valid in the limits and .