Functional Approach to Chemical Potential

In this work we emphasize on the physical role of chemical potential as the quantity which enforces the conservation of particle number in a closed system. On the basis of this role, we developed a functional approach towards the evaluation of chemical potential of a closed system (here an ideal Fermi-gas). We start with a well-known integral equation which could be solved analytically for the chemical potential of the system at high temperatures/low densities and low-temperature/highdensity extreme limit. We also derived a differential equation for the chemical potential of the system. The differential equation is solved analytically at low temperatures/high densities to desired precision. However, the differential equation as well as the integral equation is numerically solvable for the chemical potential at all temperatures and densities. The obtained numerical solution is used to devise a formula for the chemical potential of ideal Fermi-gas at moderate temperatures/densities with a maximal relative error of about 0.15 percent. The introduced functional approach is not restricted to ideal Fermigas and may well be generalized to other thermodynamic systems.