Assuming that the concentration of fermions does not change with temperature, then the total chemical potential µ (Fermi level) of the three-dimensional ideal Fermi gas is related to the zero temperature Fermi energy E by a Sommerfeld expansion (assuming ):
where T is the temperature.
Hence, the internal chemical potential, µ-E, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature T. This characteristic temperature is on the order of 10 K for a metal, hence at room temperature (300 K), the Fermi energy and internal chemical potential are essentially equivalent.