A simple relationship between the pressure, internal energy, and Fermi energy of an ideal ultradegenerate Fermi gas is derived in two ways. The conditions for its validity and its use in simplifying calculations are discussed.
we derive the quantum state density, the relation of internal energy and the pressure of arbitrary dimensional ideal gases that have energy spectrum of e = ap5 , and then offer the universal descriptions of chemistry potential, internal energy ,degenerate pressure and relative fluctuation of arbitrary dimensional ideal Fermi gases, through analysis and comparison, we draw a conclusion that when temperature approaches zero, thermodynamic quantities of high degenerate Fermi gases under low temperature trend to that of the complete degenerate Fermi gases.