Thermodynamics of Quantum Gases for the Entire Range of Temperature

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible, especially in the intermediate regime between the classical and quantum limits. (Contains 3 figures.)