Statistical Thermodynamics of an Ideal Gas: General Expressions of Some Properties

Using the fundamental approach of statistical mechanics and distribution formulae, we study some well-known thermodynamic properties of an ideal gas in any positive dimensionality and with any positive-exponent dispersion relation. We have derived general expressions for the density of states and canonical partition function following the formalism of classical statistics and have calculated properties like average energy, average pressure, entropy, etc., for an ideal classical gas. The general expression for the density of states and quantum statistical distribution functions are used to determine the general expressions for the thermal de Broglie wavelength, critical temperature and critical wavelength for an ideal Bose gas and the Fermi energy, Fermi wavelength, average energy for an ideal Fermi gas. These properties are compared with what we commonly find in standard textbooks for a nonrelativistic ideal gas of material particles or massless particles like photons in three dimensions.