Using the fundamental approach of statistical mechanics anddistribution formulae, we study some well-known thermodynamic properties of an ideal gas in any positive dimensionality and with anypositive-exponent dispersion relation. We have derived generalexpressions for the density of states and canonical partition functionfollowing the formalism of classical statistics and have calculatedproperties like average energy, average pressure, entropy, etc., foran ideal classical gas. The general expression for the density ofstates and quantum statistical distribution functions are used todetermine 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 Fermigas. These properties are compared with what we commonly find instandard textbooks for a nonrelativistic ideal gas of materialparticles or massless particles like photons in three dimensions.