(a) Evaluate the partition function and the major thermodynamic properties of an ideal gas consisting of \(N_{1}\) molecules of mass \(m_{1}\) and \(N_{2}\) molecules of mass \(m_{2}\), confined to a space of volume \(V\) at temperature \(T\). Assume that the molecules of a given kind are mutually indistinguishable, while those of one kind are distinguishable from those of the other kind.

(b) Compare your results with the ones pertaining to an ideal gas consisting of \(\left(N_{1}+N_{2}ight)\) molecules, all of one kind, of mass \(m\), such that \(m\left(N_{1}+N_{2}ight)=m_{1} N_{1}+m_{2} N_{2}\).