\sect{Baruch's B01.}

For a single quantum particle of mass $m$,
spectra $p^2/2m$ in a volume $V$ the partition function is
$Z_1(m)=gV/\lambda^3$ with $\lambda=h/\sqrt{2\pi mk_BT}$. The particle
has a spin degeneracy $g$ ($g=2s+1$ for spin $s$).
\begin{itemize}
\item[(a)] Calculate the partition function of two such particles
if they are either bosons or fermions.
\item[(b)]  Calculate the corrections to the energy $E$, and the
heat capacity $C$, due to Bose or Fermi statistics.
\item[(c)]  Find the second virial coefficient $a_2$, defined as
$PV=NkT[1+ a_2n\lambda^3]$ to
leading order in the small parameter $n\lambda^3$.\\
\end{itemize}

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