
\sect{Baruch's  A19.}

An ideal classical gas of ${N}$ particles of mass
${\mathsf{m}}$ is in a container of height ${L}$ which is in a
gravitational field of a constant acceleration ${g}$. The gas is
in uniform temperature ${T}$.
\begin{itemize}
\item [(a)]
Find the dependence ${P\left(h\right)}$ of the pressure on the height ${h}$.
\item [(b)]
Find
the partition function and the internal energy. Examine the limits
${mgL<<k_{B}T}$ and ${mgL>>k_{B}T}$ and interpret the meaning of
these limits.

\item [(c)]
Find ${P\left(h\right)}$ for an adiabatic atmosphere, i.e.
the atmosphere has been formed by a constant entropy process in
which ${T,\,\mu}$, are not equilibrated, but ${Pn^{-\gamma}}$   =
const; equilibrium is maintained within a layer at height $h$. Find $T(h)$ and $ n(h)$
in terms of the density $n_0$ and temperature $T_0$ at $h=0$. \\
\end{itemize}

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