%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\sect{Small oscillations of piston in cylinder with Bose gas}
Consider a cylindric tank with length ${L}$ and basis area ${A}$,
divided to two parts by a partition with mass ${\mathsf{m}}$,that is
free to move. On one side of the of the partition there are
${N_{a}}$ identical bozons with mass ${\mathsf{m}_{a}}$ and from the
other side ${N_{b}}$ identical bozons with mass ${\mathsf{m}_{b}}$
(*) Assume that gas ${a}$ can be described in the Boltzmann proximity
frame.
(**) Assume that gas ${b}$ is in condensation state.
\begin {itemize}
\item[(a)]
Find the location of the partition ${\chi}$ in an equilibrium state
when the temperature is ${T}$ under the assumptions (*) (**).
\item[(b)]
Write the condition that allow the assumption (*) to be valid in a
state of equilibrium.
\item[(c)]
Write the condition on temperature ${T}$ so the assumption (**) is
indeed valid.
\item[(d)]
Find the frequency of the partition's small oscillations around the
equilibrium point.
\end {itemize}
Use only ${M,T,M_{b}, N_{b},m_{a},N_{a},A,L}$.
%%begin{figure}
\putgraph{Ex404}
%%\caption{}\label{}
%%end{figure}