
\sect{Baruch's  A12.}

${N}$ monomeric units are arranged along a straight line to
form a chain molecule. Each unit can be either in a state
${\alpha}$ (with length ${a}$ and energy ${E_{\alpha}}$ ) or in a
state ${\beta}$ (with length ${b}$ and energy ${E_{\beta}}$ ).
\begin{itemize}
\item [(a)]
Derive the relation between the length ${L}$ of the chain molecule
and the tension ${f}$ applied between at the ends of the molecule.

\item [(b)]
Find the compressibility ${\chi_{T}=(\partial L/\partial f)_{T}}$.
Plot schematically ${L\left(fa/k_{B}T\right)}$ and
${\chi_{T}\left(fa/k_{B}T \right)}$ and interpret the shape of the
plots. \\

\end{itemize}

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