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\sect{One dimensional hard sphere gas}
${N}$ spheres with diameter ${a}$ are threaded over a wire of length ${L}$.
Assume ${N\gg1}$ but ${Na \ll L}$. The system is in thermic equilibrium, temperature ${T}$.
Find the force ${F}$ that operates on the edges of the wire. Write the result
in the shape ${F=NT/L_{eff}}$. Express ${L_{eff}}$ using the
data and explain it's physical meaning. Hints:
\begin {itemize}
\item[(a)]
While calculating the distribution function, notice that if the
beads permutation were permitted, it was causing ${Z\rightarrow N!Z}$.
\item[(b)]
Assume that a typical distance between two beads is much bigger than ${a}$.
\item[(c)]
To calculate a product ${A=\prod_{n=1}^{N}a_{n}}$
look at the sum ${\ln A}$, and use reasonable approximations.
\end {itemize}
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