
\sect{Negative temperature}

%Baruch's  A04

Consider ${N}$ particles, each fixed in position and having a
magnetic moment $\mu$ , in a magnetic field ${H}$. Each particle
has then two energy states, ${\pm\mu H}$. Treat the particles as
distinguishable.

\begin{itemize}
\item [(a)]
Evaluate the entropy of the system ${S\left(n\right)}$ where n is
the number of particles in the upper energy level;
assume ${n>>1}$. Draw a rough plot of ${S\left(n\right)}$.
\item [(b)]
Find the most probable value of ${n}$ and its mean square
fluctuation.

\item [(c)]
Relate n to the energy ${E}$ of the system and find the temperature.
Show that the system can have negative temperatures. Why a negative
temperature is not possible for a gas in a box?

\item [(d)]
What happens if a system of negative temperature is in contact
with a heat bath of fixed temperature ${T_{0}}$? \\

\end{itemize}

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