
\sect{Equilibrium of a two level system}

%Baruch's  A03

Consider ${N}$ particles in a two level system, ${n_{1}}$
particles in energy level ${E_{1}}$ and ${n_{2}}$  particles in
energy level ${E_{2}}$. The system is in contact with a heat
reservoir at temperature ${T}$. Energy can be transferred to the
reservoir by a quantum emission in which ${n_{2}\rightarrow n_{2}
- 1, n_{1}\rightarrow n_{1}+1}$ and energy ${E_{2}- E_{1}}$ is
released. [Note: $n_1,n_2\gg 1$.]

\begin{itemize}
\item[(a)]
Find the entropy change of the two level system as a result of a
quantum emission.

\item[(b)]
Find the entropy change of the reservoir corresponding to (a).

\item[(c)]
Derive the ratio ${n_{2}/n_{1}}$; do not assume a known temperature
for the two level system.
(Note: equilibrium is maintained by these type of energy
transfers). \\
\end{itemize}

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