\sect{Baruch's  B09.}

The universe is pervaded by a black body radiation corresponding
to a temperature of ${3 K}$.
In a simple view, this radiation was produced from the adiabatic
expansion of a much hotter photon cloud which was produced during
the big bang.
\begin{itemize}
\item [(a)]
Why is the recent expansion adiabatic rather than, for example,
isothermal? It is also known that the expansion velocity is
sufficiently small. Smallness compared with what is needed?
explain.
\item [(b)]
If in the next ${10^{10}}$ years the volume of the universe
increases by a factor of two, what then will be the temperature of
the black body radiation?
\item [(c)]
By what factor does the energy change in the process (b)? Explain
the process by which the energy changes and show that this specific process
indeed reproduces the change in energy.
\end{itemize}

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