Consider an Einstein solid having N $=20$ atoms.

$($a$)$ What is the solid's temperature when it has an energy of $10$e$,$

assuming that e $=$ ha ~ $0\mathrm{.}02$ eV $($a physically reasonable

value for a solid$)?$ Calculate this directly from the definition of temperature by finding S at $10$ and $11$e$,$ computing dS$/$dU ~ $[$S$(11)-$ S$(10)]/$e$,$ and then applying the definition of temperature. $($You may find that your work will go faster if you use StatMech to tabulate the multiplicities.$)$