Consider a system of two Einstein solids, with NA = 300, NB = 200, and (qtotal = 100 (as discussed in Section 2.3). Compute the entropy of the most likely macrostate and of the least likely macrostate. Also compute the entropy over long time scales, assuming that all microstates are accessible. (Neglect the factor of Boltzmann’s constant in the definition of entropy; for systems this small it is best to think of entropy as a pure number.)
and and .
The maximum probable microstate is when . And minimum probable microstate is when .
Now we have to calculate the entropy as pure number (ignoring the boltzmann's constant) for the both states.Step 2<p>The total number of microstates in the most probable state is
(given in the book)
Hence the entropy is
Hence the entropy of the most probable state is 264.