Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 46

A box contains \(N\) identical gas molecules equally divided between its two halves. For \(N = 50\), what are (a) the multiplicity \(W\) of the central configuration, (b) the total number of microstates, and (c) the percentage of the time the system spends in the central configuration? For \(N = 100\), what are (d) \(W\) of the central configuration, (e) the total number of microstates, and (f) the percentage of the time the system spends in the central configuration? For \(N = 200\), what are (g) \(W\) of the central configuration, (h) the total number of microstates, and (i) the percentage of the time the system spends in the central configuration? (j) Does the time spent in the central configuration increase or decrease with an increase in \(N\)?