Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 13

13 A box contains $N$ gas molecules. Consider the box to be divided into three equal parts. (a) By extension of Eq. 20-20, write a formula for the multiplicity of any given configuration. (b) Consider two configurations: configuration $A$ with equal numbers of molecules in all three thirds of the box, and configuration $B$ with equal numbers of molecules in each half of the box divided into two equal parts rather than three. What is the ratio $W_A/W_B$ of the multiplicity of configuration $A$ to that of configuration $B$? (c) Evaluate $W_A/W_B$ for $N = 100$. (Because 100 is not evenly divisible by 3, put 34 molecules into one of the three box parts of configuration $A$ and 33 in each of the other two parts.)