Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 47

A box contains \( N \) gas molecules. Consider the box to be divided into three equal parts. (a) By extension of Eq. 20.4.1, 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.)