 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2021/paper-2/a6/f/solution

Only the two lower orientations remain populated, giving

2^{N}

equiprobable microstates. Thus

T \to 0 lim S = N k_{B} ln 2.

This residual entropy follows from the stipulated independent-site ground-state degeneracy. The zero-entropy version of the third law of thermodynamics presupposes a unique ordered ground state; that assumption does not hold here. Intermolecular interactions or a small splitting of the two in-plane states could remove this degeneracy, but they are excluded from the given model.

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