For a perfect crystal cooled to 0 K, the entropy is ...

For a perfect crystal cooled to 0 K, the entropy is ...

• A. Zero
• B. Infinite
• C. Undefined
• D. Nonzero constant

Answer: (A)

At absolute zero for a perfectly ordered crystal, there is only one possible microscopic arrangement of the atoms, so the number of accessible microstates is W = 1. Since entropy in Boltzmann form is S = k_B ln W, this gives S = k_B ln(1) = 0. This aligns with the third law of thermodynamics, which states that the entropy of a perfect crystal at 0 K is zero. Infinite entropy would require infinitely many microstates, undefined would imply a zero-or-no-states situation, and a nonzero constant would imply residual entropy from ground-state degeneracy, which doesn’t occur in a perfect crystal.

At absolute zero for a perfectly ordered crystal, there is only one possible microscopic arrangement of the atoms, so the number of accessible microstates is W = 1. Since entropy in Boltzmann form is S = k_B ln W, this gives S = k_B ln(1) = 0. This aligns with the third law of thermodynamics, which states that the entropy of a perfect crystal at 0 K is zero. Infinite entropy would require infinitely many microstates, undefined would imply a zero-or-no-states situation, and a nonzero constant would imply residual entropy from ground-state degeneracy, which doesn’t occur in a perfect crystal.