According to the third law of thermodynamics, the entropy of a perfectly organized crystal at absolute zero is

• A. Zero
• B. Infinite
• C. Undefined
• D. Negative

Answer: (A)

Entropy measures how many microscopic configurations fit a given macroscopic state. For a perfectly organized crystal at absolute zero, there is only one way to arrange the particles that matches that perfect order, so the number of accessible microstates is one. Using S = k_B ln Ω, with Ω = 1, gives S = 0. The third law sets this zero point for a perfectly crystalline substance at 0 K. In real materials there can be tiny residual entropy due to defects or degeneracy, but in the ideal case the entropy at absolute zero is zero. Therefore, the entropy is zero.