Entropy can never be 0 or _____________ for any molecule, atom, or substance.

Entropy can never be 0 or _____________ for any molecule, atom, or substance.

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

Answer: (D)

Entropy measures how many ways a system can be arranged at the microscopic level, i.e., its disorder. According to the Third Law, absolute entropy is set to zero at absolute zero for a perfectly crystalline substance. The Boltzmann relation S = k_B ln W shows that S depends on the number of accessible microstates W, and W is always at least 1. That means S is always greater than or equal to zero, with S = 0 only at 0 K for a perfect crystal; as soon as there are more accessible microstates at any finite temperature, S becomes positive. Therefore, entropy cannot be negative, making the correct completion negative. (Note: real systems can have residual entropy greater than zero due to degeneracy, but entropy values themselves are never negative.)

Entropy measures how many ways a system can be arranged at the microscopic level, i.e., its disorder. According to the Third Law, absolute entropy is set to zero at absolute zero for a perfectly crystalline substance. The Boltzmann relation S = k_B ln W shows that S depends on the number of accessible microstates W, and W is always at least 1. That means S is always greater than or equal to zero, with S = 0 only at 0 K for a perfect crystal; as soon as there are more accessible microstates at any finite temperature, S becomes positive. Therefore, entropy cannot be negative, making the correct completion negative. (Note: real systems can have residual entropy greater than zero due to degeneracy, but entropy values themselves are never negative.)