Question

If a substance is perfect crystal and existing at absolute zero K, then the specific entropy of the substance is

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

Hint:

The Third Law of Thermodynamics establishes an absolute reference point for entropy. Always remember: Perfect Crystal + Absolute Zero Kelvin ($0\text{ K}$) = Zero Entropy. Any imperfection or temperature rise will increase the entropy value above zero.

Answer 1

The Correct Option is D

Concept: The Third Law of Thermodynamics provides an absolute baseline for measuring entropy values. It states that the entropy of a perfect, pure crystalline substance approaches zero as the absolute thermodynamic temperature approaches zero Kelvin ($0 \text{ K}$). Mathematically, this condition is expressed as: \[ \lim_{T \to 0} S = 0 \] Entropy is fundamentally a measure of molecular disorder or randomness within a system. In a perfect crystal at absolute zero, all thermal motion ceases entirely, and the constituent atoms or molecules are arranged in a unique, perfectly ordered geometric microstate configuration ($W = 1$). According to Boltzmann's entropy relation: \[ S = k_B \ln(W) = k_B \ln(1) = 0 \] Therefore, both total and specific entropies drop down to zero.

Step 1: Analyze the criteria provided in the problem statement.
The problem lists two necessary structural conditions:
• The substance must be a perfect crystal (meaning there are no structural defects, dislocations, or isotopic mixing).
• The substance exists at absolute zero Kelvin ($T = 0 \text{ K}$).

Step 2: Connect the conditions to the Third Law of Thermodynamics.
Because both criteria match the exact definitions established by Planck and Nernst for the Third Law of Thermodynamics, the specific entropy ($s$) of this substance cannot be positive, negative, or infinite. It must strictly reach an absolute value of zero. This aligns with Option (D).