Question

If a system is completely ordered and the atoms are at rest at zero Kelvin, then the entropy of the system is:

• A. Zero
• B. Positive
• C. Negative
• D. Cannot be defined

Hint:

When a question involves absolute zero temperature and complete order, apply the \textbf{Third Law of Thermodynamics}: Entropy becomes zero for a perfectly crystalline system at 0 K.

Answer 1

The Correct Option is A

Step 1: Understanding Entropy and Absolute Zero
Entropy is a measure of the disorder or randomness of a system. The more disordered the system, the higher the entropy. When a system is said to be \textit{completely ordered}, it means all the particles are in a definite and predictable state — there’s no randomness in their arrangement. Step 2: Third Law of Thermodynamics
The Third Law of Thermodynamics states that:
\textit{"The entropy of a perfect crystalline substance is zero at absolute zero temperature (0 Kelvin)."} At absolute zero, the thermal motion of atoms theoretically ceases. In a perfect crystal, each atom is perfectly arranged, and there is only one microstate possible. Since entropy (\( S \)) is given by Boltzmann’s formula: \[ S = k \ln W \] where \( k \) is Boltzmann’s constant and \( W \) is the number of microstates. For a perfectly ordered system, \( W = 1 \), so: \[ S = k \ln(1) = 0 \] Step 3: Why Other Options Are Incorrect
- (B) Positive: Entropy becomes positive only if there's some degree of disorder, which is not the case here.
- (C) Negative: Entropy can never be negative because \( \ln W \geq 0 \) for \( W \geq 1 \).
- (D) Cannot be defined: Entropy is well-defined for such ideal conditions as described by the third law. Conclusion: Since the system is completely ordered and at 0 K, its entropy is exactly zero.