Question

According to the Boltzmann Equation $S = k_B \ln \Omega$, if a system is in a state of "Perfect Order" (a perfect crystal at $0\text{ K}$), the number of microstates $\Omega$ and the entropy $S$ are

• A. $\Omega = 0, S = 0$
• B. $\Omega = 1, S = 0$
• C. $\Omega = 1, S = 1$
• D. $\Omega \to \infty, S \to \infty$

Hint:

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero is exactly zero.
This corresponds to a single microstate ($\Omega = 1$), representing zero randomness.

Answer 1

The Correct Option is B