Question

The Third Law of thermodynamics states that entropy at absolute zero is:

• A. Maximum
• B. Minimum
• C. Zero for perfect crystal
• D. Infinite

Hint:

The Third Law establishes an absolute reference point for entropy, allowing us to calculate absolute entropies of substances rather than just change in entropy ($\Delta S$).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the statement or value of entropy at absolute zero ($0\text{ K}$) according to the Third Law of Thermodynamics.

Step 2: Key Formula or Approach:
The statistical definition of entropy is given by Boltzmann's formula:
\[ S = k_B \ln \Omega \]
where $\Omega$ is the number of accessible microstates corresponding to the macrostate of the system.

Step 3: Detailed Explanation:

• As temperature approaches absolute zero ($T \rightarrow 0\text{ K}$), all thermal motion of atoms in a crystal lattice ceases.

• For a perfectly ordered crystalline substance, there is only one unique, perfectly ordered ground-state configuration. This means the number of microstates is $\Omega = 1$.

• Substituting this into Boltzmann's entropy formula:
\[ S = k_B \ln(1) = 0 \]

• Therefore, the Third Law states that the entropy of a perfect crystalline substance at absolute zero is exactly equal to zero.

• If the crystal has defects, impurities, or is amorphous (like glass), there will be residual entropy greater than zero due to structural disorder ($\Omega > 1$).

Step 4: Final Answer:
The entropy at absolute zero is zero for a perfect crystal.