Question

The entropy of single crystalline Silicon at absolute zero will be:

• A. 2
• B. 1
• C. 0
• D. 10

Hint:

A perfect crystal has maximum order and only one possible microstate at 0 K. This leads to zero entropy as per the third law of thermodynamics.

Answer 1

The Correct Option is C

Entropy is a thermodynamic property that measures the degree of randomness or disorder in a system.
According to the Third Law of Thermodynamics, as the temperature of a perfect crystalline substance approaches absolute zero (0 Kelvin), the entropy approaches zero.
Mathematically, this is expressed as:
\[ \lim_{T \to 0} S = 0 \]
Single crystalline silicon is a material in which the crystal lattice is continuous and unbroken to the edges of the sample, with no grain boundaries.
This high degree of order means that at absolute zero, there are no residual configurations or microstates to contribute to entropy.
Thus, the system has only one microstate and:
\[ S = k \ln W = k \ln(1) = 0 \]
Where $k$ is the Boltzmann constant and $W$ is the number of microstates.
Therefore, the entropy of single crystalline silicon at absolute zero is zero.