3. According to the third law of thermodynamics, entropy of a perfect crystal at absolute
zero temperature is
a. always negative
b. always positive
c. equal to zero
d. equal to one

The correct answer is: c. equal to zero.
According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero (0 K) is taken as exactly zero.​

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Introduction

In thermodynamics, a very common conceptual question asks what happens to the entropy of a perfect crystal at absolute zero temperature. The third law of thermodynamics gives a precise answer: the entropy of a perfect, completely ordered crystal at 0 K is defined to be zero, providing an absolute reference point for entropy.​

The given question is:

According to the third law of thermodynamics, entropy of a perfect crystal at absolute zero temperature is
a. always negative
b. always positive
c. equal to zero
d. equal to one

Correct option: c. equal to zero

Third law of thermodynamics and entropy at 0 K

The third law of thermodynamics states that the entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches absolute zero. In a perfect crystal at 0 K, all particles occupy a single, unique ground state, meaning there is only one possible microstate for the system.​

Using Boltzmann’s formula $S=k\ln W$, where $W$ is the number of microstates, a perfect crystal at 0 K has $W=1$, so $S=k\ln 1=0$. This is why the entropy of a perfect crystal at absolute zero is defined as exactly zero.​

Detailed explanation of each option

Option (a): always negative

Entropy is a measure of disorder or the number of accessible microstates of a system and is defined to be zero or positive on the absolute scale when referenced using the third law. For a perfect crystal at 0 K, the entropy is zero, not negative; and for real systems at higher temperatures, entropy values are positive due to increased disorder and available microstates.​

Therefore, saying entropy is “always negative” contradicts the standard thermodynamic definition and the third-law reference scale, so option (a) is incorrect.​

Option (b): always positive

For many real substances at temperatures above 0 K, absolute entropy is indeed positive, because there are many accessible microstates and significant molecular motion. However, the third law specifically tells us that for a perfect crystal at 0 K, entropy becomes zero, not just some positive value.​

Thus, while entropy is usually positive for ordinary conditions, it is exactly zero at absolute zero for a perfect crystal, so option (b) is incorrect in the context of this question.​

Option (c): equal to zero (correct)

For a perfect crystal at absolute zero:

• There is only one unique ground state configuration.​

• The number of microstates $W=1$.​

• Using $S=k\ln W$, entropy $S=k\ln 1=0$.​

This is precisely the third law of thermodynamics statement: the entropy of a perfect crystalline substance at absolute zero is zero. Hence, option (c) equal to zero is the correct answer.​

Option (d): equal to one

There is no thermodynamic postulate that sets the entropy of a perfect crystal at absolute zero equal to one (in any unit system). The “one” here likely confuses the number of microstates $W=1$ with entropy itself. While $W=1$ at 0 K, entropy is $S=k\ln 1=0$, not 1.​

Therefore, option (d) is incorrect because it misrepresents the relationship between microstates and entropy.

Key exam points to remember

• The third law gives an absolute reference: a perfect crystal at 0 K has zero entropy.​

• Real crystals can have residual entropy if there are defects or multiple equivalent ground states, but the idealized “perfect crystal” used in the law has $S=0$ at 0 K.​

• Negative entropy values are not used on the third-law absolute scale for physical systems; entropy is zero or positive.​

For any MCQ asking about “entropy of a perfect crystal at absolute zero,” always choose “zero” in line with the third law of thermodynamics.​