Thermodynamic Classification of Entropy Explained

To understand the classification of entropy, we first need to define what extensive and intensive properties are in thermodynamics.

• Extensive Properties: These properties depend on the size or mass of the system. Examples include mass, volume, and internal energy. If you combine two identical systems, the value of an extensive property for the combined system is the sum of its values for the individual systems.
• Intensive Properties: These properties do not depend on the size or mass of the system. They are the same regardless of how much substance you have. Examples include temperature, pressure, and density. If you combine two identical systems, the intensive properties remain the same.

Entropy: Total vs. Specific

Entropy is a fundamental thermodynamic property that measures the degree of randomness or disorder in a system. Let's look at the two forms mentioned: total entropy ($S$) and specific entropy ($s$).

Total Entropy ($S$)

Total entropy, denoted by $S$, represents the overall entropy of a system. Since entropy is related to the number of possible microscopic arrangements of the system's components, it naturally scales with the size of the system. For instance, a larger system (more mass or volume) generally has more possible arrangements and thus higher total entropy.

Therefore, Total Entropy ($S$) is an extensive property because its value depends directly on the amount of substance (mass) in the system. If you double the mass of the system, you double the total entropy.

Specific Entropy ($s$)

Specific entropy, denoted by $s$, is defined as the total entropy ($S$) divided by the mass ($m$) of the system. The relationship is given by the formula:

$s = \frac{S}{m}$

When we calculate specific entropy, we are essentially normalizing the total entropy by the mass. If we increase the mass ($m$) of the system, the total entropy ($S$) also increases proportionally. However, their ratio ($s = S/m$) remains constant. For example, if we double the mass ($2m$), the total entropy also doubles ($2S$), but the specific entropy becomes $\frac{2S}{2m} = \frac{S}{m}$, which is the same value.

Because the value of specific entropy does not change with the size or mass of the system, Specific Entropy ($s$) is an intensive property.

Conclusion on Entropy Classification

Based on these definitions:

• Total Entropy ($S$) is an extensive property.
• Specific Entropy ($s$) is an intensive property.

This matches the second option provided in the question.