Intensive vs Extensive Expressions

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saybrook1
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Hello guys, I'm struggling to understand why some expressions are deemed to be extensive(or particularly extensive for that matter) and others are not. As far as I understand, extensive properties are physical quantities whose magnitude is additive for subsystems and this magnitude is proportional to the V or N of the system it describes. Intensive properties are physical quantities whose value does not depend on the amount of substance for which it is measured(not proportional to V or N I assume).

This would lead me to believe that expressions containing extensive properties would be extensive expressions. Or is this more of a matter of saying "well, in this situation this formula will be more extensive because the combined magnitudes of the extensive properties contained within are greater than the magnitudes of the intensive properties."? I have an example below where the author(Pathria) claims that one expression for S is not extensive(intensive?) while the other expression for S is "truly extensive!". There are many more examples of this within stat mech books and so if anyone is able to help me figure out how to discern between extensive and non-extensive or intensive expressions, it would be greatly appreciated. Thank you as always.

Extensive vs Intensive.jpg
 
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A quantity is either extensive or intensive. There's no in-between. Entropy is extensive. I have no idea what the author is saying there since the text is cut off.
 
Khashishi said:
A quantity is either extensive or intensive. There's no in-between. Entropy is extensive. I have no idea what the author is saying there since the text is cut off.

The author is just saying that the first expression (Sackur-Tetrode eqn) is Extensive vs the second equation that he references which is "not extensive." He calls many equations extensive/intensive and I don't know how to distinguish between the two in terms of entire formulas being one or the other.
 
A classmate just informed me that an extensive expression must contain a $$\frac{V}{N}$$ term.