Question

X is an extensive property and x is an intensive property of a thermodynamic system. Which of the following statement(s) is (are) correct?

• A. xX is extensive.
• B. $\frac{x}{X}$ is intensive.
• C. $\frac{X}{x}$ is extensive.
• D. $\frac{dX}{dx}$ is intensive.

Hint:

Using a simple frame or just bolding for the box Key Points:
Extensive properties scale with system size.
Intensive properties are independent of system size.
Intensive $\times$ Extensive = Extensive.
Extensive / Intensive = Extensive.
Intensive / Extensive is generally size-dependent (not intensive).
Ratio of two Extensive properties is Intensive (e.g., density).
Derivative of Extensive w.r.t Intensive is generally Extensive (e.g., heat capacity).