Question

Which one of the following is an intensive property?

• A. Chemical potential
• B. Volume
• C. Mass
• D. Entropy

Hint:

Use the scaling test: imagine doubling the system. If the property doubles, it's extensive (e.g., \(V, m, S\)); if it remains unchanged, it's intensive (e.g., \(T, P, \mu\)). Partial molar quantities are typically intensive.

Answer 1

The Correct Option is A

Step 1: Define intensive vs. extensive.
A property is \emph{intensive} if it is independent of system size; it is \emph{extensive} if it scales with the amount of matter. A quick test: if we scale the system by a factor \(k\), intensive properties stay the same; extensive properties scale as \(k\). Step 2: Classify each option using scaling and definitions.
- Chemical potential \(\mu_i = \left(\dfrac{\partial G}{\partial n_i}\right)_{T,P,n_{j\neq i}}\): ratio "per mole" driving force; independent of system size \(\Rightarrow\) \emph{intensive}.
- Volume \(V\): doubles if system size doubles \(\Rightarrow\) \emph{extensive}.
- Mass \(m\): proportional to amount of matter \(\Rightarrow\) \emph{extensive}.
- Entropy \(S\): for simple systems, approximately additive \(S\to kS\) when size \(\to k\) \(\Rightarrow\) \emph{extensive} (molar entropy \(S_m\) would be intensive, but \(S\) itself is not). Step 3: Conclude.
Only chemical potential is intensive among the given choices. \[ \boxed{\text{Chemical potential is intensive; } V,\; m,\; S \text{ are extensive.}} \]