Question

Given are statements for certain thermodynamic variables: \begin{itemize} \item[(A)] Internal energy, volume \( V \), and mass \( M \) are extensive variables. \item[(B)] Pressure \( P \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(C)] Volume \( V \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(D)] Mass \( M \), temperature \( T \), and internal energy are extensive variables. \end{itemize} Choose the correct answer from the options given below:

• (B) and (C) Only
• (C) and (D) Only
• (D) and (A) Only
• (A) and (B) Only

Hint:

- Extensive variables depend on the size or amount of the system (e.g., volume, mass). - Intensive variables do not depend on the amount of material (e.g., temperature, pressure). - Be careful with mixed quantities like density, which is intensive, but volume and internal energy are extensive.

Answer 1

The Correct Option is B

- Extensive variables are contingent on the quantity of matter, such as mass, volume, and internal energy.
- Intensive variables are not dependent on the quantity of matter, for instance, pressure, temperature, and density.

Step 1: Evaluate the assertions:

- (A) Internal energy, volume, and mass are correctly identified as extensive variables.
- (B) Pressure, temperature, and density are correctly identified as intensive variables.
- (C) Volume, temperature, and density constitute a mixed set. Volume is extensive, while temperature and density are intensive. Therefore, statement (C) is inaccurate.
- (D) Mass, temperature, and internal energy are extensive variables, which is accurate.

Consequently, the accurate pairings of statements are (C) and (D).

Thus, the answer is \( \boxed{2} \).