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 those whose value depends on the amount of matter present, e.g., mass, volume, internal energy. - Intensive variables are independent of the amount of matter, e.g., pressure, temperature, density. Step 1: Analyze the options: - (A) Internal energy, volume, and mass are indeed extensive variables. - (B) Pressure, temperature, and density are intensive variables, which is correct. - (C) Volume, temperature, and density are mixed. Volume is extensive, but temperature and density are intensive. Hence, statement (C) is incorrect. - (D) Mass, temperature, and internal energy are extensive variables, which is correct. Thus, the correct combination of statements is (C) and (D). Thus, the answer is \( \boxed{2} \).