Consider the following statements.
I. If the gas is allowed to expand freely, it is in equilibrium state throughout.
II. Volume is extensive state variable. Choose the correct option.

Options

A. Statement i Is correct
B. Statement II Is correct
C. Both the statements are correct
D. Both the statements are incorrect

Answer

To solve the question, we need to analyze the two statements provided:

### Step 1: Analyze Statement I
**Statement I:** "If the gas is allowed to expand freely, it is in equilibrium state throughout."

- **Explanation:** Free expansion of a gas occurs when it expands into a vacuum (no external pressure). In this scenario, the gas does not perform work on the surroundings because there is no opposing pressure. For a system to be in equilibrium, the pressure inside the gas must equal the pressure outside the gas at every point. However, during free expansion, the external pressure is zero (vacuum), and the internal pressure is not zero. Therefore, the gas cannot be in equilibrium throughout the process.

- **Conclusion:** This statement is **incorrect**.

### Step 2: Analyze Statement II
**Statement II:** "Volume is an extensive state variable."

- **Explanation:** An extensive property is one that depends on the amount of matter in the system. Volume is indeed an extensive property because if you have more substance (more matter), the volume will increase. For example, if you double the amount of gas, the volume will also double, assuming constant temperature and pressure.

- **Conclusion:** This statement is **correct**.

### Final Conclusion
- **Statement I:** Incorrect
- **Statement II:** Correct

Thus, the correct answer is that only Statement II is true.

### Answer:
The correct option is **Statement II only**.

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