Choose the correct statement(s)

Options

A. Work done by the system is taken as negative
B. In expansion , there is work done by the system
C. `W_("reversible") gt W_("irreversible")`.
D. All of these

Answer

To solve the question, we need to analyze the statements provided and determine their correctness based on thermodynamic principles.

### Step-by-Step Solution:

1. **Understanding Work Done by the System**:
- The work done by a system (like a gas in a piston) can be defined as the force exerted by the gas on the piston multiplied by the distance the piston moves.
- Mathematically, this is expressed as:
\[ W = -P \Delta V \]
- Here, \( \Delta V = V_2 - V_1 \), where \( V_2 \) is the final volume and \( V_1 \) is the initial volume.

2. **Analyzing Statement 1**:
- The first statement claims that "work done by the system is taken as negative".
- When a gas expands (i.e., \( V_2 > V_1 \)), the system does work on the surroundings, resulting in a negative value for work done.
- Therefore, this statement is **correct**.

3. **Analyzing Statement 2**:
- The second statement asserts that "in case of expansion, there is work done by the system".
- During expansion, the gas does work on the piston, which means work is indeed done by the system.
- Thus, this statement is also **correct**.

4. **Analyzing Statement 3**:
- The third statement states that "work done reversibly is greater than work done irreversibly".
- For an isothermal process, the work done reversibly can be expressed as:
\[ W_{\text{rev}} = -2.303 nRT \log \left(\frac{V_2}{V_1}\right) \]
- For irreversible processes, the work done is given by:
\[ W_{\text{irrev}} = -P_{\text{ext}} (V_2 - V_1) \]
- In general, for the same change in volume, the work done reversibly is greater than that done irreversibly due to the path taken in the process. Therefore, this statement is **correct**.

5. **Conclusion**:
- Since all three statements have been analyzed and found to be correct, we conclude that all the statements are indeed correct.

### Final Answer:
All the statements are correct.

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