During expansion of a gas into vaccum `(P_("ext")=0)`, Work done is zero if the process is
(A) Reversible (B) Irreversible (C ) Isothermal

Options

A. B & C are true
B. A, B & C are false
C. A & C are true
D. B & C are false

Answer

To solve the question regarding the work done during the expansion of a gas into a vacuum, we need to analyze the conditions under which the work done is zero.

### Step-by-Step Solution:

1. **Understanding Work Done in Expansion**:
The work done (W) during the expansion of a gas is given by the formula:
\[ W = -P_{\text{ext}} \Delta V \]
where \( P_{\text{ext}} \) is the external pressure and \( \Delta V \) is the change in volume.

2. **Identifying the External Pressure**:
In the given scenario, the gas is expanding into a vacuum, which means that the external pressure \( P_{\text{ext}} = 0 \).

3. **Calculating Work Done**:
Substituting \( P_{\text{ext}} = 0 \) into the work done formula:
\[ W = -0 \times \Delta V = 0 \]
This indicates that the work done during the expansion of the gas into a vacuum is zero.

4. **Considering the Type of Process**:
The question asks about the type of process (reversible, irreversible, isothermal) under which the work done is zero. Since we established that the work done is zero due to \( P_{\text{ext}} = 0 \), it applies regardless of whether the process is reversible or irreversible.

5. **Conclusion**:
Therefore, the work done is zero during the expansion of a gas into a vacuum if the process is:
- (A) Reversible
- (B) Irreversible
- (C) Isothermal

Since the work done is zero in all these cases, we can conclude that options (A), (B), and (C) are correct.

### Final Answer:
The correct options are (A), (B), and (C).

---