The pressure volume work for an ideal gas can be calculated by using the expression `w=-int_(V_(i))^(v_(f))Pex dV`. The work can also be calculated from the pV-plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (B) irreversibly from volume `V_(i)` to `V_(f)` choose the correct option.

Options

A. W (reversible) = W (irreversible)
B. W (reversible) `lt` W (irreversible)
C. W (reversible) `=` W (irreversible)
D. W (reversible) `=` W (irreversible) `+ p_(ex) . Delta V`

Explanation

To solve the question regarding the work done during the compression of an ideal gas, we will analyze the work done in both reversible and irreversible processes.

### Step-by-Step Solution:

1. **Understanding Work Done**:
The work done on or by a gas during a volume change can be expressed mathematically as:
\[ w = -\int_{V_i}^{V_f} P_{ex} \, dV \]
where \( P_{ex} \) is the external pressure and \( V_i \) and \( V_f \) are the initial and final volumes, respectively.

2. **Reversible Process**:
In a reversible process, the gas is compressed slowly, and the external pressure \( P_{ex} \) is always equal to the internal pressure of the gas. This means the process follows a specific path on the pressure-volume (PV) diagram, resulting in a curved line. The work done can be calculated as the area under this curve.

3. **Irreversible Process**:
In an irreversible process, the gas is compressed rapidly, and the external pressure is constant (often taken as the final pressure of the gas). This results in a straight line on the PV diagram. The work done in this case is represented by the area under the straight line from \( V_i \) to \( V_f \).

4. **Comparing Work Done**:
- For the reversible process, the work done is represented by the area under the curve, which is generally less than the area under the straight line for the irreversible process.
- For the irreversible process, since the external pressure is constant and typically higher than the internal pressure during compression, the work done is greater.

5. **Conclusion**:
From the analysis, we can conclude that:
\[ W_{reversible} < W_{irreversible} \]
Therefore, the correct option is that the work done in a reversible process is less than that in an irreversible process.

### Final Answer:
The correct option is **B**: Work done in a reversible process is less than work done in an irreversible process.