In an isothermal expansion of a gaseous sample the correct relation is (consider `w`(work) with sign according to new `IUPAC` convention)
[The reversible and irreversible processes are carried out between same initial and final states]

Options

A. `W_(rev) gt W_(irrev)`
B. `W_(irrev) gt W_(rev)`
C. `q_(rev) lt q_(irrev)`
D. can not be predicted

Answer

To solve the question regarding the isothermal expansion of a gaseous sample and the work done in reversible and irreversible processes, we will analyze the concepts of work done in both processes.

### Step-by-Step Solution:

1. **Understanding Isothermal Expansion**:
- In an isothermal process, the temperature of the system remains constant. For an ideal gas, this means that the internal energy change (ΔU) is zero.

2. **Work Done in Reversible Process**:
- For a reversible isothermal expansion of an ideal gas, the work done (W) can be calculated using the formula:
\[ W_{\text{reversible}} = -nRT \ln\left(\frac{V_f}{V_i}\right) \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the temperature, \( V_f \) is the final volume, and \( V_i \) is the initial volume.

3. **Work Done in Irreversible Process**:
- For an irreversible isothermal expansion, the work done is generally less than that done in a reversible process. The formula for work done in an irreversible process can be expressed as:
\[ W_{\text{irreversible}} = -P_{\text{ext}}(V_f - V_i) \]
where \( P_{\text{ext}} \) is the external pressure, which is constant and usually less than the pressure of the gas during the expansion.

4. **Comparing Work Done**:
- Since the external pressure in an irreversible process is typically less than the pressure exerted by the gas, the work done in an irreversible process is less than that in a reversible process. Therefore:
\[ W_{\text{irreversible}} < W_{\text{reversible}} \]

5. **Conclusion**:
- Based on the above analysis, the correct relation is:
\[ W_{\text{irreversible}} < W_{\text{reversible}} \]
- Hence, the correct answer is that the work done in the irreversible process is less than that in the reversible process.

### Final Answer:
- The correct relation is: **W reversible > W irreversible**.