For isothermal expansion , which is true?

Options

A. `Delta P = 0`
B. `Delta S = 0`
C. `Delta G = 0`
D. `Delta U = 0`

Answer

To solve the question regarding isothermal expansion, we need to analyze the properties involved during this process.

### Step-by-Step Solution:

1. **Understand Isothermal Expansion**:
- Isothermal expansion refers to a process where a gas expands at a constant temperature (T). This means that the temperature does not change during the expansion.

2. **Identify Relevant Thermodynamic Variables**:
- In thermodynamics, we often deal with changes in internal energy (ΔU), entropy (ΔS), Gibbs free energy (ΔG), and pressure (ΔP).

3. **Change in Internal Energy (ΔU)**:
- For an ideal gas, the internal energy (U) is a function of temperature only. Since the temperature remains constant during isothermal expansion (ΔT = 0), the change in internal energy is given by:
\[ \Delta U = 0 \]
- Therefore, ΔU is zero during isothermal expansion.

4. **Change in Entropy (ΔS)**:
- The entropy change during an isothermal process can be calculated using the formula:
\[ \Delta S = nR \ln\left(\frac{V_f}{V_i}\right) \]
- Here, \(V_f\) and \(V_i\) are the final and initial volumes, respectively. Since the volume changes during expansion, ΔS is not zero.

5. **Change in Gibbs Free Energy (ΔG)**:
- The change in Gibbs free energy is also not zero during isothermal expansion. It can be affected by changes in pressure and volume.

6. **Change in Pressure (ΔP)**:
- During expansion, the pressure of the gas will change as it occupies a larger volume. Therefore, ΔP is not zero.

7. **Conclusion**:
- Based on the analysis, the only variable that remains unchanged during isothermal expansion is the internal energy (ΔU). Thus, the correct answer is:
\[ \Delta U = 0 \]

### Final Answer:
- The correct option is **ΔU = 0**.