Following graph represents a pressure `(P)` volume `(V)` relationship at a fixed temperature `(T)` for n moles of a real gas. The graph has two regions marked `(I)` and `(II)`. Which of the following options is true.

Options

A. `Z lt 1` in the region (II)
B. `Z = 1` I the region (II)
C. `Z =1` for the curve
D. `Z` approaches 1 as we move from region (II) to region (I)

Answer

To solve the question regarding the pressure-volume relationship of a real gas at a fixed temperature, we will analyze the graph and the behavior of the gas in the marked regions (I and II).

### Step-by-Step Solution:

1. **Understanding the Graph**:
- The graph represents the relationship between pressure (P) and volume (V) for a real gas at a constant temperature (T).
- The two regions marked (I) and (II) indicate different behaviors of the gas under varying pressure and volume conditions.

2. **Analyzing Region II**:
- In Region II, the pressure is relatively high. Under high pressure, the volume of the gas is small, and the intermolecular forces become significant.
- Real gases deviate from ideal behavior in this region, often showing a compressibility factor (Z) less than 1, indicating that attractive forces dominate.

3. **Analyzing Region I**:
- In Region I, the pressure is lower and the volume is larger. At low pressure and high volume, the gas molecules are far apart, and the effects of intermolecular forces become negligible.
- In this region, the real gas behaves more like an ideal gas, and the compressibility factor (Z) approaches 1.

4. **Comparing Regions**:
- As the gas transitions from Region II to Region I, the pressure decreases, and the volume increases.
- This transition indicates that the gas is behaving more ideally as it moves to a state of lower pressure and higher volume.

5. **Conclusion**:
- The correct statements regarding the behavior of the gas in the two regions are:
- In Region II, Z < 1 (indicating non-ideal behavior due to high pressure).
- In Region I, Z approaches 1 (indicating ideal behavior due to low pressure).
- Therefore, the correct options are A (Z < 1 in Region II) and D (Z approaches 1 in Region I).

### Final Answer:
The correct options are A and D.