For a real gas , the compressibility factor Z has different values at different temperatures and pressures . Which of the following is not correct under the given conditions ?

Options

A. Z < 1 at very low pressure .
B. Z > 1 at high pressure .
C. Z = 1 under all conditions .
D. Z = 1 at intermediate pressure

Explanation

To solve the question regarding the compressibility factor \( Z \) for a real gas, we need to understand the concept of the compressibility factor and how it varies under different conditions.

### Step-by-Step Solution:

1. **Understanding Compressibility Factor \( Z \)**:
- The compressibility factor \( Z \) is defined as the ratio of the molar volume of a real gas (\( V_{\text{actual}} \)) to the molar volume of an ideal gas (\( V_{\text{ideal}} \)) at the same temperature and pressure.
- Mathematically, it is expressed as:
\[ Z = \frac{V_{\text{actual}}}{V_{\text{ideal}}} \]

2. **Behavior of \( Z \) Under Different Conditions**:
- For real gases, \( Z \) can vary with changes in temperature and pressure.
- At very low pressures, real gases tend to behave more like ideal gases, and \( Z \) can be less than 1.
- At intermediate pressures, \( Z \) can equal 1, indicating that the gas behaves ideally under those conditions.
- At high pressures, \( Z \) is generally greater than 1 due to the repulsive forces between gas molecules.

3. **Evaluating the Options**:
- The question states that \( Z \) has different values at different temperatures and pressures. We need to identify which statement is incorrect based on this information.
- Let's analyze the options:
- **Option 1**: \( Z < 1 \) at very low pressure. (This is correct.)
- **Option 2**: \( Z = 1 \) under all conditions. (This is incorrect because it contradicts the statement that \( Z \) has different values.)
- **Option 3**: \( Z = 1 \) at intermediate pressure. (This is correct.)

4. **Conclusion**:
- The statement that is not correct is: **\( Z = 1 \) under all conditions**. This contradicts the fact that \( Z \) varies with temperature and pressure.

### Final Answer:
The incorrect statement is: **\( Z = 1 \) under all conditions**.

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