To solve the question regarding why the compressibility factor (Z) of a real gas is usually less than 1 at low temperature and low pressure, we can break down the explanation into several steps:
### Step-by-Step Solution:
1. **Understanding the Compressibility Factor (Z)**:
- The compressibility factor (Z) is defined as \( Z = \frac{PV}{nRT} \), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
- For an ideal gas, Z = 1. For real gases, Z can be less than, greater than, or equal to 1 depending on the conditions.
2. **Real Gas Behavior**:
- Real gases deviate from ideal behavior due to intermolecular forces and the finite volume occupied by gas molecules.
- The Van der Waals equation corrects the ideal gas law for these deviations:
\[
\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT
\]
- Here, 'a' accounts for the attractive forces between gas molecules, and 'b' accounts for the volume occupied by the gas molecules.
3. **Low Temperature and Low Pressure Conditions**:
- At low temperatures, the kinetic energy of gas molecules decreases, leading to stronger attractive forces between them.
- At low pressures, the volume of the gas is relatively large compared to the volume occupied by the gas molecules, making the 'b' term less significant.
4. **Dominance of Attractive Forces**:
- Under these conditions (low T and low P), the attractive forces (represented by 'a') become significant compared to the repulsive forces and the volume occupied by the gas molecules (represented by 'b').
- This means that the attractive forces dominate the behavior of the gas, leading to a compressibility factor (Z) that is less than 1.
5. **Conclusion**:
- Therefore, at low temperature and low pressure, the compressibility factor (Z) of a real gas is usually less than 1 because the attractive forces between gas molecules dominate over the repulsive forces and the volume occupied by the molecules.
### Final Answer:
The compressibility factor (Z) of a real gas is usually less than 1 at low temperature and low pressure because the attractive forces dominate (A is significant) while the volume occupied by gas molecules (B) is negligible.
