The gases obey the different gas laws only theoretically. Practically all of them show some deviation from these laws. These are called real gases. The deviation are maximum under high pressure and at low temperature. These are comparatively small when the conditions are reversed. It has been found that the easily liquefiable gases show more deviations from the ideal gas behaviour as compared to the gases which are liquified with difficulty.
The van der Waals equation reduces itself to ideal gas equation at

Options

A. high pressure and low temperature
B. low pressure and low temperature
C. low pressure and high temperature
D. high pressure only.

Explanation

To solve the question regarding the conditions under which the van der Waals equation reduces to the ideal gas equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**: The ideal gas law is represented as \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature. This equation assumes that gas particles do not interact and that they occupy no volume.

2. **Understanding the van der Waals Equation**: The van der Waals equation for real gases is given by:
\[ \left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT \]
Here, \( a \) and \( b \) are constants specific to each gas, accounting for intermolecular forces and the volume occupied by gas molecules, respectively.

3. **Conditions for Ideal Behavior**: For a gas to behave ideally, the deviations from the ideal gas law must be minimized. This occurs under conditions of:
- **Low Pressure**: At low pressure, the volume available to gas molecules is large, which means that the interactions between molecules are minimal. The distance between molecules increases, reducing the effect of intermolecular forces.
- **High Temperature**: At high temperatures, the kinetic energy of gas molecules increases, which means they move faster. This high speed reduces the time molecules spend close to each other, further minimizing intermolecular interactions.

4. **Conclusion**: Therefore, the van der Waals equation reduces to the ideal gas equation under conditions of **low pressure and high temperature**.

### Final Answer:
The van der Waals equation reduces itself to the ideal gas equation at low pressure and high temperature.

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