A gas is said to behave like an ideal gas when the relation `(pV)/(T)`= constant. When do you expect a real gas to behave like an ideal gas ?

Options

A. When the temperature is low
B. When both the temperature and pressure are low
C. When both the temperature and pressure are high
D. When the temperature is high and pressure is low

Explanation

To determine when a real gas behaves like an ideal gas, we can analyze the conditions under which the ideal gas law holds true. The ideal gas law is given by the equation:

\[ PV = nRT \]

Where:
- \(P\) = pressure of the gas
- \(V\) = volume of the gas
- \(n\) = number of moles of the gas
- \(R\) = universal gas constant
- \(T\) = temperature of the gas in Kelvin

From this equation, we can derive that:

\[ \frac{PV}{T} = nR \]

This indicates that for a gas to behave ideally, the ratio \(\frac{PV}{T}\) must remain constant.

### Step-by-Step Solution:

1. **Understanding Ideal Gas Behavior**:
- An ideal gas is defined as a hypothetical gas that perfectly follows the ideal gas law under all conditions. It assumes no intermolecular forces and that the volume of the gas particles themselves is negligible.

2. **Conditions for Real Gases**:
- Real gases deviate from ideal behavior due to intermolecular forces and the finite volume of gas molecules. However, under certain conditions, they can approximate ideal gas behavior.

3. **High Temperature**:
- At high temperatures, the kinetic energy of gas molecules increases. This increase in kinetic energy means that the molecules move faster, which reduces the impact of intermolecular forces. Consequently, the attractive forces between gas molecules become less significant.

4. **Low Pressure**:
- At low pressures, the volume available to gas molecules increases. This means that the distance between molecules is greater, which further minimizes the effects of intermolecular forces. When gas molecules are far apart, the likelihood of collisions and interactions decreases.

5. **Conclusion**:
- Therefore, a real gas behaves like an ideal gas when it is at high temperatures and low pressures. Under these conditions, the effects of intermolecular forces are minimized, and the gas can be approximated as ideal.

### Final Answer:
A real gas is expected to behave like an ideal gas at **high temperature and low pressure**.

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