The average velocity of the molecules in a gas in equilibrium is

Options

A. Proportional to `sqrt(T)`
B. Proportional to `T`
C. Zero
D. Not possible to determine

Answer

To solve the question regarding the average velocity of the molecules in a gas in equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average Velocity**:
The average velocity of gas molecules is a measure of the average speed at which the molecules move in a gas. In the context of kinetic theory, this average velocity can be derived from the kinetic energy of the gas molecules.

2. **Use the Formula for Average Velocity**:
The average velocity \( V_{\text{average}} \) of gas molecules can be expressed using the formula:
\[ V_{\text{average}} = \sqrt{\frac{8RT}{\pi m}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( m \) is the mass of a gas molecule.

3. **Analyze the Relationship**:
From the formula, we can see that the average velocity \( V_{\text{average}} \) is directly proportional to the square root of the temperature \( T \). This means that as the temperature increases, the average velocity of the gas molecules also increases.

4. **Conclusion**:
Therefore, we can conclude that the average velocity of the molecules in a gas in equilibrium is directly proportional to the square root of the temperature.

### Final Answer:
The average velocity of the molecules in a gas in equilibrium is proportional to \( \sqrt{T} \).

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