The average kinetic energy of a gas molecule is

Options

A. proportional to pressure of gas
B. inversely proportional to volume of gas
C. inversely proportional to absolute temperature of gas
D. directly proportional to absolute temperature of gas

Explanation

To determine the relationship between the average kinetic energy of a gas molecule and temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Energy of Gas Molecules**:
The average kinetic energy (KE) of a gas molecule is a measure of the energy due to the motion of the molecules. It can be expressed mathematically.

2. **Using the Formula**:
The average kinetic energy of a gas molecule is given by the formula:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin.

3. **Analyzing the Formula**:
From the formula, we can see that the average kinetic energy is directly proportional to the absolute temperature \( T \). This means that as the temperature increases, the average kinetic energy of the gas molecules also increases.

4. **Evaluating the Options**:
- **Option 1**: Proportional to pressure of gas - **Incorrect**. The average kinetic energy does not depend on pressure.
- **Option 2**: Inversely proportional to volume of gas - **Incorrect**. The average kinetic energy is independent of volume.
- **Option 3**: Inversely proportional to absolute temperature - **Incorrect**. The average kinetic energy is directly proportional to temperature, not inversely.
- **Option 4**: Directly proportional to absolute temperature of gas - **Correct**. This aligns with our derived formula.

5. **Conclusion**:
Therefore, the correct answer is that the average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas.

### Final Answer:
The average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas.

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