The kinetic energy of a molecule of a gas is directly proportional to the absolute temperature of the gas.

Explanation

To determine whether the statement "The kinetic energy of a molecule of a gas is directly proportional to the absolute temperature of the gas" is correct, we can follow these steps:

### Step 1: Understand the relationship between kinetic energy and temperature
The kinetic energy (KE) of a molecule in a gas is related to its temperature. The formula for the average kinetic energy of a single molecule of an ideal gas is given by:

\[ KE = \frac{3}{2} k_B T \]

where:
- \( KE \) is the kinetic energy,
- \( k_B \) is the Boltzmann constant,
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Analyze the formula
In the formula \( KE = \frac{3}{2} k_B T \), we can see that the kinetic energy is expressed as a product of the Boltzmann constant and the absolute temperature. The term \( \frac{3}{2} k_B \) is a constant factor.

### Step 3: Identify the proportionality
Since \( k_B \) is a constant, we can say that:

\[ KE \propto T \]

This indicates that the kinetic energy is directly proportional to the absolute temperature \( T \).

### Step 4: Conclusion
Based on the analysis, we conclude that the statement "The kinetic energy of a molecule of a gas is directly proportional to the absolute temperature of the gas" is indeed correct.

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