The average kinetic energy of a molecule of a gas at absolute temperature T is proportional to

Options

A. directly temperture T is
B. inversely proportional to `T^(2)`
C. directly proportional to `T^(2)`
D. inversely proprtional to T

Explanation

To find the relationship between the average kinetic energy of a molecule of a gas and the absolute temperature \( T \), we can follow these steps:

### Step 1: Understand the Concept of Kinetic Energy
The average kinetic energy of a molecule in a gas is related to its motion. In kinetic theory, the average kinetic energy (\( KE \)) of a molecule is given by the formula:

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

where:
- \( k \) is the Boltzmann constant,
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Identify the Proportionality
From the equation \( KE = \frac{3}{2} k T \), we can see that the average kinetic energy (\( KE \)) is directly proportional to the absolute temperature \( T \). This means that if the temperature increases, the average kinetic energy of the molecules also increases.

### Step 3: State the Conclusion
Therefore, we conclude that the average kinetic energy of a molecule of a gas at absolute temperature \( T \) is directly proportional to \( T \).

### Final Answer
The average kinetic energy of a molecule of a gas at absolute temperature \( T \) is proportional to \( T \).

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