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

Options

A. 1/T
B. `sqrt(T)`
C. T
D. `T^(2)`

Answer

To solve the question regarding the average kinetic energy of a molecule of a gas at absolute temperature \( T \), we can follow these steps:

### Step 1: Understand the relationship between kinetic energy and temperature
The average kinetic energy of a molecule in an ideal gas is directly related to the temperature of the gas. According to the kinetic theory of gases, the average kinetic energy \( K \) of a molecule is given by the formula:

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

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

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

### Step 3: Write the proportionality statement
We can express this relationship in terms of proportionality:

\[ K \propto T \]

This indicates that the average kinetic energy of a molecule of gas is proportional to the absolute temperature \( T \).

### Conclusion
Thus, the average kinetic energy of a molecule of a gas at absolute temperature \( T \) is proportional to \( T \).

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