Question

The average kinetic energy of a molecule of the gas is

• A. proportional to absolute temperature
• B. proportional to volume
• C. dependent on the nature of the gas
• D. proportional to pressure

Answer 1

The Correct Option is A

The average kinetic energy of a molecule in an ideal gas can be related to the absolute temperature of the gas. This relationship is foundational in the kinetic theory of gases.

The formula for the average kinetic energy \(E_k\) of a molecule is given by:

\(E_k = \frac{3}{2} k T\)

where:

• \(k\) is the Boltzmann constant.
• \(T\) is the absolute temperature in Kelvin.

From this formula, it is evident that the average kinetic energy of a molecule is directly proportional to the absolute temperature \(T\). Therefore, as the temperature of the gas increases, the kinetic energy of its molecules also increases, following a linear relationship.

Let's evaluate the given options:

• Proportional to absolute temperature: This is correct as derived from the formula \(E_k = \frac{3}{2} k T\).
• Proportional to volume: Incorrect. The kinetic energy depends on temperature, not directly on volume.
• Dependent on the nature of the gas: Incorrect. This relationship is for ideal gases and hence is independent of the nature of the gas.
• Proportional to pressure: Incorrect. While pressure depends on temperature, the kinetic energy is directly described by temperature alone through the ideal gas law at a molecular level.

In conclusion, the average kinetic energy of a molecule of the gas is proportional to absolute temperature, validating the correct option.