Question

The average kinetic energy of a gas molecule is directly proportional to

• A. its pressure
• B. its volume
• C. the square root of its absolute temperature
• D. the square of its pressure
• E. its absolute temperature

Hint:

Distinguish between "average velocity" (proportional to \(\sqrt{T}\)) and "average kinetic energy" (proportional to \(T\)). This is a very frequent confusion in competitive exams.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
The kinetic theory of gases provides a microscopic interpretation of temperature in terms of the average translational kinetic energy of molecules.

Step 2: Key Formula or Approach:
The average kinetic energy (\(KE_{avg}\)) per molecule is given by:
\[ KE_{avg} = \frac{3}{2} k_B T \]
where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in Kelvin.

Step 3: Detailed Explanation:
From the equation \(KE = \frac{3}{2} k_B T\), it is evident that the average kinetic energy is independent of the mass or type of the gas molecule.
The only variable parameter on the right side is \(T\).
Therefore, \(KE_{avg} \propto T\).
This means that if the absolute temperature of the gas is doubled, the average kinetic energy of its molecules also doubles.

Step 4: Final Answer:
The average kinetic energy is directly proportional to its absolute temperature.