The average translational kinetic energy of gas molecules depends on

Analyze the question: It asks what the average translational kinetic energy of a gas molecule depends on. This comes from the kinetic theory of gases.

Explain the concept: For an ideal gas, the average translational kinetic energy per molecule is

KE_avg = (3/2) kT

where:

• k = Boltzmann constant (a fixed number, 1.38 × 10⁻²³ J/K)
• T = absolute temperature in kelvin

For one mole, the total translational energy is (3/2)RT.

Step-by-step solution:

1. From kinetic theory, pressure is P = (1/3)(N/V)m⟨c²⟩, and combining this with the ideal gas law PV = NkT gives: (1/2)m⟨c²⟩ = (3/2)kT
2. The right-hand side contains only constants and T. It has no pressure, volume or number of moles.
3. So the average kinetic energy per molecule depends only on the absolute temperature.
4. Pressure and number of moles can change (for example, by adding more gas or compressing it at constant temperature). The average energy per molecule stays the same as long as T is constant.

Checking the options:

• A. Temperature only: correct.
• B. Number of moles and temperature: wrong. The number of moles changes the total energy, not the average per molecule.
• C. Pressure and temperature: wrong. Pressure does not independently affect the average energy per molecule.
• D. Pressure only: wrong.

Answer: A. Temperature only.

Exam tip: Remember "KE average = (3/2)kT, with T only." Words like "average KE per molecule" point to temperature alone. Words like "total internal energy" bring in the number of moles too, as in U = (3/2)nRT.