For an ideal gas, the average translational kinetic energy per molecule depends only on which parameter?

Introduction / Context:Kinetic theory links macroscopic temperature to microscopic molecular motion. In the ideal gas model, translational kinetic energy is solely temperature dependent.

Given Data / Assumptions:

• Ideal gas behavior.
• Equipartition theorem applies.
• Focus on translational degrees of freedom.

Concept / Approach:The average translational kinetic energy per molecule is (3/2) k_B T, where k_B is Boltzmann’s constant and T is absolute temperature. It is independent of the gas species or molecular size in the ideal approximation.

Step-by-Step Solution:Write relation: E_trans,avg = (3/2) k_B T.Note species independence: no molecular parameter other than T appears.Hence, the correct determinant is absolute temperature.

Verification / Alternative check:Root-mean-square speed v_rms ∝ sqrt(T/M) varies with molar mass, but energy ~ (1/2) m v^2 averages to (3/2) k_B T, removing species dependence.

Why Other Options Are Wrong:Nature or size of the gas affects collision dynamics and real-gas deviations, not the ideal-gas energy–temperature relation.

Common Pitfalls:Confusing speed dependence on molar mass with energy dependence on temperature.

Final Answer:absolute temperature