Physics

The mean time between collisions depends on how often a molecule encounters others, which is set by both the collision cross-section and the relative speed of molecules. As temperature rises, molecules move faster (increasing collision rate), but the gas also expands at constant pressure (decreasing density). The key insight is recognizing which effect dominates: density drops as $1/T$ while molecular speed grows as $\sqrt{T}$, so the collision frequency—and thus mean time between collisions—changes in a specific, predictable way.

The mean time between collisions depends on how often a molecule encounters others, which is set by both the collision cross-section and the relative speed of molecules. As temperature rises, molecules move faster (increasing collision rate), but the gas also expands at constant pressure (decreasing density). The key insight is recognizing which effect dominates: density drops as $1/T$ while molecular speed grows as $\sqrt{T}$, so the collision frequency—and thus mean time between collisions—changes in a specific, predictable way.