According to the kinetic theory of gases, how does the average kinetic energy of gas molecules change with temperature?

Introduction / Context:
This question belongs to physical chemistry and the kinetic theory of gases. The theory connects microscopic motion of gas molecules with macroscopic properties like temperature and pressure. Understanding how average kinetic energy depends on temperature is essential for explaining phenomena such as diffusion, pressure changes and gas laws.

Given Data / Assumptions:
- The focus is on average kinetic energy of gas molecules, not on individual instantaneous speeds.
- Temperature is measured on an absolute scale, typically in kelvin (K).
- We assume the gas behaves ideally so that kinetic theory relationships apply.

Concept / Approach:
According to kinetic theory, the average translational kinetic energy of an ideal gas molecule is directly proportional to the absolute temperature. The formula is usually written as average kinetic energy per molecule equals (3/2) k T, where k is Boltzmann constant and T is temperature in kelvin. Because of this direct proportionality, when temperature increases, average kinetic energy also increases; when temperature decreases, average kinetic energy decreases. Temperature is therefore a measure of the average kinetic energy of gas molecules.

Step-by-Step Solution:
Step 1: Recall the expression for average kinetic energy of a gas molecule: KE(avg) = (3/2) k T, where k is Boltzmann constant and T is absolute temperature. Step 2: Note that k is a constant and (3/2) is a constant factor, so KE(avg) is directly proportional to T. Step 3: If T increases, the product (3/2) k T increases, so average kinetic energy must increase. Step 4: If T decreases, the average kinetic energy decreases accordingly. Step 5: Therefore, the correct description is that average kinetic energy increases with increase of temperature.

Verification / Alternative check:
This relationship is consistent with everyday observations. When a gas is heated, its molecules move faster, pressure tends to increase at constant volume and the gas expands at constant pressure. All these behaviours are explained by higher kinetic energy at higher temperatures. Conversely, cooling a gas slows molecular motion and reduces kinetic energy. None of these observations support the idea that kinetic energy remains constant or moves in the opposite direction to temperature.

Why Other Options Are Wrong:
Unaffected by temperature: This would imply no connection between microscopic motion and temperature, contradicting kinetic theory and experimental evidence.
Decreases as temperature increases: This is opposite to the theoretical and observed relationship; heating cannot cause molecules to slow down on average.
Increases as temperature decreases: Also opposite to reality; cooling slows particles rather than making them more energetic.

Common Pitfalls:
Some students mix up average kinetic energy with total internal energy or confuse the effect of volume changes with temperature changes. Another pitfall is thinking in terms of Celsius and forgetting that absolute zero on the Kelvin scale corresponds to zero average kinetic energy. To avoid confusion, always associate higher absolute temperature with higher average kinetic energy for ideal gases.

Final Answer:
The average kinetic energy of gas molecules increases as temperature increases.