Which statement describes the relationship between temperature and the average kinetic energy of gas particles?

Which statement describes the relationship between temperature and the average kinetic energy of gas particles?

• A. Temperature is proportional to the average kinetic energy.
• B. Temperature is inversely proportional to the average kinetic energy.
• C. Temperature is independent of the average kinetic energy.
• D. Temperature equals the square of the average kinetic energy.

Answer: (A)

Temperature is a measure of how much energy the gas particles have on average. In kinetic theory, especially for an ideal gas, the average translational kinetic energy increases directly with temperature. More precisely, the average kinetic energy per molecule is proportional to temperature (for a monatomic ideal gas, it’s (3/2) k_B T). So as temperature rises, the particles move faster and their average kinetic energy rises in direct proportion. This is why the statement that temperature is proportional to the average kinetic energy is the best description. The other ideas—being inversely related, independent, or related by a square—don’t fit because hotter gas clearly has more molecular energy, and the relationship is linear with temperature in Kelvin.

Temperature is a measure of how much energy the gas particles have on average. In kinetic theory, especially for an ideal gas, the average translational kinetic energy increases directly with temperature. More precisely, the average kinetic energy per molecule is proportional to temperature (for a monatomic ideal gas, it’s (3/2) k_B T). So as temperature rises, the particles move faster and their average kinetic energy rises in direct proportion. This is why the statement that temperature is proportional to the average kinetic energy is the best description. The other ideas—being inversely related, independent, or related by a square—don’t fit because hotter gas clearly has more molecular energy, and the relationship is linear with temperature in Kelvin.