Kinetic Theory
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
A gas is a huge number of molecules flying around and bouncing off the walls. Temperature measures their average kinetic energy: Kavg = (3/2)kBT, with T in kelvins. Pressure comes from the molecules hitting the walls.
1. Temperature is kinetic energy
2. What the molecules are doing
Higher temperature means faster molecules. Doubling the kelvin temperature doubles Kavg, but the speed only goes up by √2.
Molecules don’t all move at the same speed: there’s a spread, and vrms is a typical value.
Pressure is the average force of collisions per area. Heat a gas in a rigid box and the molecules hit the walls harder and more often, so the pressure rises.
More molecules in the same box at the same temperature also means more collisions, so more pressure.
3. Example, then try it
What is the average kinetic energy of an air molecule at room temperature, 300 K?
Kavg = (3/2)(1.38 × 10⁻²³)(300) ≈ 6.2 × 10⁻²¹ J.
Tiny for one molecule, but a room holds about 10²⁷ of them.
A gas is heated from −73 °C to 527 °C. By what factor does the average kinetic energy change? The rms speed? Then compare helium (4 u) and oxygen (32 u) molecules at the same temperature.
Convert to kelvins: −73 + 273 = 200 K; 527 + 273 = 800 K. The temperature is 4 times as large.
Kinetic energy: Kavg ∝ T, so it becomes 4 times as large.
Speed: vrms ∝ √T, so it becomes √4 = 2 times as large.
Helium vs. oxygen: same T, so same Kavg. vrms ∝ 1/√m, so helium is √(32/4) = √8 ≈ 2.8 times faster.
Answer: KE × 4, speed × 2; helium moves about 2.8 times as fast as oxygen.
4. Common mistakes
A container holds nitrogen and helium at the same temperature. How does the average kinetic energy of a nitrogen molecule compare with that of a helium atom?
Average kinetic energy depends only on temperature: Kavg = (3/2)kBT. The helium atoms move faster, but they have less mass.
Ready to practice?
5 questions on Kinetic Theory, each with a hint and an explanation for every wrong answer.