Kinetic Theory: Pressure from Molecular Motion
Treating a gas as many small particles in random motion, pressure comes from their collisions with the walls, which gives pV as one third of N m times the mean square speed. Comparing that with pV = nRT shows temperature to be a measure of mean molecular kinetic energy.
What a learner can do afterwards
- States the assumptions the model rests on and names one place a real gas departs from them
- Uses the root mean square speed and explains why the mean velocity is zero
- Links mean kinetic energy to three halves kT and compares two gases held at the same temperature
1 · Read
Gases are crowds of tiny particles in ceaseless random motion. Pressure is the average push of their collisions with the walls, so more particles or faster ones raise the pressure.
Heat a sealed can and the pressure climbs. Faster molecules hit harder and more often, and the same story gives p V as one third of N m times mean square speed.
Matching that result with p V equals N k T shows temperature measures mean molecular kinetic energy: three halves k T. At one shared temperature every gas has the same mean energy, though lighter molecules move faster to carry it.
Mean velocity is zero, since directions cancel, but mean square speed is not. The model assumes tiny elastic particles with no forces between hits, and real gases depart from it when squeezed or cooled.
Wall collisions make pressure, and temperature sets the mean kinetic energy.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.