---
title: "Kinetic Theory: Pressure from Molecular Motion"
description: "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 = n"
canonical: https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu
source: https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Matter & Materials · Ages 16 to 18
Page: https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu

## Ready when they can

- 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

## Lesson: Pressure from bouncing molecules

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.

**Example.** 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.

**Tip.** 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.

**Recap.** Wall collisions make pressure, and temperature sets the mean kinetic energy.

## Practice

13 questions on this page, each with its working shown.

## Needs first

- [The Gas Laws and the Ideal Gas Equation](https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM)
- [Drawing Particle Diagrams](https://lightmysky.com/learn/science/drawing-particle-diagrams-mt_htAYR-iCFF)
- [Elastic and Inelastic Collisions](https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq)

## Opens up

- [The Maxwell-Boltzmann Distribution of Molecular Speeds](https://lightmysky.com/learn/science/the-maxwell-boltzmann-distribution-of-molecular-speeds-mt_njr5r5YtuT)