Kinetic Particle Model and Gases

Everything is made of tiny particles in constant motion. In solids they vibrate in fixed positions; in liquids they move past each other; in gases they move fast and far apart. Gas pressure comes from particles hitting the walls. Temperature in kelvin starts at absolute zero, and for a fixed mass of gas at constant temperature $pV$ is constant.

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Section 1 of 14

Learning objectives

Describe solids, liquids and gases using the particle model.
Explain Brownian motion and gas pressure in terms of particles.
Convert between °C and K, and explain absolute zero.
Use $p_1V_1=p_2V_2$ for a gas at constant temperature.

Pause and think

You squeeze a sealed syringe of air with your thumb over the end. It gets harder to push. Why, in terms of air particles?

Section 2 of 14

Core idea

Start hereDancing smoke

Under a microscope, specks of smoke jiggle about randomly even in still air. They're being knocked by air molecules far too small to see. That jiggling, Brownian motion, is evidence that all matter is made of moving particles.

The big idea

Solids vibrate in place; liquids slide past each other; gases move fast and freely. Gas pressure is from collisions with walls. At constant temperature $pV$ = constant. $T(\text{K})=\theta(^\circ\text{C})+273$ .

1. States of matter

Solid, liquid and gas

Solids keep their shape; liquids take the shape of the container but keep their volume; gases fill any container.

Solid: close, regular, vibrate; fixed shape and volume.
Liquid: close, irregular, moving; fixed volume.
Gas: far apart, fast, random; fills the container.

2. Gas pressure

Gas at constant temperature: halve the volume, double the pressure

Squeezing the gas into less space means particles hit each square centimetre of wall more often.

p_1V_1=p_2V_2

Why

pV

is constant (qualitatively)

$V\to\tfrac12V$
Same particles in half the space.
$\text{collisions per second}\times2$
Particles hit the walls twice as often (same speed: same temperature).
$p\to2p$
So $pV$ is unchanged.

Worked exampleSqueezing a gas

6 L at 100 kPa squeezed to 3 L, same temperature.

Goal: New pressure.
Strategy: $p_1V_1=p_2V_2$ .

$100\times6=p_2\times3$
Boyle's law.
$p_2=200\text{ kPa}$
Solve.

Answer

200

kPa.

✓ CheckVolume halved, pressure doubled ✓.

Edge caseAbsolute zero At

0

=-273^\circ

C particles have minimum energy; nothing can be colder.

Pause and think

Why does a balloon shrink in a freezer?

Summary

Kinetic model of matter.
Pressure from collisions; $pV=$ const.

Brownian motion: Random motion of small particles from molecular collisions.

HistoryRobert Brown's pollen. In

1827

the botanist Robert Brown saw tiny particles from pollen grains jiggling in water under his microscope. He couldn't explain it. In

1905

Einstein showed it was caused by invisible water molecules bumping into them: some of the first convincing evidence that atoms are real.

Fun factAir molecules are faster than jets. At room temperature, a typical oxygen molecule moves at about

450

m/s, faster than a passenger jet. They don't get far, though: each one collides with another roughly every

0.0000000001

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