Physics 9702 · Paper 4

Brownian Motion & the Kinetic Model

Before deriving anything from “molecules in motion”, two questions deserve answers: how do we know they move, and what exactly are we allowed to assume about them?

The evidence: Brownian motion

A smoke particle in air, watched under a microscope, moves in short straight lines with sudden random turns. Each turn is a collision with air molecules — too small to see, but clearly moving, fast, and random.

In the classic smoke-cell experiment, light shines into a small box of air holding a little smoke, and a microscope watches the smoke particles. They jitter along erratic, zig-zag paths — .
Each sudden turn is the visible result of invisible air molecules striking the smoke particle unevenly. The jitter is direct evidence that air molecules move, move randomly, and — since a big smoke grain gets knocked around by tiny molecules — move fast.

The assumptions of the kinetic model

The kinetic theory treats a gas as an enormous crowd of tiny moving particles. Its standard assumptions — papers ask for any two or three of the five (9702/42/O/N/24 Q4(a)) (9702/41/M/J/23 Q4(a)):

Assumption	Why it is reasonable
A gas contains a very large number of molecules	even a small air cube holds ~10²⁰ of them
Molecules move randomly, in straight lines between collisions	Brownian motion shows exactly this
Intermolecular forces are negligible (except during collisions)	molecules sit ~10 diameters apart, far outside each other's reach
The volume of the molecules is negligible compared with the gas volume	same spacing argument — the gas is mostly empty space
Collisions are perfectly elastic	no kinetic energy is lost, or the gas would cool by itself

Many molecules; random straight-line motion; negligible forces; negligible volume; elastic collisions. Quote them in this compressed form — each is one mark.

The last three assumptions are also the reason real gases fail at high pressure: pushed close together, molecular volume and attractions are no longer negligible, and $pV \propto T$ breaks (9702/41/O/N/23 Q3(d)).

PreviouspV = nRT NextWhere Pressure Comes From

Brownian Motion & the Kinetic Model

Before deriving anything from “molecules in motion”, two questions deserve answers: how do we know they move, and what exactly are we allowed to assume about them?

The evidence: Brownian motion

In the classic smoke-cell experiment, light shines into a small box of air holding a little smoke, and a microscope watches the smoke particles. They jitter along erratic, zig-zag paths — .
Each sudden turn is the visible result of invisible air molecules striking the smoke particle unevenly. The jitter is direct evidence that air molecules move, move randomly, and — since a big smoke grain gets knocked around by tiny molecules — move fast.

The assumptions of the kinetic model

The kinetic theory treats a gas as an enormous crowd of tiny moving particles. Its standard assumptions — papers ask for any two or three of the five (9702/42/O/N/24 Q4(a)) (9702/41/M/J/23 Q4(a)):

Assumption	Why it is reasonable
A gas contains a very large number of molecules	even a small air cube holds ~10²⁰ of them
Molecules move randomly, in straight lines between collisions	Brownian motion shows exactly this
Intermolecular forces are negligible (except during collisions)	molecules sit ~10 diameters apart, far outside each other's reach
The volume of the molecules is negligible compared with the gas volume	same spacing argument — the gas is mostly empty space
Collisions are perfectly elastic	no kinetic energy is lost, or the gas would cool by itself

Many molecules; random straight-line motion; negligible forces; negligible volume; elastic collisions. Quote them in this compressed form — each is one mark.

The last three assumptions are also the reason real gases fail at high pressure: pushed close together, molecular volume and attractions are no longer negligible, and $pV \propto T$ breaks (9702/41/O/N/23 Q3(d)).