The Kinetic Model

A balloon is pushed outward by nothing you can see. Kinetic theory explains pressure, temperature and the gas laws from one picture: a huge number of tiny molecules flying about and colliding.

From molecules to gas laws#

Real gases at low density obey pV = nRT closely; an ideal gas obeys it exactly. A gas is made of molecules, and its measurable behaviour comes from what those molecules do. Kinetic theory builds a simple model of molecular motion and shows it leads to the ideal gas laws.

The assumptions#

1. A gas is made of molecules moving randomly in all directions.
2. A molecule is much smaller than the average spacing between molecules.
3. Molecules exert no forces on each other or on the walls except during collisions.
4. All collisions (molecule–molecule and molecule–wall) are perfectly elastic and take negligible time.
5. Molecules obey Newton’s laws.
6. Left alone, the gas reaches a steady state: the density, and the way molecules are spread over different velocities, are the same everywhere, in every direction, at all times.

Why we can ignore molecule–molecule collisions#

Assumption 6 has a handy consequence. Suppose a collision changes the velocity of some molecule in a small region. Since the number of molecules with each velocity in that region never changes, another collision must, on average, give some nearby molecule the velocity the first one lost. So in calculations we can pretend each molecule simply keeps its velocity.

How realistic is it?#

• At 0.1 atm and room temperature, molecules are about 100 times smaller than their spacing.
• Real molecules do attract each other, but weakly when they are far apart.
• Collisions are elastic unless the temperature is so high that molecules are damaged; collisions with walls are elastic once the walls are at the gas temperature.
• With about 6 × 10²³ molecules in a mole, a steady, uniform distribution is almost guaranteed.