Kinetic Theory of Gases Where restless particles shape every puff of air.

What is Kinetic Theory?

Kinetic Theory

A gas is a swarm of tiny particles in nonstop, random, straight-line motion. Their collisions with container walls produce the observed gas pressure.

Quick check → Gas pressure arises from: (A) gravity, (B) particle collisions, or (C) magnetic forces?

Ideal Gas Model

Ideal Gas

A theoretical gas whose molecules have zero size and interact only through perfectly elastic collisions.

Key Assumptions:

  • Molecules are point particles; their own volume is negligible.
  • No attractive or repulsive forces except during impact.
  • Collisions are perfectly elastic, conserving kinetic energy.
  • A large number of molecules move randomly in all directions.

How Pressure Happens

Follow one molecule, then many, to see pressure grow.

1

One Hit

A single molecule strikes the wall and gives it a tiny push.

2

Millions of Hits

Countless molecules collide each second; their pushes add together.

3

Force on Wall

All impulses merge into a steady force \(F\) pressing outward.

4

Force Becomes Pressure

Pressure forms: \(P = \\frac{F}{A}\\). Faster motion or more particles raises \(F\) and so \(P\).

Pro Tip:

Pressure equals the combined momentum change delivered during molecular collisions.

Energy ∝ Temperature

Kinetic energy vs temperature graph

Average kinetic energy rises linearly with absolute temperature.

In an ideal gas, each molecule’s kinetic energy increases directly as the Kelvin temperature increases.

Key Points:

  • \( \langle E_k \rangle = \frac{3}{2}k_B T \)
  • Double \(T\) → double average kinetic energy.
  • Straight-line graph passes through the origin; slope \( \frac{3}{2}k_B \).

Key Takeaways

Particles in constant motion

Gas molecules move randomly at every instant.

Pressure from wall impacts

Each molecular hit on the container wall exerts force, producing pressure.

Ideal-gas model

We treat molecules as non-interacting points to simplify theory.

Energy ↔ temperature

Average kinetic energy is directly proportional to absolute temperature, \(E_k \propto T\).