Kinetic Theory & Ideal Gases

Revise Kinetic Theory & Ideal Gases for Physics 5 (IAL) WPH15 (A2 Level) — revision notes and instant AI marking.

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Kinetic Theory & Ideal Gases

The Big Idea: Gases are just huge swarms of tiny particles zooming around randomly — and by tracking their energy, speed, and collisions, we can predict exactly how a gas's pressure, volume, and temperature relate to each other.

Quick Overview

Internal energy = sum of the kinetic + potential energy of every molecule in a substance.
Absolute zero (0 K) is the coldest possible temperature — where molecules have zero kinetic energy.
The Kelvin and Celsius scales have equal-sized divisions — a change of 1°C = a change of 1 K.
The ideal gas equation pV = NkT links pressure, volume, molecule number, and temperature.
Boyle's Law, Charles's Law and the Pressure Law are special cases of the ideal gas equation where one variable is held constant.
Core Practical 14 uses a syringe + weights to verify Boyle's Law experimentally.
The average molecular kinetic energy of a gas molecule is E_k = ³⁄₂kT — directly proportional to temperature.

1. Internal Energy

Every substance — solid, liquid, or gas — is made of molecules that are constantly jiggling, vibrating, or zooming around. Each of those molecules carries two kinds of energy:

Kinetic energy — because the molecule is moving (vibrating in a solid, sliding past neighbours in a liquid, or flying freely in a gas). This is what gives a substance its temperature.
Potential energy — because of the molecule's position relative to its neighbours, and the intermolecular forces pulling or pushing on it.

Add up every single molecule's kinetic and potential energy in a given mass of substance, and you get its internal energy.

Definition

Internal energy (U) = ΣKE + ΣPE of all molecules in a substance

Units: Joules (J). Symbol: U.

Analogy: Picture a glass of water. Every water molecule is a tiny bouncing ball with its own personal speed (kinetic energy) and its own personal "stretchiness" of the bonds holding it to its neighbours (potential energy). Internal energy is just the total scorecard if you added up the KE and PE of every single ball in the glass.

What determines internal energy?

Temperature — higher temperature means higher average kinetic energy.
Random motion of molecules — the more chaotic/energetic the motion, the higher the KE contribution.
Phase of matter — gases have the highest internal energy (particles are free and fast), solids have the lowest (particles are locked in place, just vibrating).
Intermolecular forces — stronger forces between particles mean higher potential energy (this ties directly to the phase of matter).

How internal energy changes

Internal energy increases when...	Internal energy decreases when...
Work is done on the substance	Heat is lost to the surroundings
Heat is added to the substance	The substance changes state from gas → liquid or liquid → solid

Common Mix-Up

Students often think a fast-moving object (like a thrown egg) has "high internal energy" because it's moving fast. Wrong! The egg's kinetic energy from flying through the air is separate from its internal energy. Internal energy only counts the vibration/motion of molecules inside the egg — not the movement of the whole object.

Practice Question 1

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