Particle Motion in Gases

📖 In-Depth Theory

Gas molecules are in CONSTANT, RANDOM MOTION — moving in all directions at high speeds.

TEMPERATURE AND KINETIC ENERGY:

The TEMPERATURE of a gas is related to the AVERAGE KINETIC ENERGY of its molecules.

Higher temperature → molecules move FASTER → higher average KE.

Lower temperature → molecules move SLOWER → lower average KE.

At ABSOLUTE ZERO (0 K = −273°C):

Particles have minimum possible energy — minimum motion.

Kelvin (K) scale: K = °C + 273

Examples:

0°C = 273 K (freezing point of water)

100°C = 373 K (boiling point of water)

−273°C = 0 K (absolute zero — theoretical minimum)

The Kelvin scale is the absolute temperature scale — used in gas law calculations.

Gas Pressure

GAS PRESSURE is caused by the COLLISIONS of gas molecules with the WALLS of the container.

Each collision exerts a tiny force on the wall — the total of billions of collisions per second creates the measurable pressure.

Pressure is measured in PASCALS (Pa) or N/m².

1 Pa = 1 N/m².

FACTORS AFFECTING PRESSURE:

TEMPERATURE (constant volume):

Higher temperature → molecules move FASTER → MORE FREQUENT collisions with walls → HIGHER PRESSURE → MORE FORCEFUL collisions.

At constant volume: pressure is proportional to absolute temperature (Kelvin).

VOLUME (constant temperature):

Smaller volume → molecules travel LESS DISTANCE between collisions → MORE FREQUENT collisions with walls → HIGHER PRESSURE.

At constant temperature: pressure increases when volume decreases (Boyle's Law).

Pressure, Volume and Temperature Relationships

BOYLE'S LAW (constant temperature):

Pressure × Volume = constant

pV = constant

Doubling volume → halves pressure. Halving volume → doubles pressure.

EXAMPLE:

Gas at 100 kPa occupies 2 m³. What pressure when compressed to 0.5 m³?

p₁V₁ = p₂V₂

100 × 2 = p₂ × 0.5

p₂ = 200 ÷ 0.5 = 400 kPa

PRESSURE–TEMPERATURE LAW (constant volume):

p ÷ T = constant (T in kelvin)

Double absolute temperature → double pressure.

APPLICATIONS:

TYRES: pressurised air — less volume of air compressed inside → high pressure.

SYRINGES: pushing plunger → smaller volume → higher pressure → liquid/gas pushed out.

AEROSOLS: gas under high pressure pushes liquid out when valve opened.

BIKE PUMP: compressing air into small volume → high pressure → inflates tyre.

⚠️ Common Mistake

Temperature in gas law calculations MUST be in KELVIN — not Celsius. Add 273 to convert. 0°C = 273 K, NOT 0 K. Pressure is caused by COLLISIONS of molecules with the walls — not by the weight or speed alone, but by the RATE and FORCE of collisions.

📐 Variables

pPressure (p) is measured in pascals (Pa)

VVolume (V) is measured in m³ (m³)

TTemperature (T) is measured in kelvin (K)

EkAverage kinetic energy (Ek) is measured in joules (J)

📐 Key Equations

p × V = constant (Boyle's Law, constant temperature)

p ÷ T = constant (constant volume, T in kelvin)

T (K) = T (°C) + 273

📌 Key Note

Gas pressure: caused by molecular collisions with container walls. Higher T → faster molecules → more frequent, harder collisions → higher pressure. Smaller V → more frequent collisions → higher pressure. Boyle's Law: pV = constant. T in kelvin: K = °C + 273. Absolute zero = 0 K = −273°C.

🎯 Matching Activity — Pressure and Particle Motion

Match each change to its effect on gas pressure (assuming everything else stays constant). — drag the symbols on the right to match the component names on the left.

Pressure increases

Drop here

Pressure increases

Drop here

Pressure decreases

Drop here

Pressure decreases

Drop here

Volume of container decreases at constant temperature — more frequent collisions with walls

Temperature of gas increases at constant volume — faster molecules, more forceful collisions

Volume of container increases at constant temperature — molecules travel further between collisions

Temperature of gas decreases at constant volume — slower molecules, less frequent collisions

⚽ FIFA Worked Examples

Boyle's Law

A gas at 200 kPa occupies 3 m³. The gas is compressed to 1 m³ at constant temperature. Calculate the new pressure.

F

p₁V₁ = p₂V₂ (Boyle's Law — constant temperature)

I

p₁ = 200 kPa, V₁ = 3 m³, V₂ = 1 m³

F

p₂ = p₁V₁ ÷ V₂ = 200 × 3 ÷ 1 = 600

A

p₂ = 600 kPa

🎯 Test Yourself

Question 1 of 2

1. Why does the pressure inside a tyre increase when a car has been driven for a while?

2. A gas is at 27°C and 100 kPa. It is heated to 327°C at constant volume. What is the new pressure?

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⚡ Particle Motion in Gases

Particle Motion in Gases

Gas Pressure

Pressure, Volume and Temperature Relationships

Mr. Badmus AI