Particle motion in gases
A gas is a swarm of tiny particles in rapid, random motion. The particles travel in straight lines between collisions and are well separated compared to their size.
Temperature and kinetic energy
Temperature is a measure of the average kinetic energy of particles. So:
- Higher temperature → particles move faster on average.
- Doubling the absolute (Kelvin) temperature roughly doubles the mean square speed of particles (and the average KE).
To convert °C to K: $T(K) = \theta(°C) + 273$.
Pressure of a gas
Pressure on a container's wall arises from particles colliding with it. Each collision exerts a tiny force; trillions per second add up to a steady pressure.
Pressure depends on:
- Number of particles per unit volume (particle density).
- Average particle speed (and so temperature).
- The mass of each particle.
Constant volume — temperature ↑ → pressure ↑
If the gas is held at fixed volume and heated:
- Particles move faster.
- They hit the walls more often AND each collision exerts more force.
- Pressure rises proportionally to the absolute temperature: $P \propto T$ (in K).
This is why a sealed deodorant can must NOT be left in a fire — the hot gas inside creates huge pressure, and the can may explode.
Why volume changes affect pressure
If volume halves at constant temperature, particle density doubles, so collisions per second double, so pressure doubles. (See P3.7 for the gas law $pV = $ constant.)
✦Worked example— Worked example 1
A gas at 27 °C is heated to 327 °C at constant volume. How does the pressure change?
- Convert: T₁ = 300 K, T₂ = 600 K.
- P/T constant → P₂ = P₁ × (600/300) = 2 P₁.
- Pressure doubles.
✦Worked example— Worked example 2
A car tyre is at 200 kPa at 20 °C. After driving, the tyre warms to 50 °C. New pressure?
- T₁ = 293 K, T₂ = 323 K.
- P₂ = 200 × (323/293) ≈ 220 kPa.
⚠Common mistakes
- Using °C instead of K when comparing temperatures — always convert to Kelvin.
- Forgetting that "doubling temperature" must be in K — going from 20 °C to 40 °C is NOT doubling.
- Confusing speed and velocity — temperature relates to mean square speed, an average.
- Saying "particles slow down at low T" but then treating them as stationary — even at near-absolute zero, particles still vibrate (zero-point motion), but for GCSE we treat them as having no KE at 0 K.
AI-generated · claude-opus-4-7 · v3-deep-physics