The big idea: A gas is just tiny particles flying around and bouncing off the walls.
Pressure is caused by those particles hitting the walls — each collision gives the wall a tiny push, and billions of them together make a steady force on every bit of wall.
Temperature measures how fast the particles move: the hotter the gas, the faster they go.
What 'absolute temperature' means: Absolute temperature is measured in kelvin (K), starting from absolute zero (0 K = −273 °C), the coldest possible point where particle motion is least.
To go from Celsius to kelvin, add 273: 27 °C = 300 K. Always use kelvin in the kinetic-model formulas.
The key link — energy and temperature: The average kinetic energy of the particles (the energy of their motion) is proportional to the absolute temperature.
In short: average KE ∝ T (with T in kelvin). Double the temperature in kelvin → double the average kinetic energy.
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Spot it: Faster particles → harder, more frequent wall collisions → higher pressure.
Higher temperature → more average kinetic energy → faster particles. Temperature and average kinetic energy go up together.
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The link between average kinetic energy and absolute temperature is given as a formula. kB is the Boltzmann constant — a fixed number (1.38 × 10⁻²³ J K⁻¹) that connects energy to temperature for a single particle.
- average kinetic energy of one particle (J)
- Boltzmann constant (1.38 × 10⁻²³ J K⁻¹)
- absolute temperature, in kelvin (K)
Two things to get right: 1. Always put T in kelvin — add 273 to a Celsius temperature first.
2. This is the average kinetic energy of one particle. It does not depend on the gas's mass or what gas it is — only on the temperature.
A sample of helium is at 27 °C, with kB = 1.38 × 10⁻²³ J K⁻¹. Find the average kinetic energy of one helium particle.
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How this is tested — this micro is tested mostly as explanation, not just calculation:
Paper 1A
- A quick explain / identify question — e.g. why molecular speed rises when a gas is compressed.
- Or why two gases at the same temperature have the same average kinetic energy.
Paper 2
- Link the particle picture to pressure and temperature in words.
The classic trap: Thinking a heavier gas has more kinetic energy at the same temperature. It does not — at the same temperature every gas has the same average kinetic energy (the heavier particles just move more slowly).
Compression and speed: When a piston pushes in quickly, it does work on the gas. That work goes into the particles' motion, so their average kinetic energy rises — which means a higher temperature and faster particles.
Faster particles also hit the walls harder and more often, so the pressure goes up too.
A gas is sealed in a cylinder by a piston. The piston is suddenly pushed in, quickly compressing the gas. Explain, using the kinetic model, why the average speed of the gas molecules increases.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.