P3.3 Particle Model and Pressure
Gas pressure — the particle model explanation
Gas pressure arises because gas molecules are in continuous, random motion and collide with the walls of their container. Each collision exerts a tiny force on the wall; the total effect of billions of collisions per second creates a measurable pressure.
Key equation:
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure | P | Pa (pascals) |
| Volume | V | m³ |
| Temperature | T | K (kelvin) |
For a fixed mass of gas at constant temperature (isothermal process):
P₁V₁ = P₂V₂ (Boyle's Law)
For a fixed mass of gas at constant volume (Gay-Lussac):
P/T = constant, or P₁/T₁ = P₂/T₂
Temperature and pressure — microscopic explanation
- When temperature increases, gas molecules gain more kinetic energy and move faster.
- Faster molecules hit the walls more frequently and with greater force.
- Both effects increase pressure (if volume is constant).
Important: Temperature must always be converted to kelvin (K):
T(K) = T(°C) + 273
Volume and pressure — microscopic explanation
If volume decreases (e.g., a piston compresses gas):
- The same number of molecules occupies a smaller space.
- Collisions with walls happen more frequently.
- Pressure increases.
This is why P₁V₁ = P₂V₂: halving the volume doubles the pressure.
✦Worked example— Worked example 1: Boyle's Law
A gas has pressure 100,000 Pa and volume 0.5 m³. The gas is compressed to volume 0.25 m³ at constant temperature.
P₂ = P₁V₁ / V₂ = (100,000 × 0.5) / 0.25 = 200,000 Pa
Pressure doubles — matches kinetic model (molecules collide twice as often).
✦Worked example— Worked example 2: Pressure–temperature
A gas at 27°C has pressure 200 kPa. It is heated to 127°C at constant volume.
T₁ = 27 + 273 = 300 K; T₂ = 127 + 273 = 400 K
P₂ = P₁ × T₂/T₁ = 200,000 × (400/300) = 266,667 Pa ≈ 267 kPa
Absolute zero
At absolute zero (0 K = −273°C), gas molecules have minimum kinetic energy. In theory, pressure would be zero because molecules would not move and exert no force on the walls.
Absolute zero cannot be reached in practice — it is a theoretical limit.
Common exam errors
- Using Celsius instead of kelvin in pressure–temperature calculations — always add 273.
- Confusing which quantities are constant in each law — state clearly what is held constant.
- Saying "molecules stop moving at 0°C" — only at absolute zero (0 K = −273°C).
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