Three gas laws
For a fixed mass of gas, three laws describe how pressure P, volume V and absolute temperature T (in kelvin) are related.
- Boyle's law (constant temperature): pressure is inversely proportional to volume. PV = constant, so P₁V₁ = P₂V₂.
- Charles's law (constant pressure): volume is directly proportional to absolute temperature. V / T = constant, so V₁/T₁ = V₂/T₂.
- Pressure law (constant volume): pressure is directly proportional to absolute temperature. P / T = constant, so P₁/T₁ = P₂/T₂.
Key formula / 关键公式
Combined gas law: PV / T = constant, i.e. P₁V₁ / T₁ = P₂V₂ / T₂.
Temperature must be in kelvin: T(K) = θ(°C) + 273.
Explaining the laws with particles
Gas pressure is caused by particles colliding with the container walls. Reducing the volume packs the particles closer, so they hit the walls more often, raising the pressure (Boyle's law). Heating the gas makes particles move faster, increasing pressure or volume (pressure law and Charles's law).
Worked example / 例题
A gas at pressure 1.0 × 10⁵ Pa occupies 300 cm³. At constant temperature it is compressed to 100 cm³. Find the new pressure.
Boyle's law: P₁V₁ = P₂V₂.
P₂ = P₁V₁ / V₂ = (1.0 × 10⁵ × 300) / 100 = 3.0 × 10⁵ Pa.
Remember / 记住
- Always convert temperature to kelvin before using Charles's or the pressure law.
- Boyle: P up, V down (inverse). Charles and pressure law: direct with T.
- The mass of gas must stay fixed.