The gas laws describe the relationships between the pressure, volume, and temperature of a fixed mass of gas. At constant temperature, pressure and volume are inversely proportional (Boyle's law). At constant volume, pressure and absolute temperature are directly proportional. Both relationships follow from the particle model: gas pressure arises from particle collisions with container walls.
Why do gases exert pressure?
Before any equation, build the particle picture. A gas consists of particles moving rapidly and randomly in all directions. When these particles collide with the walls of their container, each collision exerts a tiny force on the wall. The pressure of a gas is the total force of all these collisions per unit area of the container walls.
This particle model immediately predicts the gas laws:
- If you reduce the volume at constant temperature, the particles are in a smaller space and hit the walls more frequently → pressure increases.
- If you increase the temperature at constant volume, particles move faster and hit the walls more energetically and more frequently → pressure increases.
- If you increase the volume at constant temperature, particles have further to travel between collisions with the walls → pressure decreases.
What is Boyle's law?
Boyle's law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional:
$$P_1 V_1 = P_2 V_2$$
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
A graph of pressure against volume (at constant temperature) produces a hyperbola (a curve that approaches but never touches the axes). A graph of pressure against 1/volume gives a straight line through the origin.
Units: Pressure is in pascals (Pa) or kilopascals (kPa); volume is in cubic metres (m³) or cm³. As long as the same unit is used consistently on each side, the calculation works.
How do you use Boyle's law — worked example?
Worked example: A gas occupies a volume of 0.40 m³ at a pressure of 100 kPa. The gas is compressed at constant temperature to a volume of 0.10 m³. Calculate the new pressure.
- Write the equation: P₁V₁ = P₂V₂
- Substitute known values: 100 × 0.40 = P₂ × 0.10
- Calculate the left side: 100 × 0.40 = 40 kPa·m³
- Rearrange for P₂: P₂ = 40 ÷ 0.10
- Calculate: P₂ = 400 kPa
The pressure quadrupled because the volume was reduced to one quarter. This makes sense: same number of particles, four times smaller space → four times more collisions per unit area per second → four times greater pressure.
What is the pressure–temperature law?
The pressure–temperature law (sometimes called Gay-Lussac's law) states that for a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature:
$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$
Critical rule: temperature MUST be in kelvin (K), not degrees Celsius (°C).
The conversion is: T(K) = T(°C) + 273
Using Celsius temperatures in this equation gives completely wrong answers because the law holds only for the absolute temperature scale (kelvin), where 0 K is absolute zero — the temperature at which particles have minimum kinetic energy.
| Temperature in °C | Temperature in K |
|---|---|
| −273 °C | 0 K (absolute zero) |
| 0 °C | 273 K |
| 27 °C | 300 K |
| 100 °C | 373 K |
| 200 °C | 473 K |
How do you use the pressure–temperature law — worked example?
Worked example: A sealed gas cylinder contains gas at 20 °C and a pressure of 150 kPa. The cylinder is heated to 80 °C. Calculate the new pressure, assuming constant volume.
- Convert temperatures to kelvin: T₁ = 20 + 273 = 293 K; T₂ = 80 + 273 = 353 K
- Write the equation: P₁/T₁ = P₂/T₂
- Rearrange for P₂: P₂ = P₁ × (T₂/T₁)
- Substitute: P₂ = 150 × (353 ÷ 293)
- Calculate: P₂ = 150 × 1.205 = 180.7 kPa (3 significant figures: 181 kPa)
Common exam error: using T₁ = 20 and T₂ = 80 (in °C) gives P₂ = 150 × (80/20) = 600 kPa — completely wrong and physically impossible (the ratio of absolute temperatures is 353/293 ≈ 1.2, not 4).
What is absolute zero?
Absolute zero is the lowest possible temperature: 0 K (−273 °C). At absolute zero, particles in a gas would have minimum kinetic energy and exert zero pressure on the container walls. In practice, all gases liquefy or solidify before reaching absolute zero, so it is a theoretical limit.
Evidence for absolute zero comes from extrapolating gas law graphs:
- A graph of pressure vs temperature (in °C) for a fixed volume of gas is a straight line. Extrapolating to P = 0 always gives −273 °C — the same result regardless of the gas type or initial conditions. This universal intersection point is defined as absolute zero, 0 K.
Frequently asked questions
What is Boyle's law in GCSE physics?
Boyle's law states that for a fixed mass of gas at constant temperature, the pressure multiplied by the volume is constant: P₁V₁ = P₂V₂. If volume halves, pressure doubles; if volume doubles, pressure halves. The particle model explains this: squeezing the gas into a smaller volume means more collisions per second per unit area of wall, producing greater pressure. Temperature must remain constant so that particle speed (and therefore collision force) is unchanged.
Why must temperature be in kelvin for gas law calculations?
Gas law equations such as P₁/T₁ = P₂/T₂ are only valid when temperature is measured on the absolute (kelvin) scale. This is because the laws are based on the idea that at 0 K (absolute zero), gas particles have minimum kinetic energy and exert zero pressure. At 0 °C (273 K), particles are still moving and still exert pressure — so 0 °C is not a true zero for these relationships. Using Celsius temperatures in the equations assumes zero pressure occurs at 0 °C, which is incorrect and produces wrong answers.
What happens to gas pressure when temperature increases at constant volume?
When temperature increases at constant volume, gas particles gain kinetic energy and move faster. They collide with the container walls more frequently and with greater force at each collision. Both effects increase the pressure. The pressure–temperature law quantifies this: pressure is directly proportional to absolute temperature at constant volume, so doubling the absolute temperature (e.g., from 300 K to 600 K) doubles the pressure.
How do the gas laws apply to everyday situations?
Boyle's law explains why a bicycle pump gets warm and harder to push as you compress air: the volume decreases, increasing pressure, and the work done on the gas slightly raises temperature. The pressure–temperature law explains why car tyre pressures are higher after a long journey — the tyre temperature rises with friction, increasing the pressure of the fixed mass of air inside. It also explains why an aerosol can should not be placed near heat sources: rising temperature increases the gas pressure inside, which can cause the sealed can to rupture.
For Socratic GCSE physics with Professor Newton — predict what happens to the pressure before any calculation, then check your particle model reasoning — visit aitutors.me.