Section 1 of 6Relationships Between p, V and T
In every case the mass of gas is fixed.
Pressure and volume
- At constant temperature, pressure rises when volume falls, so pressure and volume are inversely proportional.
Pressure and temperature
- At constant volume, pressure increases with temperature, and is directly proportional to it on the kelvin scale.
Volume and temperature
- At constant pressure, volume increases with temperature, directly proportional on the kelvin scale.
Graphs
- Pressure-temperature and volume-temperature graphs are straight lines through the origin only when temperature is in kelvin.
Section 2 of 6Explaining with Particles
Explaining with Particles
Compressing a gas
- The same number of particles in a smaller space hit the walls more often, so pressure rises.
Expanding a gas
- Particles are further apart and collide less often with the walls, so pressure falls.
Heating at constant volume
- Particles move faster, collide more often and with greater force, so pressure rises.
Cooling at constant volume
- Particles slow down, so collisions are less frequent and weaker, and pressure falls.
| Change | Constant | Effect |
|---|---|---|
| Volume decreases | Temperature | Pressure increases |
| Temperature increases | Volume | Pressure increases |
| Temperature increases | Pressure | Volume increases |
Section 3 of 6Boyle’s Law (Higher Tier)
Boyle’s Law (Higher Tier)
Statement
- For a fixed mass of gas at constant temperature, pressure × volume is constant.
Equation
- p₁V₁ = p₂V₂, where 1 is before and 2 is after the change.
Units
- Use the same units for both volumes and both pressures, for example pascals and m³.
Rearranged
- p₂ = p₁V₁ ÷ V₂, which makes it easy to find the final pressure.
Section 4 of 6Using p₁V₁ = p₂V₂
1
Check the temperature and mass of gas stay constant.
2
List p₁, V₁ and the second variable you know.
3
Rearrange the equation to make the unknown the subject.
4
Substitute the values into the equation and calculate the answer.
5
Check that the result makes sense: compressing the gas must raise the pressure.
Section 5 of 6Worked Example
Question
- A gas occupies 0.50 m³ at a pressure of 150 000 Pa.
- It expands at constant temperature to 0.75 m³.
- Calculate the new pressure.
- Write p₁V₁ = p₂V₂, so p₂ = p₁V₁ ÷ V₂.
- Substitutep₂ = (150 000 × 0.50) ÷ 0.75.
- p₂ = 75 000 ÷ 0.75 = 100 000 Pa.
- Checkthe volume increased, so the pressure fell, which agrees.
Answer New pressure = 100 000 Pa (100 kPa)
Section 6 of 6Exam Checklist & Tips
1.8.3 – Key Points for the Exam
- Boyle's law For a fixed mass of gas at constant temperature, pV is constant.
- Directly proportional A relationship in which doubling one quantity doubles the other.
- Inversely proportional A relationship in which doubling one quantity halves the other.
- Fixed mass The number of gas particles does not change.
Common Mistakes
- Using Celsius temperatures in a gas law relationship that needs kelvin.
- Adding p₁V₁ to p₂V₂ instead of equating them.
- Forgetting that the temperature must stay constant when using Boyle's law.
- Saying heating a gas increases pressure because particles get bigger.